Knowledge transfer (KT) plays an essential role in evolutionary multitask optimization (EMTO), whereas ”what to transfer” and ”how to transfer” are the key focuses that influence the KT performance. For the issue ”what to transfer”, many EMTO algorithms often transfer the top individuals directly during the KT process. However, the transferred individual information is not always effective, especially when the tasks own the low similarity. For the issue ”how to transfer”, many KT methods mainly focus on learning from all dimensions in a single individual, causing the lack of learning diversity. Therefore, in this paper, we propose a novel directional combination learning method for multitask optimization, termed as DCLMTO, tries to address these two issues effectively. Specifically, for the issue ”what to transfer”, a directional learning (DL) strategy is developed to deeply extract the useful directional knowledge, which is behind the individual information and shows the trend of moving toward better position, for KT preparation. For the issue ”how to transfer”, a combination learning (CL) strategy is designed to fully combine the superiorities of different individuals for enriching the learning diversity. Moreover, DCLMTO can be easily extended to many-task optimization problems (MaTOPs) and can directly avoid the difficulty of task selection, showing its convenience and scalability. Experimental results demonstrate that DCLMTO significantly outperforms other state-of-the-art EMTO and EMaTO algorithms on the multitask benchmarks CEC17 and CEC22, and the many-task benchmarks CEC19 and WCCI20. Finally, DCLMTO is applied to a real-world multitask planar kinematic arm control application, further demonstrating its applicability.

Large-scale optimization problems (LSOPs) have attracted increasing attention in the big data era. Recently, matrix-based evolutionary computation (MEC) has been proposed as a new diagram for solving LSOPs within a short running time. However, compared with its corresponding classical non-matrix-based evolutionary computation (EC) algorithm, the MEC has not yet essentially improved its problem-solving ability or convergence speed. Therefore, how to enhance the problem-solving ability and convergence speed of MEC while maintaining its advantage of fast computational speed (i.e., short running time) has become a significant research topic. With this concern, this paper proposes a novel random matrix-based particle swarm optimization (RMPSO) algorithm, together with two novel designs. Firstly, a random matrix-based learning strategy is proposed, which enables each particle to learn from its superior particles by utilizing random matrices. Therefore, the RMPSO can effectively enhance the global search efficiency of the particles to improve problem-solving ability while maintaining fast computational speed. Secondly, a matrix-based knowledge and data-driven analysis strategy based on the dynamic system theory is proposed to analyze the algorithm convergence of RMPSO and help configure its parameters for fast convergence speed. To evaluate the proposed RMPSO, extensive experiments are conducted using 20 LSOPs, including 12 scalable problems with up to 10,000 dimensions and all the 8 multimodal LSOPs used in the latest IEEE CEC Large-Scale Global Optimization competition. Experimental results show that the RMPSO outperforms the compared state-of-the-art algorithms, including the champion algorithms from the LSGO competition, particularly on LSOPs with many local optima.

Multiple Sequence Alignment (MSA) is a fundamental challenge in bioinformatics, forming the basis for addressing numerous computational biology problems, e.g., protein structure prediction and phylogenetic modeling. Evolutionary computation (EC) has been used to deal with the MSA due to its remarkable ability to unearth optimal or near-optimal solutions and various EC-based MSA methods have been proposed. However, the accuracy of existing EC-based MSA methods can be further improved by leveraging a novel evolutionary framework and designing evolutionary operators that align with the unique characteristics of MSA. Moreover, as the length and number of sequences increase, the MSA problem scales up, making it challenging for existing EC-based methods to achieve high accuracy within a reasonable timeframe. In this article, we propose a chance and control-based multi-population genetic algorithm (CC-MPGA), which incorporates a novel multi-population framework with genetic algorithm (GA). Moreover, according to the characteristics of MSA problems, the chance-based crossover operator and control-based mutation operator are designed to boost the accuracy. The proposed CC-MPGA is tested on well-known benchmark Balibase and large-scale benchmark ExtHomfam and compared with diverse MSA approaches. Experimental results show the superiority of CC-MPGA with a good balance of accuracy and speed, indicating the effectiveness and efficiency of CC-MPGA on large-scale MSA problems.

Cognitive diagnosis (CD) is a fundamental task within computational social systems, essential for personalizing learning in intelligent education by assessing a learner’s fine-grained knowledge proficiency. A critical dilemma exists in designing cognitive diagnosis models (CDMs): conventional psychometric models are interpretable but often simplistic, while complex deep learning models achieve high accuracy at the cost of becoming uninterpretable “opaque models.” This lack of transparency is a major barrier to trust and adoption in real-world educational social systems. To address this challenge, this article introduces probabilistic model-building for cognitive architecture search (PMB-CAS), a novel framework that automates the discovery of CDMs that balance diagnostic accuracy with structural interpretability. We reframe the design process as a multi-objective optimization problem, balancing diagnostic performance [area under the curve (AUC)] with a refined, operator-weighted model interpretability score (MIS) that fairly assesses topological complexity. The framework navigates a flexible, tree-based search space using a probabilistic model-building strategy to efficiently discover promising architectures. Extensive experiments on benchmark datasets demonstrate that PMB-CAS discovers a portfolio of Pareto-optimal models that not only achieve state-of-the-art accuracy, outperforming established baselines, but also offer varying degrees of structural transparency. This work provides educators and stakeholders with a spectrum of trustworthy solutions and establishes a new paradigm for developing effective and verifiable models for computational social systems.

Large-scale optimization problem (LSOP) is an essential research topic in the field of evolutionary computation community. Many large-scale optimization algorithms often maintain a large population for diversity enhancement. However, updating such a large population consumes a significant number of fitness evaluations (FEs), which may lead to the insufficient evolution of the population. In light of this, this article proposes a small-scale learning particle swarm optimization (SSLPSO) for solving LSOPs. In the small-scale learning mechanism, only up to two representative individuals are updated in every generation to effectively save FEs and prolong the evolutionary generations, so as to refine the solution accuracy. Specifically, we first design a representative individual selection (RIS) strategy to select the convergence representative individual and the diversity representative individual for updating. Then, we develop a representative individual learning (RIL) strategy, which includes a convergence learning method and a diversity learning method for the convergence representative individual and the diversity representative individual, respectively. Meanwhile, we further propose an adaptive strategy adjustment (ASA) method based on evolutionary state assessment to determine whether the representative individuals should be updated, further achieving the adaptive adjustment of the evolutionary behavior in the population. Experimental results on the commonly used large-scale test suites, IEEE CEC2010 and IEEE CEC2013, show that the performance of SSLPSO is significantly better than, or at least comparable to other state-of-the-art large-scale optimization algorithms, including the winners of large-scale competitions. Finally, the application of SSLPSO to a large-scale constrained water distribution network optimization problem further demonstrates its real-world applicability.

Set meal design (SMD) for online-to-offline (O2O) restaurant services presents a complex optimization problem, requiring the simultaneous satisfaction of diverse customer preferences, operational constraints, and profit maximization objective. To address this challenge, this article proposes a comprehensive mathematical formulation for the O2O-SMD problem. This formulation integrates complex operational requirements, such as dish variety, pricing, nutritional balance, and profitability, into a unified optimization problem with well-defined objective and constraints. To efficiently solve the O2O-SMD problem, we propose a tensor-based ant colony optimization (TACO) algorithm. Distinct from traditional ant colony optimization (ACO) variants, the core of TACO lies in reformulating the fundamental ACO operations into a tensor computational structure, enabling parallel optimization over O2O-SMD tasks at the algorithmic level. Furthermore, a dedicated local search strategy is integrated to refine solutions and accelerate convergence of the algorithm. The performance of TACO is evaluated on real-world restaurant data and benchmark instances. The experimental results show that TACO significantly outperforms a wide range of comparison algorithms in terms of solution quality, scalability, and computational efficiency, confirming its effectiveness and practical value for real-world O2O-SMD problems.

evolutionary multitask optimization (EMTO) aims to optimize multiple tasks simultaneously. In recent years, various EMTO algorithms based on knowledge transfer (KT) have been developed to utilize the information from other tasks and promote the optimization of the current task. However, most of them often use the fixed KT probability (ktp) and a single evolutionary search operator (ESO) during the evolution process, which lacks an adaption mechanism and cannot meet the different searching requirements among multiple tasks. Fuzzy system can effectively express the qualitative knowledge with unclear boundaries, which has good adaptability to nonindependent EMTO. Therefore, this article proposes a fuzzy adaptive multitask optimization (FAMTO), which employs a fuzzy adaptive transfer (FAT) strategy for intertask KT to achieve the adaptive adjustment of the ktp by designing a comprehensive evaluation in KT performance from two aspects, including the survival rate and the quality of transferred offspring. In FAT strategy, the fuzzy logical is employed to handle the interdependent relationships among multiple indicators, further achieving the more robust and adaptive ktp adjustment. In addition, an individual-based random selection (IRS) strategy is developed for each individual to choose the suitable ESO for intratask self-evolution in fuzzy adaptive multitasking optimization (FAMTO). Experimental results show that FAMTO achieves significantly better performance than other state-of-the-art EMTO algorithms on two well-known multitask benchmarks, CEC17 and CEC22. Furthermore, FAMTO is applied to a real-world multitask planar kinematic arm control application, demonstrating its applicability. Finally, the extended experiments on many-task optimization problems (MaTOPs) illustrate the scalability of FAMTO.

How to simultaneously locate multiple global peaks and achieve certain accuracy on the found peaks are two key challenges in solving multimodal optimization problems (MMOPs). In this article, a landscape-aware differential evolution (LADE) algorithm is proposed for MMOPs, which utilizes landscape knowledge to maintain sufficient diversity and provide efficient search guidance. In detail, the landscape knowledge is efficiently utilized in the following three aspects. First, a landscape-aware peak exploration helps each individual evolve adaptively to locate a peak and simulates the regions of the found peaks according to search history to avoid an individual re-locating an already found peak. Second, a landscape-aware peak distinction distinguishes whether an individual locates a new global peak, a new local peak, or an already found peak. Accuracy refinement can thus only be conducted on the global peaks to enhance the search efficiency. Third, a landscape-aware reinitialization specifies the initial position of an individual adaptively according to the distribution and distinction of the found peaks, which helps explore more peaks. The experiments are conducted on the widely-used benchmark MMOPs and multimodal nonlinear equation system problems. Experimental results show that LADE obtains generally better or competitive performance compared with seven well-performing recent algorithms and four winner algorithms in the IEEE CEC competitions for multimodal optimization.

In dynamic environments, optimization algorithms tend to track the changing optima. However, frequent changes to decision solutions often cause high switching costs and system instability. Decision solutions are expected to be robust to changes. Such problems bring new challenges to existing algorithms, i.e., solution evaluation in future environments and solution selection. Though multiple surrogate models are developed for fitness evaluation, they mainly focus on predicting absolute fitness in static environments. Thus, this paper proposes conditional-surrogate-assisted particle swarm optimization (CSPSO), which adopts a conditional surrogate model to predict the relative fitness of solutions in future for robust solution selection. In CSPSO, a problem is decomposed into multiple subproblems, which are optimized by multiple swarms. Searching data of swarms is collected to learn network models for predicting the future fitness of solutions. In order to coordinate with the multi-modal, decoupled, and dynamic property of the problem, networks are conditioned on some extra information, i.e., time, subproblems, and peaks. Particularly, neural networks are first trained to predict new optimal solutions and fitness conditioned on time and subproblems, and a surrogate model is then trained to predict the relative fitness of solutions conditioned on the closest peak, corresponding subproblem, and time. By combining the current fitness with future ones, solutions with the highest fitness are selected for decision making. Experimental results show that the proposed algorithm outperforms state-of-the-art algorithms on problem instances up to 1000-D in terms of solution optimality. The proposed conditional surrogate model can well predict future fitness to assist decision making.

Evolutionary algorithms serve as a pivotal tool in addressing black-box problems, finding widespread applications across diverse academic disciplines and engineering domains. Despite their utility, these algorithms often confront challenges when navigating complex search spaces, impeding a comprehensive exploration of potential solutions. Solely depending on the algorithm’s exploration abilities falls short of fully harnessing the rich information contained within search spaces. To unlock the full potential of solution spaces, we introduce a deep learning method for the reconstruction of the search path. Specifically, discrete data sampled by evolutionary operators during the exploration process are collected, and a uniquely designed fully connected neural network is employed to reconstruct the exploration paths. The neural network’s robust fitting capability facilitates the transformation of initially discrete sampled information into a continuous form. By capitalizing on the reconstructed solution space information, the algorithm excels in identifying superior solutions. We refer to this method of deep learning-based search path reconstruction evolution strategy algorithm (DLES). The effectiveness of DLES is validated across multiple datasets, including CEC 2014, CEC 2018, CEC 2022 and BBOB. Experimental results, compared to several state-of-the-art algorithms, affirm the superiority of the DLES algorithm.

The fragment reconstruction problem aims to assemble the original object from a collection of fragmented pieces. Traditional manual reconstruction techniques heavily rely on expert knowledge and can potentially damage fragile fragments, necessitating the development of automated reconstruction methods. Current reconstruction algorithms often suffer from the curse of dimensionality, compromising both accuracy and efficiency as the number of fragments increases. These algorithms primarily rely on fragment content, limiting their adaptability and scalability. To address these challenges, this paper introduces a novel reconstruction method grounded in a cooperative coevolutionary (CC) optimization framework. This approach encompasses both the formalization of the fragment reconstruction problem and the development of a tailored algorithm to solve it. Notably, our modeling approach is content-independent, relying solely on the edge shapes of the fragments. With this modeling approach, the solution itself represents the reconstruction process of the fragments. To encode candidate solutions efficiently, we employ a tree structure. This encoding scheme renders traditional CC processes and genetic algorithm operators, such as crossover and mutation, inapplicable. Therefore, this paper proposes a tree-structured CC genetic algorithm (T-CCGA) specifically tailored to our reconstruction task. We aim to overcome the limitations of current reconstruction algorithms and pave the way for more accurate and efficient fragment reconstruction methods. To evaluate the effectiveness of the proposed method, we conducted a series of comprehensive experiments. The results demonstrate that T-CCGA achieves promising outcomes in terms of solution quality, convergence speed, and robustness.

Multiobjective optimization problems (MOPs) arise in numerous real-world scenarios, yet finding their solutions with optimal trade-offs can be a formidable challenge. This article studies the continuous optimization problem involving large-scale variables, many objectives, and intricate constraints, which is rarely comprehensively discussed in existing works, due to the coexisting difficulties posed by the curse of dimensionality, selection pressure, and feasibility restrictions. To address these problems, this work pioneers a novel optimization framework, optimization pattern learning, embedded with machine learning (ML) techniques. Within this framework, the concept of measurable order and its corresponding learning mechanism are proposed to extract valuable knowledge from solutions. This measurable order is a general form of those orders used explicitly or implicitly in the existing studies, providing a more flexible means to evaluate solutions for efficient optimization adaptively. By substituting original solutions with their measurable orders, this framework effectively avoids the selection pressure from many objectives and the feasibility restrictions from intricate constraints. Furthermore, two novel ML models based on measurable orders are developed to progressively learn effective optimization patterns from iterative data in high-dimensional search spaces. Leveraging these learned patterns, this framework successfully addresses the curse of dimensionality from large-scale variables and thus achieves efficient optimization. Owing to the strong adaptability and search capabilities of this framework, it also demonstrates excellent scalability as the number of variables, objectives, and constraints increases. Extensive simulations validate the effectiveness of the framework and underscore its competitiveness relative to state-of-the-art algorithms in this field.

Crowdsourcing contests have become an important approach for organizations to tackle complex problems by gathering innovative solutions from globally distributed participants. However, as platforms always host an increasing number of concurrent contests, the voluntary and selective nature of participants usually leads to coordination difficulties and unpredictable outcomes, which present a critical challenge to guide multicontest settings toward success. To address this issue, this article proposes a novel and effective dynamic link prediction-based recommendation algorithm tailored for crowdsourcing platforms named the heterogeneous temporal graph generative adversarial network (HTGGAN). The HTGGAN leverages participants’ historical interaction data to predict the optimal set of participants for each future task. This ensures that participants’ skills and interests align with the contest requirements, thereby improving the success of crowdsourcing contests. Specifically, the HTGGAN contains four modules. First, the metapath-relation aggregation (MRA) module integrates information from multiple metapaths of the heterogeneous temporal graph (HTG) into a unified spatial embedding. Second, the group-relation aggregation (GRA) module incorporates learnable group-level features into node-level representation learning to enhance the expressiveness of the target node. Third, the across-time aggregation (ATA) module captures interactions between the target node and its temporal neighbors, enabling the learning of an initial spatiotemporal embedding. Finally, the optimized recommendation (OR) module incorporates a generative adversarial network and performs link prediction to recommend appropriate users for competitions or posts. Using a large real-world dataset constructed from the Kaggle platform, we demonstrate that HTGGAN outperforms several state-of-the-art algorithms across multiple metrics and delivers clear practical value.

Unmanned aerial vehicles (UAVs) are increasingly used for firefighting due to security. Multiple UAVs depart from a site and cooperate to execute tasks with time-varying demands in different locations. To better execute firefighting tasks, the reasonable scheduling of UAVs is crucial. Although multiple methods have been developed to solve the multi-UAV scheduling problem, they mainly focus on instances with sufficient UAV resources. They face challenges on instances with limited resources and multiple objectives in terms of solution diversity and convergence, especially when the number of tasks is larger than that of UAVs. This paper models the problem as a bi-objective optimization problem, aiming to minimize two important objectives: the makespan and the total travel distance of UAVs. A dual-encoding-based genetic algorithm (DEGA) is developed to solve the problem. In DEGA, a dual-encoding scheme is adopted for solution representation, in which the execution order of all tasks is represented as a sequence and the task assignment for UAVs is represented as a binary matrix. Correspondingly, solutions can be constructed in two steps: task sequence generation first and then task assignment. Crossover and mutation operations are specifically designed to explore the search space for enhancing solution diversity. In addition, a local search is employed to improve solution quality. Experimental results on instances with various scales demonstrate that DEGA outperforms state-of-the-art algorithms on most instances in terms of solution optimality and diversity.

The gateway placement optimization (GPO) is a critical issue in satellite network that aims to obtain an optimal scheme to deploy different gateways in a network to achieve high-performed satellite-ground communication. Existing studies usually treat the GPO as a single-objective optimization problem, which significantly deviates from real-world scenarios and limits practical applicability. However, numerous performances like the gateway traffic load balancing, the distance between gateways, the traffic load of satellites, and the number of gateways within the satellite’s management range should be considered in the GPO problem, indicating that it is inherently a many-objective optimization problem (MaOP). Therefore, in this paper, a new mathematical model is designed which constructs the GPO as an MaOP. To address it, this paper further proposes a bi-velocity coevolutionary multiswarm particle swarm optimization (BCMPSO) algorithm. The BCMPSO follows the multiple populations for multiple objectives framework, running different populations in parallel, each optimizing a specific objective to search different parts of the Pareto front sufficiently. Meanwhile, a binary PSO with a bi-velocity update mechanism and a discrete position update mechanism is proposed as the optimizer in each population. Comparison experiments with several state-of-the-art methods confirm the effectiveness and competitiveness of the BCMPSO for many-objective GPO.

In problem-independent theoretical studies of evolutionary computation (EC) algorithms, convergence is one of the most frequently mentioned properties of an algorithm’s search capability. However, we have observed that the term convergence represents different, and sometimes even contradictory, properties in different researches. This paper briefly reviews and summarizes some key works in these two directions and subsequently demonstrates that some results from stable convergence and global convergence are mutually exclusive properties. The mutual exclusivity between these two convergences inspires us to propose a scope and domain measure comparison-based (SDMC) method, by comparing the measures of the population’s search scope and the problem’s feasible domain. The SDMC method is simple yet complete for analyzing the global convergence of EC algorithms instead of modeling the algorithms as homogeneous Markov chains. The linear decreasing inertia weight particle swarm optimization (LDIW-PSO) is taken as an example to show how to analysis the global convergence with the proposed SDMC method.

The terminal’s resource management is a significant topic in maritime technology that directly affects the operational efficiency of ports. As an important resource in the terminal, the berth allocation problem (BAP) has been widely studied. In this article, to meet the requirement for unified management of multiple independent BAPs by terminal managers, we model such a complex BAP variant as a multitasking BAP (MBAP) that dealing with multiple berths simultaneously. To efficiently solve the MBAP, we propose an improved evolutionary multitask algorithm (IEMA) to simultaneously minimize the total waiting time with three novel designs. Firstly, the solution space is represented by a single population of multiple variables, which is suitable for implicit knowledge transfer and can avoid infeasible solutions. Secondly, a first come first served strategy is adopted to reinitialize a part of individuals to accelerate convergence. Finally, we develop a hybrid genetic mechanism based on the two-dimensional representation characteristics of the MBAP. Experimental results on a series of generated cases show the effectiveness and superiority of the proposed approach.

Feature selection can increase the classification accuracy and reduce the scale of feature subset, which is important in various machine learning tasks. However, there are various preferences and limitations for the usage of features in different application scenes, and thus different scenes may require different feature subsets. To this end, multimodal feature selection, which aims to simultaneously find multiple feature subsets with low overlap and promising classification accuracy, is also important but does not attract enough attention yet. Therefore, a new multimodal feature selection model is formulated and two grouping-based crowding differential evolution approaches are proposed in this paper. Mutual information is utilized to cluster features with high correlation and the two proposed grouping-based crowding differential evolution approaches incorporate a shuffle-based grouping strategy and a threshold-based grouping strategy, respectively, so as to simultaneously search for multiple low-overlap feature subsets with promising classification accuracy. Experimental results on eight widely used datasets validate the effectiveness of the proposed approaches.

Prompt engineering has become an effective tool for numerous large language models (LLMs)-based tasks. However, it is still a challenge to adaptively optimize the prompt for the target task, where gradients are inaccessible via APIs and the search space is highly complex. Due to the ability to robustly handle complex and multimodal landscapes, and to adaptively explore complex search spaces without explicit gradient information, evolutionary computation (EC) algorithms have garnered significant attention in black-box optimization. However, the performance of different EC algorithms for prompt optimization remains uncertain, which cannot provide guidance for algorithm selection and design in prompt optimization. To alleviate this, a series of investigative experiments are conducted in this paper to evaluate the efficiency of EC algorithms in prompt optimization, which results in three novel findings. First, different EC algorithms, including XNES, CMA-ES, DE, and PSO, are compared on various few-shot learning tasks. The findings indicate that XNES can outperform other algorithms, achieving faster or smoother convergence and higher final accuracy under high-dimensional settings. Second, the role of truncation strategies is also investigated. Results show that moderate bounds effectively help the algorithm balance exploration and exploitation, whereas overly small or large bounds diminish performance. Third, the influence of different k-shot values is examined on the optimization performance for few-shot tasks, which shows that k=32 consistently provides the best trade-off between convergence speed and final model accuracy. In conclusion, these investigations validate the efficacy of the investigated EC algorithms and highlight the advantages of XNES for complex prompt optimization. They further underscore the importance offering valuable guidance for future black-box prompt tuning scenarios. These insights pave the way for future work on more diverse and complex tasks with larger LLMs.

It is a challenging task to select the informative features that can maintain the manifold structure in the original feature space. Many unsupervised feature selection methods still suffer the poor cluster performance in the selected feature subset. To tackle this problem, a feature subspace learning-based binary differential evolution algorithm is proposed for unsupervised feature selection. Firstly, a new unsupervised feature selection framework based on evolutionary computation is designed, in which the feature subspace learning and the population search mechanism are combined into a unified unsupervised feature selection. Secondly, a local manifold structure learning strategy and a sample pseudo-label learning strategy are presented to calculate the importance of the selected feature subspace. Thirdly, the binary differential evolution algorithm is developed to optimize the selected feature subspace, in which the binary information migration mutation operator and the adaptive crossover operator are designed to promote the searching for the global optimal feature subspace. Experimental results on various types of realworld datasets demonstrate that the proposed algorithm can obtain more informative feature subset and competitive cluster performance compared with eight state-of-the-art unsupervised feature selection methods.

Evolutionary multitasking (EMT) is an emerging approach for solving multitask optimization problems (MTOPs) and has garnered considerable research interest. The implicit EMT is a significant research branch that utilizes evolution operators to enable knowledge transfer (KT) between tasks. However, current approaches in implicit EMT face challenges in adaptability, due to the limited use of different evolution operators with different parameter settings and insufficient utilization of evolutionary states for performing KT. This results in suboptimal exploitation of implicit KT's potential to tackle a variety of MTOPs. To overcome these limitations, we propose a novel learning-to-transfer (L2T) framework to automatically discover efficient KT policies for the MTOPs at hand. Our framework conceptualizes the KT process as a learning agent's sequence of strategic decisions within the EMT process. We propose an action formulation for deciding when and how to transfer, a state representation with informative features of evolution states, a reward formulation concerning convergence and transfer efficiency gain, and the environment for the agent to interact with MTOPs. We employ an actor-critic network structure for the agent and learn the policy via proximal policy optimization. This learned agent can be integrated with various evolutionary algorithms, enhancing their ability to address unseen MTOPs. Comprehensive empirical studies on both synthetic and real-world MTOPs, encompassing diverse intertask relationships, function classes, and task distributions are conducted to validate the proposed L2T framework. The results show a marked improvement in the adaptability and performance of implicit EMT when solving a wide spectrum of unseen MTOPs.

Feature selection (FS) is a significant research topic in machine learning and artificial intelligence, but it becomes complicated in the high dimensional search space due to the vast number of features. Evolutionary computation (EC) has been widely used in solving FS by modeling it as an expensive wrapper-form optimization task, where a classifier is used to obtain classification accuracy for fitness evaluation (FE). In this article, we propose that the FS problem can be also modeled as a cheap filter-form optimization task, where the FE is based on the relevance and redundancy of the selected features. The wrapper-form optimization task is beneficial for classification accuracy while the filter-form optimization task has the strength of a lighter computational cost. Therefore, different from existing multitask-based FS that uses various wrapper-form optimization tasks, this article uses a multiform optimization technique to model the FS problem as a wrapper-form optimization task and a filter-form optimization task simultaneously. An evolutionary multitask FS (EMTFS) algorithm for parallel tacking these two tasks is proposed followed by, in which a two-channel knowledge transfer strategy is proposed to transfer positive knowledge across the two tasks. Experiments on widely used public datasets show that EMTFS can select as few features as possible on the premise of superior classification accuracy than the compared state-of-the-art FS algorithms.

Although knowledge transfer methods are developed for many-task optimization problems, they tend to utilize solutions from a single task for knowledge transfer. Indeed, there are usually multiple relevant source tasks with commonality. Multisource data fusion can capture complementary knowledge of distinct source tasks to better assist the optimization of target tasks. However, biases potentially flow with the interaction between tasks during multisource fusion, resulting in performance degeneration. Thus, how to select multiple relevant source tasks and perform multisource knowledge transfer is challenging. To address these issues, this article proposes a multisource knowledge fusion (MKF) method based on graph attention networks. In MKF, tasks are structured using a relational graph, in which each vertex represents a task and each directed edge from vertex u to v represents that u is a source task of v. Particularly, for each task, multiple source tasks are selected based on the distribution similarity and evolutionary performance. In the graph, local message is passed from source tasks to target tasks using graph attention networks, which automatically learn the adjacency weight of each directed edge and aggregate solutions from multiple source tasks to obtain fused representations for target tasks. These fused representations are adopted to generate new solutions through mutation. In this way, multisource knowledge is fused and transferred according to their importance to the target task. Integrating MKF into differential evolution, a new algorithm named MKF-DE is put forward. Experimental results on GECCO2020MaTOP and CEC2022MaTOP show that MKF-DE outperforms state-of-the-art algorithms on most instances.

Protein structure prediction (PSP) is an important scientific problem because it helps humans to understand how proteins perform their biological functions. This paper models the PSP problem as a multi-objective optimization problem with three fast and accurate knowledge-based energy functions. This way, using evolutionary computation (EC)-based artificial intelligence (AI) approach to solve this multi-objective PSP problem to find the optimal structure is explainable. Considering that the multiple populations for multiple objectives (MPMO) framework shows efficient performance in solving lots of multi-objective benchmarks and real-world problems, this paper proposes a new AI approach named improved MPMO-based differential evolution (IMPMO-DE) to solve the multi-objective PSP problem. To our best knowledge, this is the first time that MPMO is applied to PSP, with three novel strategies. First, an adaptive archive-based mutation strategy is proposed to better balance the exploration and exploitation abilities by adaptively using different archive-based mutation operators in different evolutionary stages. Second, a mixed individual transfer strategy is proposed to share search information among the multiple populations to accelerate the convergence speed. Third, an evolvable archive update strategy is proposed to generate more promising solutions through evolving the archived solutions. IMPMO-DE is tested on 28 representative proteins and all the available template-free modeling proteins up to 404 residues in the famous Critical Assessment of Protein Structure Prediction (CASP14) competition. Experimental results show that IMPMO-DE performs better than the compared state-of-the-art EC-based PSP methods and ranks above average compared with all the CASP14 competitors. More importantly, IMPMO-DE is a new efficient AI approach that opens a promising optimization-based evolutionary and explainable way for efficient PSP rather than deep learning approaches like AlphaFold2, especially for newly discovered proteins without similar known protein structures.

As a challenging research topic in evolutionary multitask optimization (EMTO), evolutionary many-task optimization (EMaTO) aims at solving more than three tasks simultaneously. The design of the EMaTO algorithm generally needs to consider two major open issues, which are how to obtain useful knowledge from similar source tasks and how to effectively transfer knowledge to the target task. In this paper, we discover that knowledge structure plays a significant role in dealing with these two issues and propose a novel knowledge structure preserving-based evolutionary algorithm (KSP-EA) to efficiently solve many-task optimization problems. KSP-EA aims to achieve two goals, which are firstly to obtain useful structure-preserved knowledge from similar source tasks and secondly to effectively transfer both direct and indirect knowledge to the target task. To achieve the first goal, we propose a local-structure-preserved knowledge acquisition strategy that projects the knowledge of similar source tasks into a unified subspace without loss of the knowledge structure, thus enhancing the quality of the obtained knowledge. To achieve the second goal, we propose a tree-based knowledge propagation strategy that constructs a knowledge propagating tree to connect all the tasks and propagates knowledge along the edges of this tree. This way, the target task can obtain both direct and indirect knowledge, improving the effectiveness of knowledge transfer. We conduct extensive experiments on CEC19 and WCCI22 many-task optimization test suites and a real-world application scenario to evaluate the performance of KSP-EA. The experimental results show that our KSP-EA generally outperforms state-of-the-art algorithms.

Evolutionary computation (EC) is a kind of meta-heuristic algorithm that takes inspiration from natural evolution and swarm intelligence behaviors. In the EC algorithm, there is a huge amount of data generated during the evolutionary process. These data reflect the evolutionary behavior and therefore mining and utilizing these data can obtain promising knowledge for improving the effectiveness and efficiency of EC algorithms to better solve optimization problems. Considering this and inspired by the ability of human beings that acquire knowledge from the historical successful experiences of their predecessors, this paper proposes a novel EC paradigm, named knowledge learning EC (KLEC). The KLEC aims to learn from historical successful experiences to obtain a knowledge library and to guide the evolutionary behaviors of individuals based on the knowledge library. The KLEC includes two main processes named “learning from experiences to obtain knowledge” and “utilizing knowledge to guide evolution”. First, KLEC maintains a knowledge library model and updates this model by learning the successful experiences collected in every generation. Second, KLEC not only adopts the evolutionary operation but also utilizes the knowledge library model to guide individuals for better evolution. The KLEC is a generic and effective framework, and we propose two algorithm instances of KLEC, which are knowledge learning-based differential evolution and knowledge learning-based particle swarm optimization. Also, we combine the knowledge learning framework with several state-of-the-art EC algorithms, showing that the performance of the state-of-the-art algorithms can be significantly enhanced by incorporating the knowledge learning framework.

Handling conflicting objectives and finding multiple Pareto optimal solutions are two challenging issues in solving multiobjective optimization problems (MOPs). Inspired by the efficiency of multitask optimization (MTO) in finding multiple optimal solutions of multitask optimization problem (MTOP), we propose to treat MOP as a MTOP and solve it by using MTO. By transforming the MOP into a MTOP, not only that the difficulty in handling conflicting objectives can be avoided, but also that MTO can help efficiently find well-distributed multiple optimal solutions for MOP. With the above idea, this paper proposes a new multiobjective optimization method via MTO, with the following three contributions. Firstly, a theorem is proposed to theoretically show the relationship between MOP and MTOP and how MOP can be transformed into a MTOP. Secondly, based on the theoretical analysis, a multiple tasks for multiple objectives (MTMO) framework is proposed for solving MOP efficiently. Thirdly, a MTMO-based evolutionary algorithm is developed to solve MOP, together with two novel strategies. One is a target point estimation strategy for transforming the MOP into a MTOP automatically and accurately. The other is an archive-based implicit knowledge transfer strategy for efficiently transferring knowledge across multiple tasks to enhance the optimization results of multiple tasks together. The superiority of the proposed algorithm is validated in extensive experiments on 15 MOPs with objective numbers varying from 3 to 20 and with six state-of-the-art algorithms as competitors. Therefore, solving MOP and even many-objective optimization problem via MTO is a new, promising, and efficient method.

Differential evolution (DE) is a widely recognized method to solve complex optimization problems as shown by many researchers. Yet, non-adaptive versions of DE suffer from insufficient exploration ability and uses no historical information for its performance enhancement. This work proposes Fractional Order Differential Evolution (FODE) to enhance DE performance from two aspects. Firstly, a bi-strategy co-deployment framework is proposed. The population-based and parameter-based strategies are combined to leverage their respective advantages. Secondly, the fractional order calculus is first applied to the differential vector to enhance DE’s exploration ability by using the historical information of populations, and ensures the diversity of population in an evolutionary process. We use the 2017 IEEE Congress on Evolutionary Computation (CEC) test functions, and CEC2011 real-world problems to evaluate FODE’s performance. Its sensitivity to parameter changes is discussed and an ablation study of multi-strategies is systematically performed. Furthermore, the variations of exploration and exploitation in FODE are visualized and analyzed. Experimental results show that FODE is superior to other state-of-the-art DE variants, the winners of CEC competitions, other fractional order calculus-based algorithms, and some powerful variants of classic algorithms.

Knowledge transfer (KT) has been regarded as an efficient method in evolutionary multitask optimization (EMTO) by utilizing the information of other tasks to promote the optimization of the current task. Most KT methods achieve information communication across index-aligned dimensions. However, the index-aligned dimensions are not always similar or related, which is not always suitable for communication and causes the low efficiency in KT. Moreover, when the KT occurs in the heterogeneous tasks with different dimensions, the task with lower dimensions often pads the extra dimensions to make their dimensions equal. However, the dimension-padding often involves the redundant or useless information, which may mislead the KT process. In this article, a novel multilevel and multisegment learning multitask optimization (MMLMTO) algorithm based on niching technique is proposed to achieve high-quality KT. First, a multilevel learning strategy is proposed to divide the population into three levels according to fitness values for better selecting the individuals for KT. Second, a multisegment learning strategy is proposed to split some top individuals in each level into several segments, and each segment will find its closest segment to form a niche, where the KT is executed. This ensures that KT occurs in the similar or related dimensions and avoids the dimension-padding to eliminate the influence of the redundant information. Experimental results on IEEE CEC2017 and IEEE CEC2022 multitask benchmarks fully demonstrate the effectiveness of MMLMTO, which can significantly outperform other state-of-the-art multitask algorithms. Finally, MMLMTO is applied to a real-world multitask rover navigation application problem to further demonstrate its applicability.

The Kriging model has been widely used in regression-based surrogate-assisted evolutionary algorithms (SAEAs) for expensive multiobjective optimization by using one model to approximate one objective, and the fusion of all the models forms the fitness surrogate. However, when tackling expensive many-objective optimization problems, too many models are required to construct such a fitness surrogate, which incurs cumulative prediction uncertainty and higher computational cost. Considering that the fitness surrogate works to predict different objective values to help select promising solutions with good convergence and diversity, this article proposes a novel model reduction idea to change the many-models-based fitness surrogate to a two-models-based indicator surrogate (TIS) that directly approximates convergence and diversity indicators. Based on TIS, a hierarchical and ensemble SAEA (HES-EA) is proposed with three stages. First, the HES-EA transforms the many objectives of the real-evaluated solutions into two indicators (i.e., the convergence and diversity indicators) and divides these solutions into different clusters. Second, an HES consisting of a cluster surrogate and different TISs is trained through these clustered solutions and their indicators. Third, during the optimization process, the HES can predict the candidate solutions’ cluster information via the cluster surrogate and indicator information via the TISs. Promising solutions can thus be selected based on the predicted information via a clustering-based sequential selection strategy without real fitness evaluation consumption. Compared with state-of-the-art SAEAs on three widely used benchmark suites up to 184 instances and one real-world application, HES-EA shows its superiority in both optimization performance and computational cost.

In a capacitated vehicle routing problem (CVRP), multiple vehicles are planned to travel for serving customers so as to reduce transportation costs in logistics. Taking each CVRP as a task, multiple CVRPs can form a multi-task optimization problem. Based on the similarity between tasks, knowledge transfer methods are developed to improve optimization performance by utilizing the search experience of related tasks. However, existing methods tend to use one task only for knowledge transfer. Indeed, in a target task, the different parts of customer distributions are similar to that of multiple related tasks. The information of multiple source tasks can be fused to assist the optimization of target tasks. Thus, this paper proposes a genetic algorithm with fragment-based knowledge transfer (FKT-GA), which fuses route fragments from multiple related tasks to assist the optimization of target tasks. In FKT-GA, multiple source tasks are selected for each target task based on distribution features that are invariant to rotation, shift, and scaling. Solutions of source tasks are aligned to target spaces for sampling route fragments, which are integrated to construct high-quality solutions for target tasks. In addition, mutation and crossover operators are developed to enhance solution diversity. Experimental results on fifteen 6-task instances show that FKT-GA outperforms state-of-the-art algorithms in terms of solution optimality. The proposed FKT can improve algorithm performance.

In dynamic time-linkage optimization, current decisions influence the future state of environments. To make good decisions that have a positive impact on future states, existing methods usually build a model to predict the future rewards of solutions for decision making. However, these prediction models present low accuracy since decision data are not enough to train such a complex model. To address this issue, this article proposes a contrastive-learning-based decision making (CLDM) method, which builds a contrastive model to learn the relationship between solutions but not absolute rewards and adopts a quick decision strategy to select solutions. In CLDM, a clustering-based time-linkage detection (CD) strategy is developed to measure the intensity of the time linkage, which determines whether to make decisions based on future rewards. To represent the relative relationship between solutions, a large number of contrastive samples are constructed using the limited historical decisions. A contrastive model is trained for solution comparison in terms of the combination of current fitness and future rewards. Candidate solutions are clustered into multiple groups to filter poor ones, and a few solutions are preserved to rank using the contrastive model. The winner is taken as the decision solution. Integrating CLDM into particle swarm optimization (PSO), a new algorithm named contrastive-learning-based PSO (CL-PSO) is put forward. Experimental results on multiple dynamic time-linkage optimization instances demonstrate that CL-PSO outperforms state-of-the-art algorithms in terms of solution quality. CL-PSO can also well solve the mobile robot path planning problem.

Traffic signal timing optimization (TSTO) is a significant problem in smart cities. Evolutionary computation (EC) algorithms have been widely studied to solve the TSTO problem. However, as existing EC-based algorithms usually use iterative-based evolution and simulation-based evaluation to optimize the timing plan for certain traffic situations, they still suffer from two difficulties, which are the time-consuming optimization process in certain traffic situations and the weak adaptation ability to unseen traffic situations. Therefore, this article proposes a novel learning for adaptation (LA) framework for real-time TSTO by changing the optimization process from evolution to adaptation. The LA learns a map model from the traffic volume input to the traffic signal timing. Then, the learned map model is expected to adapt to unseen traffic situations faster and better. The LA framework includes a data collection stage and a model learning (ML) stage. First, in the data collection stage, a multisource transfer-based particle swarm optimization (MTPSO) algorithm is proposed to avoid the under-optimizing issue. Second, in the ML stage, a multilevel smoothness regularization (MSR) method is proposed to deal with the over-fitting issue. The proposed LA framework with MTPSO and MSR is named as LMM method. This way, the TSTO process is changed from time-consuming evolution to time-efficient adaptation, which is significant in practical real-time applications. Comprehensive experiments with ten different synthetic and real-world road networks under different traffic volume distributions are carried out. The results show that the LMM method adapts better to unseen traffic volume inputs and can achieve real-time TSTO.

Crowdsourcing contests have become an important method for individuals and organizations to solve complex problems by obtaining innovative solutions from external participants. As the number of participants continues to grow, the likelihood of undesirable outcomes increases, posing a great requirement for effective community detection algorithms. To provide platform owners with actionable and timely management strategies, this article proposes a multimodule-based dynamic community detection (MDCD) algorithm to facilitate the achievement of efficient, high-quality, and sustainable innovation. The MDCD algorithm uses a multimodule task learning framework containing four different modules, including heterogeneous temporal aggregation (HTA), representation reconstruction (RR), link prediction (LP), and node clustering (NC) modules, to gradually detect the community structure accurately. First, the HTA module obtains the initial node representation by capturing both spatial heterogeneity and temporal dependencies. Second, the RR module considers reconstructed topology and node attribute information to update the node representation via an encoder–decoder collaboration mechanism. Third, the LP module further optimizes the node representation by exploiting the predicted graph links, which helps increase the accuracy of community detection. Finally, the NC module leverages two metric learning methods to optimize a learnable clustering process based on the predicted node presentations, which helps platform owners achieve comprehensive results across multiple dimensions of innovation performance. The experimental results from real-world crowdsourcing platforms indicate that MDCD shows effectiveness in simultaneously improving the multidimensional innovation performance of crowdsourcing platforms and increasing solver engagement.

Feature selection (FS), which aims to minimize the classification error and the number of selected features, can essentially be modeled as a multiobjective optimization problem. To deal with such multiobjective FS (MOFS) problems, many multiobjective evolutionary algorithms (MOEAs) have been proposed. These MOEAs can find multiple optimal solutions, whereas substantial computational resources are required for fitness evaluations (FEs). More seriously, due to the high dimensionality and sparsity of FS problems, many FEs will be spent on unpromising solutions, resulting in a meaningless loss of computational resources. In this paper, two innovations are made so as to improve the performance of MOEAs for MOFS. First, we propose a surrogate-assisted flip (SF) strategy for MOEAs to reduce the FE waste on potentially unpromising solutions and improve search efficiency. This SF strategy is free of FE consumption and theoretically can be embedded in any MOEA to deal with MOFS problems. The experimental results show that this SF can improve the performance of different MOEAs, especially in reducing the number of selected features. Second, based on SF, we propose a more efficient SF -assisted MOEA for dealing with high-dimensional MOFS problems. The proposed algorithm divides the whole search space into different subspaces based on redundant feature subsets clustering to achieve parallel search, so as to reduce the search difficulty. The experimental results show that this algorithm is even more competitive than other SF -assisted MOEAs.

Evolutionary multitasking (EMT), as a very popular research topic in the evolutionary computation community, has been used to solve high-dimensional FS problems and has shown good performance recently. However, most of the existing EMT-based methods still have two drawbacks. First, they only consider using filter-based task generation strategies to retain highly relevant features for generating the additional tasks, whereas the redundancy between features is ignored. Second, they always consider a complete variable vector (e.g., global optimum or mean positional information of a population at current generation) as positive knowledge and transfer it, which greatly weakens the variety of transferred knowledge and increases the possibility of falling into local optimality. To deal with these two drawbacks, we propose a new EMT-assisted multitask particle swarm optimization (MPSO) algorithm with two innovations for high-dimensional FS. First, we propose a dual clustering-based task generation strategy to generate tasks by considering both feature relevance and redundancy. Second, we propose a fine-grain knowledge transfer strategy to realize explicit transfer of knowledge between different tasks. Experimental results on 15 public datasets show the effectiveness and competitiveness of our proposed MPSO algorithm over other state-of-the-art FS methods in dealing with high-dimensional FS problems.

Evolutionary multitask optimization (EMTO) has been increasingly employed in addressing high-dimensional feature selection challenges, but current EMTO algorithms still have three deficiencies: First, in task generation, they just consider the linear correlation among features but ignore the nonlinear correlation. Second, they commonly encounter negative knowledge transfer. Third, they are hard to strike an optimal balance between global search capability and computational efficiency. This paper proposes an adaptive aggregative multitask competitive swarm optimization (AAMCSO) for high-dimensional feature selection, which contains three novel and effective strategies to address the above deficiencies. Firstly, AAMCSO proposes a linear-and-nonlinear-correlation-based task generation strategy to generate multiple tasks while considering both linear and nonlinear correlation between features and labels. Secondly, AAMCSO proposes an adaptive aggregative knowledge transfer strategy to adaptively transfer positive knowledge among related tasks. Thirdly, AAMCSO proposes a bi-directional asymmetric flip strategy to guide the population to search for a smaller feature subset with better classification performance. We have conducted extensive comparative experiments on AAMCSO and multiple state-of-the-art feature selection algorithms in high-dimensional feature selection problems with up to 10000 dimensions. The results show that AAMCSO achieves significantly superior performance to the state-of-the-art comparison algorithms in terms of both classification accuracy and feature number.

Ant colony system algorithm (ACS), as an important evolutionary computation (EC) algorithm, has demonstrated significant advantages in solving complex optimization problems. However, traditional EC algorithms and traditional ACS algorithm often face the challenge of slow computational speed when dealing with large-scale problems. In recent years, matrix-based EC approaches have been proposed to accelerate the computational speed, which has obtained promising results in dealing with large-scale problems. However, most existing matrix-based EC algorithms are designed for continuous optimization problems, while the matrix-based approach integrated with ACS has not attracted enough attention, which will be efficient for solving large-scale discrete optimization problems. Therefore, in this paper, we propose a matrix-based ACS (MACS) algorithm and apply it to solve the traveling salesman problem (TSP). MACS is an innovative improvement over the traditional ACS algorithm, utilizing matrix operations to parallelly let ants select city and update pheromone. Experimental results show that the MACS algorithm has significantly better efficiency in accelerating computational speed while maintaining the remarkable problem-solving ability in solving large-scale TSP.

The rapid growth of electric vehicles (EVs) has led to significant challenges in providing efficient and sustainable charging solutions. This paper addresses the battery swapping station (BSS) recommendation problem by proposing a novel conflict-free genetic algorithm (CFGA) integrated with a Nash equilibrium seeking (NES) approach to identify optimal Nash equilibrium (ONE) solutions to such a non-cooperative optimization problem. The CFGA employs specialized crossover and mutation operators to generate offspring that satisfy the constraints of the problem, ensuring that each EV decides a unique battery swap strategy without conflict. Firstly, an order crossover operator is proposed to preserve the order of genes in the chromosomes. Secondly, a replacement and exchange mutation operator is proposed to enhance mutation diversity. The resulting optimal solution is then used as the initial strategy for the NES, which iteratively converges to the ONE. The proposed CFGA with NES algorithm is evaluated under both small-scale and large-scale cases, demonstrating its effectiveness in achieving a balance between costs for EVs and utilization for BSSs. The study's findings have practical implications for the smart grid and EV integration, offering a robust method for optimizing EV infrastructure and operations.

Sudoku puzzles are not only popular intellectual games but also NP-hard combinatorial problems related to various real-world applications, which have attracted much attention worldwide. Although many efficient tools, such as evolutionary computation (EC) algorithms, have been proposed for solving Sudoku puzzles, they still face great challenges with regard to hard and large instances of Sudoku puzzles. Therefore, to efficiently solve Sudoku puzzles, this paper proposes a genetic algorithm (GA)-based method with a novel local search technology called local search-based GA (LSGA). The LSGA includes three novel design aspects. First, it adopts a matrix coding scheme to represent individuals and designs the corresponding crossover and mutation operations. Second, a novel local search strategy based on column search and sub-block search is proposed to increase the convergence speed of the GA. Third, an elite population learning mechanism is proposed to let the population evolve by learning the historical optimal solution. Based on the above technologies, LSGA can greatly improve the search ability for solving complex Sudoku puzzles. LSGA is compared with some state-of-the-art algorithms at Sudoku puzzles of different difficulty levels and the results show that LSGA performs well in terms of both convergence speed and success rates on the tested Sudoku puzzle instances.

Evolutionary multitask optimization is an emerging research topic that aims to solve multiple tasks simultaneously. A general challenge in solving multitask optimization problems (MTOPs) is how to effectively transfer common knowledge between/among tasks. However, knowledge transfer in existing algorithms generally has two limitations. First, knowledge is only transferred between the aligned dimensions of different tasks rather than between similar or related dimensions. Second, the knowledge transfer among the related dimensions belonging to the same task is ignored. To overcome these two limitations, this article proposes an interesting and efficient idea that divides individuals into multiple blocks and transfers knowledge at the block-level, called the block-level knowledge transfer (BLKT) framework. BLKT divides the individuals of all the tasks into multiple blocks to obtain a block-based population, where each block corresponds to several consecutive dimensions. Similar blocks coming from either the same task or different tasks are grouped into the same cluster to evolve. In this way, BLKT enables the transfer of knowledge between similar dimensions that are originally either aligned or unaligned or belong to either the same task or different tasks, which is more rational. Extensive experiments conducted on CEC17 and CEC22 MTOP benchmarks, a new and more challenging compositive MTOP test suite, and real-world MTOPs all show that the performance of BLKT-based differential evolution (BLKT-DE) is superior to the compared state-of-the-art algorithms. In addition, another interesting finding is that the BLKT-DE is also promising in solving single-task global optimization problems, achieving competitive performance with some state-of-the-art algorithms.

Knowledge transfer (KT) is crucial for optimizing tasks in evolutionary multitask optimization (EMTO). However, most existing KT methods can only achieve superficial KT but lack the ability to deeply mine the similarities or relationships among different tasks. This limitation may result in negative transfer, thereby degrading the KT performance. As the KT efficiency strongly depends on the similarities of tasks, this article proposes a neural network (NN)-based KT (NNKT) method to analyze the similarities of tasks and obtain the transfer models for information prediction between different tasks for high-quality KT. First, NNKT collects and pairs the solutions of multiple tasks and trains the NNs to obtain the transfer models between tasks. Second, the obtained NNs transfer knowledge by predicting new promising solutions. Meanwhile, a simple adaptive strategy is developed to find the suitable population size to satisfy various search requirements during the evolution process. Comparison of the experimental results between the proposed NN-based multitask optimization (NNMTO) algorithm and some state-of-the-art multitask algorithms on the IEEE Congress on Evolutionary Computation (IEEE CEC) 2017 and IEEE CEC2022 benchmarks demonstrate the efficiency and effectiveness of the NNMTO. Moreover, NNKT can be seamlessly applied to other EMTO algorithms to further enhance their performances. Finally, the NNMTO is applied to a real-world multitask rover navigation application problem to further demonstrate its applicability.

Distributed database system (DDBS) technology has shown its advantages with respect to query processing efficiency, scalability, and reliability. Moreover, by partitioning attributes of sensitive associations into different fragments, DDBSs can be used to protect data privacy. However, it is complex to design a DDBS when one has to optimize privacy and utility in a time-varying environment. This paper proposes a distributed prediction-randomness framework for the evolutionary dynamic multiobjective partitioning optimization of databases. In the proposed framework, two sub-populations contain individuals representing database partitioning solutions. One sub-population utilizes a Markov chain-based predictor to predict discrete-domain solutions for database partitioning when the environment changes, and the other sub-population utilizes the random initialization operator to maintain population diversity. In addition, a knee-driven migration operator is utilized to exchange information between two sub-populations. Experimental results show that the proposed algorithm outperforms the competing solutions with respect to accuracy, convergence speed, and scalability.

Cooperative coevolutionary algorithms are popular to solve large-scale dynamic optimization problems via divide-and-conquer mechanisms. Their performance depends on how decision variables are grouped and how changing optima are tracked. However, existing decomposition methods are computationally expensive, resulting in limitations under dynamic variable interactions. Quick online decomposition is still a challenging issue, along with solution reconstruction for new subproblems. This paper proposes transfer-based particle swarm optimization, which adopts a dynamic differential grouping for online decomposition and a solution transfer strategy in response to environmental changes. Particularly, once an environmental change occurs, the dynamic differential grouping readjusts historical groupings based on the change severity of variable interactions. In addition, according to the similarity between subproblems in successive environments, the solution transfer strategy constructs new solutions from historical ones through dimension mapping. Multiple swarms are created to explore subareas of subproblems. Experimental results show that the proposed algorithm outperforms state-of-the-art algorithms on problem instances up to 1000-D in terms of solution optimality. The dynamic differential grouping obtains accurate groupings using less function evaluations.

Surrogate-assisted evolutionary algorithms (SAE-As), mainly including regression-based SAEAs and classification-based SAEAs, are promising for solving expensive multi-objective optimization problems (EMOPs). Regression-based SAEAs usually use complex regression models to approximate the fitness evaluation, which will suffer from high training costs to obtain a fine-accuracy surrogate. In contrast, classification-based SAEAs can achieve solution selection via coarse binary relations predicted by classifiers, thus avoiding high requirements in prediction accuracy and training costs. However, most of the binary relations in existing classification-based SAEAs mainly only involve convergence comparison whereas diversity maintenance is neglected. Considering the capacity of the grid technique in maintaining both convergence and diversity, we propose a new classification method called grid classification to discretize the objective space into grids and train a lightweight grid classification-based surrogate (GCS), for which low training costs are needed. The GCS can evaluate the solution performance in terms of both convergence and diversity simultaneously according to the predicted grid locations, which opens up a new field for follow-up research on classification-based SAEAs. Following this, a GCS-assisted particle swarm optimization algorithm is proposed for tackling EMOPs. Experimental results on widely-used benchmark problems (including high-dimensional EMOPs) and a 222-high-dimensional real-world application problem show its competitiveness in terms of both optimization performance and computational cost.

Multiple autonomous underwater vehicles (AUVs) are popular for executing submarine missions, which involve multiple targets distributed in a large and complex underwater environment. The path planning of multiple AUVs is a significant and challenging problem, which determines the location of surface points for AUV launch and plans the paths of AUVs for target traveling. Most existing works model the problem as a single-objective static optimization problem. However, the target missions may change over time, and multiple optimization objectives are usually expected for decision making. Thus, this article models the problem as a dynamic multiobjective optimization problem and proposes a cooperative evolutionary computation algorithm to provide diverse and high-quality solutions for decision makers. In the proposed method, solutions are represented using a bilayer encode scheme, in which the first layer indicates the surface location points and the second layer represents the traveling sequences of target missions. Multiple populations for multiple objectives framework is adopted to efficiently solve the dynamic multiobjective AUV optimization problem. In addition, a recombination-based sampling strategy is developed to improve convergence by fusing the information of multiple populations. Once a change occurs, an incremental response strategy is adopted to generate high-quality solutions for population evolution. Based on the dataset of New Zealand bathymetry, six complex underwater scenarios are constructed with a size of 50 km × 50 km× 10 km and 400 target missions for tests. Experimental results show that the proposed method outperforms the state-of-the-art algorithms in terms of solution diversity and optimality.

Many-task optimization problem (MaTOP) is a kind of problem in that more than three optimization tasks are required to be solved simultaneously. How to utilize multiple different kinds of similarities among many tasks for knowledge transfer (KT) is a challenging issue in solving MaTOP. To this end, this paper proposes a multi-view transfer (MVT)-based differential evolution (MVTDE) for effectively transferring knowledge in solving MaTOP. In particular, a perspective of task alignment is regarded as a view of performing KT. By combining different views including marginal and conditional distribution alignment, MVT can better fully utilize various task similarities from different aspects to solve MaTOP efficiently. This paper is with two contributions. First, we propose the MVT method that incorporates multiple KT methods from the views of marginal and conditional distribution alignment to enhance the search efficiency on the target tasks. Second, we propose to control the occurrence of different KT methods in MVT according to probability parameters and propose a parameter update strategy to adaptively adjust the probability parameters according to the feedback of different KT methods. In the experimental study, we carry out comparative experiments on three widely used MaTOP benchmarks to validate the effectiveness of MVTDE. The results show that MVTDE obtains competitive performance compared to several state-of-the-art many-task optimization algorithms.

Feature selection is an important data processing technique, aiming to reduce the redundant and irrelevant features of data. However, as the number of features increases, feature selection algorithms based on particle swarm optimization (PSO) face the challenges of low search efficiency and huge computational consumption due to the enormous search space. A recently proposed bi-directional feature fixation (BDFF) framework for PSO has shown its effectiveness in solving high-dimensional feature selection problems, but it may mislead the particles to search in the wrong direction and requires a long time to find a small feature subset. Utilizing the prior knowledge of feature selection is expected to further enhance the performance of BDFF. Therefore, this paper first designs two tasks to introduce the prior knowledge of feature selection into BDFF while retaining its global search ability. Then, the multitasking bi-directional PSO (MBDPSO) is proposed by combining BDFF and the evolutionary multitasking optimization (EMTO) technique, which can help transfer knowledge between the two tasks effectively. Experimental results on 10 public classification datasets demonstrate that the proposed MBDPSO has an excellent performance on high-dimensional feature selection problems.

Traffic signal timing optimization (TSTO) is a significant topic in the smart city. However, there are two challenges when solving TSTO. Firstly, it often uses time-consuming simulation software to evaluate candidate solutions, therefore it is an expensive optimization problem. Secondly, as the traffic flow changes rapidly in TSTO, providing a timing scheme to respond to the change immediately is difficult. To address the above challenges, we propose a region-based evaluation particle swarm optimization algorithm (REPSO) with dual solution libraries, which has three novel designs. First, two solution libraries are built for undersaturated and oversaturated traffic flow states, respectively, which can be used to fast provide a signal timing scheme for a traffic flow in real-time. Second, a knowledge-assisted initialization strategy is proposed and adopted to assist the initialization of new solutions based on the knowledge in the two solution libraries. Third, a region-based evaluation strategy is proposed to reduce the number of fitness evaluations, which can also greatly reduce the construction time of the solution libraries. The performance of REPSO is validated by comparing with six signal timing methods in both undersaturated and oversaturated traffic flow states, showing the better general performance of REPSO.

Multimodal optimization problems (MMOPs) have multiple global optima, hence the algorithm must preserve population diversity to locate multiple global optima and ensure the precision of the obtained solutions simultaneously. To achieve these, the niching technique is widely applied. Although the niching technique shows encouraging performance, some niches may continuously evolve even though accurate enough global optima in their regions have been found. This may cause the waste of computational resources and the inefficiency of search behavior. To maintain population diversity and accuracy, and to break through the mentioned deficiency, an optimal peaks detected-based differential evolution (OPPDE) algorithm is proposed, which has three novel components. Firstly, to maintain population diversity, OPDDE designs a parameter-insensitive OPTICS-based niching strategy to automatically partition niches. Secondly, to avoid wasting computation resources on founded global optima and enhance search efficiency, OPDDE designs an optimal peaks detection strategy that uses historical information to identify the founded global optima. Thirdly, a dynamic step local search strategy is used to refine solutions. The proposed OPDDE algorithm generally superiors some state-of-the-art algorithms regarding both the accuracy and completeness of solutions, according to experiments on widely used MMOP benchmarks.

Trip planning service can save the time and energy of tourists for preparing a trip and provide a more comfortable and satisfying travel experience. This paper particularly considers the planning of transportation mode between point of interests (POI) and formulates a multiobjective trip planning model to simultaneously maximize the visit time in POIs, minimize the travel time between POIs, and minimize the travel fare needed for the trip. To simulate the real-world environment, the formulated model incorporates the real-world POI and transportation data crawled from Tripadvisor and Baidu Map API, respectively. To obtain efficient trip planning schemes, a multipopulation ant colony system algorithm for trip planning, abbreviated as MACS-TP, is proposed. First, MACS-TP uses two colonies to optimize the time-related objective and fare-related objective respectively, which enhances the search efficiency. Second, an archive is employed to store the nondominated solutions found by both colonies and a new pheromone global update rule is designed based on the archive to help colonies optimize their corresponding objective sufficiently. Third, an elite learning strategy is proposed to further enhance the quality of solutions in the archive. Experimental results on a real-world dataset of Guangzhou, China illustrate the effectiveness of MACS-TP.

Community detection is an important research direction in complex network analysis that can help us discover valuable network structures. The community detection algorithms based on multiobjective particle swarm optimization encode community membership of nodes in particles and employ evolutionary strategies to search for the optimal community division. Existing algorithms face two challenges: (1) they are inapplicable to large networks because the evolution process is time-consuming; (2) they are easy to fall into local optima. In this paper, we propose a novel algorithm that combines a label-propagation-based multiobjective particle swarm optimization algorithm with a graph attention variational autoencoder to realize community detection. On the one hand, the label propagation strategy is involved in the update of a swarm's particles to speed up its evolution. The optimal solutions found by the particle swarm optimization algorithm are embedded into the objective of the autoencoder to improve the embedding vectors’ quality. On the other hand, the embedding vectors are used to improve the solutions of the particle swarm optimization algorithm to avoid its early convergence. The experiments on artificial and real-world networks demonstrate the feasibility and effectiveness of our algorithm compared with some state-of-the-art algorithms.

Feature selection, which aims to improve the classification accuracy and reduce the size of the selected feature subset, is an important but challenging optimization problem in data mining. Particle swarm optimization (PSO) has shown promising performance in tackling feature selection problems, but still faces challenges in dealing with large-scale feature selection in Big Data environment because of the large search space. Hence, this paper proposes a bi-directional feature fixation (BDFF) framework for PSO and provides a novel idea to reduce the search space in large-scale feature selection. BDFF uses two opposite search directions to guide particles to adequately search for feature subsets with different sizes. Based on the two different search directions, BDFF can fix the selection states of some features and then focus on the others when updating particles, thus narrowing the large search space. Besides, a self-adaptive strategy is designed to help the swarm concentrate on a more promising direction for search in different stages of evolution and achieve a balance between exploration and exploitation. Experimental results on 12 widely-used public datasets show that BDFF can improve the performance of PSO on large-scale feature selection and obtain smaller feature subsets with higher classification accuracy.

Many real-world optimization problems require searching for multiple optimal solutions simultaneously, which are called multimodal optimization problems (MMOPs). For MMOPs, the algorithm is required both to enlarge population diversity for locating more global optima and to enhance refine ability for increasing the accuracy of the obtained solutions. Thus, numerous niching techniques have been proposed to divide the population into different niches, and each niche is responsible for searching on one or more peaks. However, it is often a challenge to distinguish proper individuals as niche centers in existing niching approaches, which has become a key issue for efficiently solving MMOPs. In this article, the niche center distinguish (NCD) problem is treated as an optimization problem and an NCD-based differential evolution (NCD-DE) algorithm is proposed. In NCD-DE, the niches are formed by using an internal genetic algorithm (GA) to online solve the NCD optimization problem. In the internal GA, a fitness-entropy measurement objective function is designed to evaluate whether a group of niche centers (i.e., encoded by a chromosome in the internal GA) is promising. Moreover, to enhance the exploration and exploitation abilities of NCD-DE in solving the MMOPs, a niching and global cooperative mutation strategy that uses both niche and population information is proposed to generate new individuals. The proposed NCD-DE is compared with some state-of-the-art and recent well-performing algorithms. The experimental results show that NCD-DE achieves better or competitive performance on both the accuracy and completeness of the solutions than the compared algorithms.

Distributed differential evolution (DDE) is an efficient paradigm that adopts multiple populations for cooperatively solving complex optimization problems. However, how to allocate fitness evaluation (FE) budget resources among the distributed multiple populations can greatly influence the optimization ability of DDE. Therefore, this article proposes a novel three-layer DDE framework with adaptive resource allocation (DDE-ARA), including the algorithm layer for evolving various differential evolution (DE) populations, the dispatch layer for dispatching the individuals in the DE populations to different distributed machines, and the machine layer for accommodating distributed computers. In the DDE-ARA framework, three novel methods are further proposed. First, a general performance indicator (GPI) method is proposed to measure the performance of different DEs. Second, based on the GPI, a FE allocation (FEA) method is proposed to adaptively allocate the FE budget resources from poorly performing DEs to well-performing DEs for better search efficiency. This way, the GPI and FEA methods achieve the ARA in the algorithm layer. Third, a load balance strategy is proposed in the dispatch layer to balance the FE burden of different computers in the machine layer for improving load balance and algorithm speedup. Moreover, theoretical analyses are provided to show why the proposed DDE-ARA framework can be effective and to discuss the lower bound of its optimization error. Extensive experiments are conducted on all the 30 functions of CEC 2014 competitions at 10, 30, 50, and 100 dimensions, and some state-of-the-art DDE algorithms are adopted for comparisons. The results show the great effectiveness and efficiency of the proposed framework and the three novel methods.

Cooperative coevolution (CC) algorithms based on variable decomposition methods are efficient in solving large-scale optimization problems (LSOPs). However, many decomposition methods, such as the differential grouping (DG) method and its variants, are based on the theorem of function additively separable, which may not work well on problems that are not additively separable and will result in a bottleneck for CC to solve various LSOPs. This deficiency motivates us to study how the decomposition method can decompose more kinds of separable functions, such as the multiplicatively separable function, to improve the general problem-solving ability of CC on LSOPs. With this concern, this article makes the first attempt to decompose multiplicatively separable functions and proposes a novel method called dual DG (DDG) for better LSOP decomposition and optimization. The novelty and advantage of DDG are that it can be suitable for not only additively separable functions but also multiplicatively separable functions, which can considerably expand the application scope of CC. In this article, we will first define the multiplicatively separable function, and then mathematically show its relationship to the additively separable function and how they can be transformed into each other. Based on this, the DDG can use two kinds of differences to detect the separable structure of both additively and multiplicatively separable functions. In addition, the time complexity of DDG is analyzed and a DDG-based CC algorithm framework is developed for solving LSOPs. To verify the superiority of DDG, experiments and comparisons with some state-of-the-art and champion algorithms are conducted not only on 30 LSOPs based on the test suite of the IEEE CEC large-scale global optimization competition, but also on a case study of the parameter optimization for a neural network-based application.

The job-shop scheduling problem (JSSP) is a challenging scheduling and optimization problem in the industry and engineering, which relates to the work efficiency and operational costs of factories. The completion time of all jobs is the most commonly considered optimization objective in the existing work. However, factories focus on both time and cost objectives, including completion time, total tardiness, advance time, production cost, and machine loss. Therefore, this article first time proposes a many-objective JSSP that considers all these five objectives to make the model more practical to reflect the various demands of factories. To optimize these five objectives simultaneously, a novel multiple populations for multiple objectives (MPMO) framework-based genetic algorithm (GA) approach, called MPMOGA, is proposed. First, MPMOGA employs five populations to optimize the five objectives, respectively. Second, to avoid each population only focusing on its corresponding single objective, an archive sharing technique (AST) is proposed to store the elite solutions collected from the five populations so that the populations can obtain optimization information about the other objectives from the archive. This way, MPMOGA can approximate different parts of the entire Pareto front (PF). Third, an archive update strategy (AUS) is proposed to further improve the quality of the solutions in the archive. The test instances in the widely used test sets are adopted to evaluate the performance of MPMOGA. The experimental results show that MPMOGA outperforms the compared state-of-the-art algorithms on most of the test instances.

The evolutionary multitask optimization (EMTO) algorithm is a promising approach to solve many-task optimization problems (MaTOPs), in which similarity measurement and knowledge transfer (KT) are two key issues. Many existing EMTO algorithms estimate the similarity of population distribution to select a set of similar tasks and then perform KT by simply mixing individuals among the selected tasks. However, these methods may be less effective when the global optima of the tasks greatly differ from each other. Therefore, this article proposes to consider a new kind of similarity, namely, shift invariance, between tasks. The shift invariance is defined that the two tasks are similar after linear shift transformation on both the search space and the objective space. To identify and utilize the shift invariance between tasks, a two-stage transferable adaptive differential evolution (TRADE) algorithm is proposed. In the first evolution stage, a task representation strategy is proposed to represent each task by a vector that embeds the evolution information. Then, a task grouping strategy is proposed to group the similar (i.e., shift invariant) tasks into the same group while the dissimilar tasks into different groups. In the second evolution stage, a novel successful evolution experience transfer method is proposed to adaptively utilize the suitable parameters by transferring successful parameters among similar tasks within the same group. Comprehensive experiments are carried out on two representative MaTOP benchmarks with a total of 16 instances and a real-world application. The comparative results show that the proposed TRADE is superior to some state-of-the-art EMTO algorithms and single-task optimization algorithms.

Many-task optimization problem is a kind of challenging multi-task optimization problem with more than three tasks. Two significant issues in solving many-task optimization problems are measuring inter-task similarity and transferring knowledge among similar tasks. However, most existing algorithms only use a single similarity measurement, which cannot accurately measure the inter-task similarity because the inter-task similarity is a concept with multiple different aspects. To address this limitation, this paper proposes a bi-objective knowledge transfer framework, which aims firstly to accurately measure different types of inter-task similarity using two different measurements and secondly to effectively transfer knowledge with different types of similarity via specific strategies. To achieve the first goal, a bi-objective measurement is designed to measure inter-task similarity from two different aspects, including shape similarity and domain similarity. To achieve the second goal, a similarity-based adaptive knowledge transfer strategy is designed to choose the suitable knowledge transfer strategy based on the type of inter-task similarity. We compare the bi-objective knowledge transfer framework-based algorithms with several state-of-the-art algorithms on two challenging many-task optimization test suites with 16 instances and on real-world many-task optimization problems with up to 500 tasks. The experimental results show that the proposed algorithms generally outperform the compared algorithms.

Dynamic multiobjective optimization poses great challenges to evolutionary algorithms due to the change of optimal solutions or Pareto front with time. Learning-based methods are popular to extract the changing pattern of optimal solutions for predicting new solutions. They tend to use all variables as features (i.e., inputs) to build prediction models. However, there are usually some irrelevant and redundant variables, which increase training difficulty and decrease prediction accuracy. This article proposes a new interaction-based prediction (IP) method, which captures the correlation of variables with prediction targets and selects the most relevant variables to build prediction models using neural networks. In particular, the interaction between variables is detected to remove redundant variables. In addition, a correction procedure is developed to further improve predicted solutions according to the prediction error in past environments. The predicted solutions are used to update the population according to a specifically designed update strategy. Integrating the IP method into the framework of multiobjective evolutionary algorithm based on decomposition (MOEA/D), a new algorithm named IP-DMOEA is put forward. Experimental results on a typical dynamic multiobjective test suite demonstrate the better performance of the proposed IP-DMOEA than state-of-the-art algorithms in terms of convergence speed and solution quality. The proposed IP-DMOEA is also successfully applied to the multirobot task scheduling problem.

Large-scale optimization problems (LSOPs) are challenging because the algorithm is difficult in balancing too many dimensions and in escaping from trapped bottleneck dimensions. To improve solutions, this paper introduces targeted modification to the certain values in the bottleneck dimensions. Analogous to gene targeting (GT) in biotechnology, we experiment on targeting the specific genes in candidate solution to improve its trait in differential evolution (DE). We propose a simple and efficient method, called GT-based DE (GTDE), to solve LSOPs. In the algorithm design, a simple GT-based modification is developed to perform on the best individual, comprising probabilistically targeting the location of bottleneck dimensions, constructing a homologous targeting vector, and inserting the targeting vector into the best individual. In this way, all the bottleneck dimensions of the best individual can be probabilistically targeted and modified to break the bottleneck and to provide global guidance for more optimal evolution. Note that the GT is only performed on the globally best individual and is just carried out as a simple operator that is added to the standard DE. Experimental studies compare the GTDE with some other state-of-the-art large-scale optimization algorithms, including the winners of CEC2010, CEC2012, CEC2013, and CEC2018 competitions on large-scale optimization. The results show that the GTDE is efficient and performs better than or at least comparable to the others in solving LSOPs.

Knowledge transfer (KT) plays a key role in multitask optimization. However, most of the existing KT methods still face two challenges. First, the tasks may commonly have different dimensionalities (DDs), making the KT between heterogeneous search spaces very difficult. Second, the tasks may have different degrees of similarity in different dimensions, making that treating all dimensions with equal importance may be harmful to the KT process. To address these two challenges, this article proposes a novel orthogonal transfer (OT) method that is enabled by a cross-task mapping (CTM) strategy, which can achieve high-quality KT among heterogeneous tasks. For the first challenge, the CTM strategy maps the global best individual of one task from its original search space to the search space of the target task via an optimization process, which can handle the difference in task dimensionality. For the second challenge, the OT method is performed on the CTM-obtained individual and a random individual of the target task to find the best combination of different dimensions in these two individuals rather than treating all the dimensions equally, so as to achieve high-quality KT. To verify the effectiveness of the proposed OT method and the resulted OT-based multitask optimization (OTMTO) algorithm, this article not only uses the existing multitask optimization benchmark but also proposes a new benchmark test suite named multitask optimization problems (MTOPs) with DDs. Comprehensive experimental results on the existing and the proposed benchmarks show that the proposed OT method and the OTMTO algorithm are very advantageous in providing high-quality KT and in handling the heterogeneity of search space in MTOPs compared to the existing competitive evolutionary multitask optimization (EMTO) algorithms.

The convergence and diversity enhancement of multiobjective evolutionary algorithms (MOEAs) to efficiently solve many-objective optimization problems (MaOPs) is an active topic in evolutionary computation. By considering the advantages of the multiple populations for multiple objectives (MPMO) framework in solving multiobjective optimization problems and even MaOPs, this article proposes an MPMO-based algorithm with a bias sorting (BS) method (termed MPMO-BS) for solving MaOPs to achieve both good convergence and diversity performance. For convergence, the BS method is applied to each population of the MPMO framework to enhance the role of nondominated sorting by biasedly paying more attention to the objective optimized by the corresponding population. This way, all the populations in the MPMO framework evolve together to promote the convergence performance on all objectives of the MaOP. For diversity, an elite learning strategy is adopted to generate locally mutated solutions, and a reference vector-based maintenance method is adopted to preserve diverse solutions. The performance of the proposed MPMO-BS algorithm is assessed on 29 widely used MaOP test problems and two real-world application problems. The experimental results show its high effectiveness and competitiveness when compared with seven state-of-the-art MOEAs for many-objective optimization.

Learning and optimization are the two essential abilities of human beings for problem solving. Similarly, computer scientists have made great efforts to design artificial neural network (ANN) and evolutionary computation (EC) to simulate the learning ability and the optimization ability for solving real-world problems, respectively. These have been two essential branches in artificial intelligence (AI) and computer science. However, in humans, learning and optimization are usually integrated together for problem solving. Therefore, how to efficiently integrate these two abilities together to develop powerful AI remains a significant but challenging issue. Motivated by this, this paper proposes a novel learning-aided evolutionary optimization (LEO) framework that plus learning and evolution for solving optimization problems. The LEO is integrated with the evolution knowledge learned by ANN from the evolution process of EC to promote optimization efficiency. The LEO framework is applied to both classical EC algorithms and some state-of-the-art EC algorithms including a champion algorithm, with benchmarking against the IEEE Congress on Evolutionary Computation competition data. The experimental results show that the LEO can significantly enhance the existing EC algorithms to better solve both single-objective and multi-/many-objective global optimization problems, suggesting that learning plus evolution is more intelligent for problem solving. Moreover, the experimental results have also validated the time efficiency of the LEO, where the additional time cost for using LEO is greatly deserved. Therefore, the promising LEO can lead to a new and more efficient paradigm for EC algorithms to solve global optimization problems by plus learning and evolution.

In recent years, themulti-task learning forknowledge graph-basedrecommender system, termed MKR, has shown its promising performance and has attracted increasing interest, because a recommendation task and a knowledge graph embedding (KGE) task can help each other to improve the recommendation. However, MKR still has two difficult issues. The first is how fully to capture users’ historical behavior pattern in the recommendation task and how fully to utilize deep multi-relation semantic information in the KGE task. The second is how to deal with datasets with different sparsity. Tackling these challenging issues, this paper proposes an enhanced MKR (EMKR) approach with two novelties. First, we propose to utilize the attention mechanism to aggregate users’ historical behavior for more accurately mining preferences in the recommendation task, and utilize the relation-aware graph convolutional neural network to fully capture the deep multi-relation neighborhood features in the KGE task, so as to address the first issue. Second, a two-part modeling strategy is proposed for a better representation of users in the recommendation task to expand the expressive ability of the model for adapting to datasets with different sparsity, so as to address the second issue. Extensive experiments are conducted on widely-used datasets and 11 approaches are used for comparison. The results show that the proposed EMKR can achieve substantial gains over the compared state-of-the-art approaches, especially in the situation where user-item interactions are sparse.

The performance of a convolutional neural network (CNN) heavily depends on its hyperparameters. However, finding a suitable hyperparameters configuration is difficult, challenging, and computationally expensive due to three issues, which are 1) the mixed-variable problem of different types of hyperparameters; 2) the large-scale search space of finding optimal hyperparameters; and 3) the expensive computational cost for evaluating candidate hyperparameters configuration. Therefore, this article focuses on these three issues and proposes a novel estimation of distribution algorithm (EDA) for efficient hyperparameters optimization, with three major contributions in the algorithm design. First, a hybrid-model EDA is proposed to efficiently deal with the mixed-variable difficulty. The proposed algorithm uses a mixed-variable encoding scheme to encode the mixed-variable hyperparameters and adopts an adaptive hybrid-model learning (AHL) strategy to efficiently optimize the mixed-variables. Second, an orthogonal initialization (OI) strategy is proposed to efficiently deal with the challenge of large-scale search space. Third, a surrogate-assisted multi-level evaluation (SME) method is proposed to reduce the expensive computational cost. Based on the above, the proposed algorithm is named s urrogate-assisted hybrid-model EDA (SHEDA). For experimental studies, the proposed SHEDA is verified on widely used classification benchmark problems, and is compared with various state-of-the-art methods. Moreover, a case study on aortic dissection (AD) diagnosis is carried out to evaluate its performance. Experimental results show that the proposed SHEDA is very effective and efficient for hyperparameters optimization, which can find a satisfactory hyperparameters configuration for the CIFAR10, CIFAR100, and AD diagnosis with only 0.58, 0.97, and 1.18 GPU days, respectively.

Cooperative heterogeneous multirobot systems have attracted increasing attention in recent years. They use multiple heterogeneous robots to execute complex tasks in a coordinated way. The allocation of heterogeneous robots to cooperative tasks is a significant and challenging optimization problem. However, little work has gone into scheduling large-scale cooperative tasks with precedence constraints and multiple conflicting optimization objectives. Existing methods are insufficient to address the issue. We propose a multiobjective model and develop strength learning particle swarm optimization (SLPSO) to optimize multiple objectives. In this article, the problem is converted into a two-step problem of task permutation construction and robot subset selection. In order to coordinate with the time-extended property of the problem, SLPSO utilizes a hybrid encode scheme: an element-based representation for task permutations and a binary representation for robot coalitions. A strength learning strategy with heuristic information guides particles to enhance their best-performing objectives for improving swarm convergence. In addition, an estimation-based local search is developed to improve spare solutions for enhancing swarm diversity, which determines the search direction by estimating fitness improvements. Experimental results on thirty problem instances are elaborated to demonstrate that the proposed SLPSO significantly outperforms the state-of-the-art algorithms in terms of inverted generational distance and hypervolume metrics. The proposed SLPSO can obtain a set of high-quality and diversified solutions.

Decomposition methods play a critical role in cooperative co-evolutionary algorithms (CCEAs) for solving large-scale optimization problems. Although some well-performing decomposition methods have been designed based on the interactions among variables (IaV), their grouping accuracy is still limited due to the poor performance on the overlapping problems and the computational roundoff errors of IaV in the implementation. To deal with these limitations, a graph-based deep decomposition (GDD) method is proposed to obtain more accurate grouping results, especially for the overlapping problems. On the one hand, the GDD mines the IaV information and obtains the minimum vertex separator of the interaction graph of variables, so as to group variables deeply and recursively. On the other hand, the GDD has the ability of fault tolerance to deal with the computational roundoff errors of IaV and can improve the grouping accuracy. For better experimental studies of overlapping problems, a novel overlapping function generator is designed with the random and complicate overlap type, and two new metrics are proposed to evaluate the grouping accuracy. Comprehensive experiments show that GDD can greatly improve the grouping accuracy and help CCEAs perform better than other existing algorithms, especially on the overlapping problems. In addition, the GDD is highly fault tolerant and can divide problems accurately even on the inaccurate IaV.

Multimodal optimization problems (MMOPs) are sorts of optimization problems that have many global optima. To discover as many peaks as possible and increase the accuracy of the solutions, MMOP requires algorithms with great exploration and exploitation abilities. However, exploration and exploitation are in an adversarial relationship, since exploration aims to locate more optima via searching the global space rather than small regions, whereas exploitation targets to enhance the accuracy of solutions via searching in small areas. The key to efficiently solving MMOPs lies in striking a balance between exploration and exploitation. To achieve the goal, this paper proposes an adversarial differential evolution (ADE), containing an adversarial reproduction strategy and an adversarial selection strategy. Firstly, adversarial reproduction strategy generates offspring for exploration and offspring for exploitation and lets these two types of offspring compete for survival. Secondly, adversarial selection strategy employs a diversity-optimization-based selection and a crowding-based selection to select the offspring with both good diversity and good fitness. Diversity-optimization-based selection transforms the problem of selecting diverse individuals into an optimizing problem and solves it via an extra genetic algorithm to get the offspring with optimal diversity. Extensive experiments are conducted on CEC2013 MMOP benchmark to verify the effectiveness and efficiency of the proposed ADE. Experimental results show that ADE has advantages over the state-of-the-art MMOP algorithms.

Surrogate-assisted evolutionary algorithms (SAEAs) have performed well on low- and medium-scale expensive optimization problems (EOPs). However, with the dimensionality increasing, existing SAEAs have trouble getting reliable surrogates for solving large-scale EOPs. In this paper, we propose a progressive sampling surrogate-assisted particle swarm optimization (PS-SAPSO) to efficiently solve the large-scale EOPs from the perspective of data collection and model training. For the data collection, a progressive sampling strategy with restart operation is proposed to collect the new sample solutions during the evolution process for training the radial basis function network (RBFN) surrogate. Specifically, a social learning particle swarm optimization is employed to generate the new sample solutions under the control of a progressively varying stop criterion. For the model training, a dynamic tunning strategy is proposed to obtain a reliable RBFN by adaptively adjusting the hyperparameter setting during the evolution process. The experimental result shows that PS-SAPSO can achieve competitive or better performance compared with four state-of-the-art SAEAs on widely used benchmark functions. Moreover, ablation experiments are conducted to show the effectiveness of the components of the PS-SAPSO algorithm.

Data-driven evolutionary algorithms (DDEAs) have shown strong capacity in solving optimization problems with the help of surrogate models. However, current DDEAs often fall into the trap of inaccurate surrogates if no additional data can be obtained for the surrogates update during the optimization process. In addition, when dealing with multiobjective optimization problems, the surrogates in DDEAs will further suffer the difficulty of aggravating cumulative predicted fitness error. To overcome these difficulties, we propose a two-surrogate collaboration (TSC) management method, in which a Kriging surrogate and a radial basis function network (RBFN) surrogate are adopted to approximate the real fitness evaluation for the parent solutions and the newly generated offspring solutions, respectively. This TSC management method can effectively reduce the prediction uncertainty and improve the prediction performance of each surrogate without any other surrogate update process. During the optimization process, we use a modified social learning particle swarm optimization (SLPSO) as the basic search method and propose an offline DDEA. With the help of TSC, our resulting SLPSO-TSC algorithm can search for potential optimal solutions quickly and effectively without the help of any real fitness evaluation during the optimization process. The performance of the proposed SLPSO-TSC algorithm is verified on eleven widely used benchmark problems and compared with five different offline DDEAs. The experimental results show the high competitiveness of our proposed SLPSO-TSC for offline data-driven multiobjective optimization.

Scientific articles contain rich knowledge that can significantly assists scientific research, but it is difficult to precisely extract knowledge information due to the complexity of the discourse structure of scientific articles. To provide more accurate scientific research knowledge for researchers in a specific academic domain, it is necessary to study the discourse structure of domain scientific articles and to propose an automatic annotation approach to automatically annotate discourse information from articles. Unfortunately, few works have studied the discourse structure of domain scientific articles and the corresponding automatic discourse annotation. To fill this gap, we take scientific articles of the wastewater-based epidemiology domain as a case to study how to automatically and efficiently annotate discourse information. This paper has three contributions. Firstly, we propose a hierarchical discourse model with two layers to cover all potential discourses in various domain scientific articles. Specifically, the first layer defines four core discourse concepts to describe the main process of a scientific research which can be applied in all scientific articles in various domains. The second layer defines fine-granular domain-specific structure, which can accurately describe the entire research contents of a specific domain. Secondly, based on the proposed model, we build a corpus dataset of 100 annotated scientific articles in the wastewater-based epidemiology domain. Thirdly, based on the model and dataset, we propose a simple yet efficient Top-K resampling-based approach to train a more effective classifier for automatic annotation. Extensive experiments verify the effectiveness and efficiency of our proposed hierarchical discourse model and the Top-K resampling-based classification approach.

Artificial intelligence (AI) has fast developed nowadays especially in the deep learning field that most of the deep neural networks pursue the better problem-solving ability by making the network models deeper, larger, and more complex. However, too large and too complex AI algorithms/models require too large computational burden, which is not reality in academic researches nor the right way to real human intelligence. Moreover, in another research branch of AI named evolutionary computation (EC), which is inspired by the biological evolution of nature and swarm intelligence behaviours, will the EC algorithms become more efficient with larger and more complex algorithm model when solving complicated optimization problems like the large-scale optimization problems (LSOPs)? To this concern, this paper investigates whether some existing large-scale optimization EC algorithms can further improve their performance in solving LSOPs by only increasing the population size. We select 12 representative algorithms for investigation, including 4 standard EC algorithms and 8 well-known large-scale optimization algorithms. Then, we adopt the widely-used IEEE Congress on Evolutionary Computation (CEC 2010) LSOPs benchmark test suite to compare the performance of the same algorithms with different population sizes. The experimental results show that simply increasing the population size does not necessarily improve the performance of algorithms in solving LSOPs.

It is known that many-objective optimization problems (MaOPs) often face the difficulty of maintaining good diversity and convergence in the search process due to the high-dimensional objective space. To address this issue, this article proposes a novel multiobjective framework for many-objective optimization (Mo4Ma), which transforms the many-objective space into multiobjective space. First, the many objectives are transformed into two indicative objectives of convergence and diversity. Second, a clustering-based sequential selection strategy is put forward in the transformed multiobjective space to guide the evolutionary search process. Specifically, the selection is circularly performed on the clustered subpopulations to maintain population diversity. In each round of selection, solutions with good performance in the transformed multiobjective space will be chosen to improve the overall convergence. The Mo4Ma is a generic framework that any type of evolutionary computation algorithm can incorporate compatibly. In this article, the differential evolution (DE) is adopted as the optimizer in the Mo4Ma framework, thus resulting in an Mo4Ma-DE algorithm. Experimental results show that the Mo4Ma-DE algorithm can obtain well-converged and widely distributed Pareto solutions along with the many-objective Pareto sets of the original MaOPs. Compared with seven state-of-the-art MaOP algorithms, the proposed Mo4Ma-DE algorithm shows strong competitiveness and general better performance.

Knowledge transfer plays a vastly important role in solving multitask optimization problems (MTOPs). Many existing methods transfer task-specific knowledge, such as the high-quality solution from one task to other tasks to enhance the optimization ability, which, however, may not work well or even have a negative effect if the tasks have very different task-specific knowledge. Hence, this article proposes a meta-knowledge transfer (MKT)-based differential evolution (MKTDE) algorithm by using a more general MKT method to solve MTOPs more efficiently. The meta-knowledge defined in this article refers to the knowledge that can evolve task-specific knowledge during the evolutionary search. That is, the meta-knowledge is a kind of “knowledge of knowledge,” which denotes the knowledge of “how to solve problem via evolution” and “the feature/way/method of evolving high-quality solution.” The evolutionary search for solving different tasks can share common meta-knowledge even though these tasks involve heterogeneous data and have very different task-specific knowledge. Therefore, the MKT can associate the heterogeneous multisource data of different tasks via transferring the meta-knowledge to help solve MTOPs more efficiently in a more general way. Moreover, to further enhance the MKTDE, two novel and efficient methods are proposed. One is multiple populations for the multiple tasks framework using a unified search space for making knowledge transfer flexibly. The other is an elite solution transfer method for achieving positive high-quality solution transfer. The superior performance of the proposed MKTDE is verified via extensive numerical experiments on both widely used MTOP benchmark problems and real-world robot navigation problems, with comparisons with some state-of-the-art and the latest well-performing algorithms.

Supply chain management (SCM) is a significant and complex system in a smart city that requires advanced artificial intelligence (AI) and optimization techniques. The multiobjective supply chain configuration (MOSCC) in SCM is to set the optimal configurations for supply chain members to minimize both the cost of goods sold ($CoGS$) and the lead time ($LT$). Although some algorithms have been proposed for the MOSCC, they do not make the best use of the problem-related knowledge and cannot perform well on the large-scale instances with many members and configuration options. Therefore, this article proposes a multipopulation ant colony system with knowledge-based local searches (MPACS-KLSs). First, the multiobjective algorithm is based on the multiple populations for multiple objectives framework. Two ant colonies are used to separately minimize$CoGS$and$LT$, which helps to search in the biobjective space sufficiently. Second, with the considerations of the problem-related knowledge, a priority-based solution construction method, a rank-based heuristic strategy, and an objective-oriented global pheromone updating strategy are proposed. Third, to speed up the convergence, especially for large-scale MOSCC instances, two knowledge-based local searches are designed to minimize$CoGS$and$LT$of solutions, respectively. Exhaustive experiments are conducted on both the instances from the real life and the randomly generated instances with different problem scales. The results show that MPACS-KLS is superior to the contestant algorithms, especially on the large-scale MOSCC instances, which significantly extends the AI and optimization techniques in practical applications of the smart city.

As transportation system plays a vastly important role in combatting newly-emerging and severe epidemics like the coronavirus disease 2019 (COVID-19), the vehicle routing problem (VRP) in epidemics has become an emerging topic that has attracted increasing attention worldwide. However, most existing VRP models are not suitable for epidemic situations, because they do not consider the prevention cost caused by issues such as viral tests and quarantine during the traveling. Therefore, this paper proposes a multi-objective VRP model for epidemic situations, named VRP4E, which considers not only the traditional travel cost but also the prevention cost of the VRP in epidemic situations. To efficiently solve the VRP4E, this paper further proposes a novel algorithm named multi-objective ant colony system algorithm for epidemic situations, termed MOACS4E, together with three novel designs. First, by extending the efficient “multiple populations for multiple objectives” framework, the MOACS4E adopts two ant colonies to optimize the travel and prevention costs respectively, so as to improve the search efficiency. Second, a pheromone fusion-based solution generation method is proposed to fuse the pheromones from different colonies to increase solution diversity effectively. Third, a solution quality improvement method is further proposed to improve the solutions for the prevention cost objective. The effectiveness of the MOACS4E is verified in experiments on 25 generated benchmarks by comparison with six state-of-the-art and modern algorithms. Moreover, the VRP4E in different epidemic situations and a real-world case in the Beijing-Tianjin-Hebei region, China, are further studied to provide helpful insights for combatting COVID-19-like epidemics.

The developments of electric vehicle (EV) technology and mobile internet technology have made the EV-oriented ride-hailing service a trend in smart cities. In the service scenario, a high-quality order allocation approach is in great need to quickly process a series of customer request orders, so as to reduce total customer waiting time and transportation cost. To simulate real-world customer-EV allocation scenarios, in this paper, a dynamic EV dispatch (DEVD) model is established by considering multi-source data association from five sources, including customer, vehicle, charging, station, and service. To solve the proposed multi-source data associated DEVD model, a memory-based ant colony optimization (MACO) approach is developed. MACO maintains a memory archive to store the historically good solutions, which not only can be used to update pheromone to guide the search, but also can be used to help the reactions to environmental changes. In response to dynamic changes, a partial reassignment strategy is also proposed to re-optimize some of the assigned customer-EV pairs in the historically best solution. Moreover, an exchange or replace local search procedure is designed to enhance the performance. The MACO algorithm is applied to a set of dynamic test cases with different customer request and EV sizes. Experimental results show that MACO generally outperforms the first-come-first-served approach and some state-of-the-art ACO-based dynamic optimization algorithms.

The berth allocation problem (BAP) is an NP-hard problem in maritime traffic scheduling that significantly influences the operational efficiency of the container terminal. This paper formulates the BAP as a permutation-based combinatorial optimization problem and proposes an improved ant colony system (ACS) algorithm to solve it. The proposed ACS has three main contributions. First, an adaptive heuristic information (AHI) mechanism is proposed to help ACS handle the discrete and real-time difficulties of BAP. Second, to relieve the computational burden, a divide-and-conquer strategy based on variable-range receding horizon control (vRHC) is designed to divide the complete BAP into a set of sub-BAPs. Third, a partial solution memory (PSM) mechanism is proposed to accelerate the ACS convergence process in each receding horizon (i.e., each sub-BAP). The proposed algorithm is termed as adaptive ACS (AACS) with vRHC strategy and PSM mechanism. The performance of the AACS is comprehensively tested on a set of test cases with different scales. Experimental results show that the effectiveness and robustness of AACS are generally better than the compared state-of-the-art algorithms, including the well-performing adaptive evolutionary algorithm and ant colony optimization algorithm. Moreover, comprehensive investigations are conducted to evaluate the influences of the AHI mechanism, the vRHC strategy, and the PSM mechanism on the performance of the AACS algorithm.

Cold chain logistics (CCL) scheduling is important for smart cities as it directly affects the service quality and operating profits of logistics companies. However, traditional CCL models seldom reflect the real transportation environment, making the solutions hardly applicable to the real CCL scenes. Hence, this paper attempts to establish a multisource data-associated CCL model oriented to the real transportation environment. This environment is considered by employing the real-captured driving duration and distance between any two places. Three scheduling objectives (namely, quality losses, personnel and vehicle costs, and transportation costs) are taken into account. To efficiently solve the proposed multisource data-associated multiobjective CCL model, a multiple population-based multiobjective ant colony system (MPMOACS) approach is proposed. Based on the multiple populations for multiple objectives framework, the MPMOACS approach can optimize multiple objectives sufficiently, and thus obtain promising solutions distributed along the entire Pareto front. To further enhance the performance of the MPMOACS, a ranking-based local search strategy is also designed. Experiments are conducted on not only the existing benchmark instances but also a real environment-aware multisource dataset that is built based on real-captured transportation data of Guangzhou and Shenzhen, China. Compared with six state-of-the-art and very recent well-performing multiobjective optimization approaches, the proposed MPMOACS approach exhibits the overall best performance.

The neural-network (NN)-based control method is a new emerging promising technique for controller design in a power electronic circuit (PEC). However, the optimization of NN-based controllers (NNCs) has significant challenges in two aspects. The first challenge is that the search space of the NNC optimization problem is such complex that the global optimization ability of the existing algorithms still needs to be improved. The second challenge is that the training process of the NNC parameters is very computationally expensive and requires a long execution time. Thus, in this article, we develop a powerful evolutionary computation-based algorithm to find a high-quality solution and reduce computational time. First, the differential evolution (DE) algorithm is adopted because it is a powerful global optimizer in solving a complex optimization problem. This can help to overcome the premature convergence in local optima to train the NNC parameters well. Second, to reduce the computational time, the DE is extended to distribute DE (DDE) by dispatching all the individuals to different distributed computing resources for parallel computing. Moreover, a resource-aware strategy (RAS) is designed to further efficiently utilize the resources by adaptively dispatching individuals to resources according to the real-time performance of the resources, which can simultaneously concern the computing ability and load state of each resource. Experimental results show that, compared with some other typical evolutionary algorithms, the proposed algorithm can get significantly better solutions within a shorter computational time.

Scientific cloud workflows enable the access to distributed computing resources in cloud environments for executing scientific computing applications. In the literature, most workflow scheduling models assume that each workflow task is mapped to only one service instance. But in computation and data-intensive applications, it is common that the computation resources provided by a single service instance are insufficient for some complicated tasks which contain several closely correlated sub-tasks. To manage such complicated workflows, this article devises a novel workflow model with composite tasks (cWFS). The model views a complicated task as a composite task and allows mapping multiple service instances to a composite task. The data transmission among sub-tasks of a composite task can also be addressed by the proposed model. To solve cWFS problem, we devise a nested particle swarm optimization (N-PSO) that utilizes two kinds of populations, i.e., the outer population and inner population. Since N-PSO is a bit time-consuming, we further devise a Fast version of N-PSO (FN-PSO), which can save more than 60 percent of running time compared with N-PSO. The proposed approaches are evaluated on five real-world workflow types. The experimental results verify that the proposed approaches can solve the new workflow model effectively.

Traffic signal timing optimization (TSTO) has aroused extensive attention, which aims to optimize the signal timing to improve the service capability of intersections. In recent years, particle swarm optimization (PSO) has played a vital role in optimization field. However, the PSO may get stuck in the local optimum when handling TSTO. In this paper, we propose a multi-exemplar learning PSO (MEL-PSO) algorithm, which enhances the exploration capability of the algorithm by letting particles have more opportunities to learn from more exemplars. Moreover, a knowledge embedded solution generating (KESG) strategy is proposed by exploiting the characteristic of input traffic volume distribution as pre-knowledge, which helps MEL-PSO generate an initial population covering promising search space. Furthermore, in order to make MEL-PSO suitable for different kinds of saturation situations of the intersection, we adopt multiple indicators to measure the performance of the signal timing scheme. Comparison experiments for validating the performance of MEL-PSO are carried out on a single intersection in both undersaturated and oversaturated traffic flow conditions. Experimental results show that MEL-PSO outperforms the classic numerical timing method, random timing method, and some other PSO-based algorithms.

Dynamic optimization problems (DOP) widely exist in many application fields and remain a challenge. The multi-population evolutionary computation approach is an efficient framework for solving the DOPs. The key issue of the multi-population approach is how to efficiently generate subpopulations in new environment by well reusing historical information in past environments. However, most existing works try to divide the population into small ones merely considering the individuals' distribution, which may have the limitation that the partition leads to the unbalanced computational resources allocation among subpopulations. To address this limitation, we propose a historical information-based differential evolution (HIDE) to effectively solve the DOP. Firstly, a region-based subpopulation initialization (RSI) strategy is proposed to generate multiple subpopulations in the new environment in a balanced way. By initializing multiple subpopulations in different regions of the search space, the diversity of the population is enhanced, which is helpful to solve the DOP with multiple peaks. Secondly, to fully make use of the found peaks of the previous environments, an archive-based historical information reuse (AHIR) strategy is put forward to manage and reuse the historical information to guide the search in the new environment. Experiments have been carried out on the moving peaks benchmark (MPB), which is a commonly used DOP test suite. Experimental results show that the proposed HIDE algorithm generally outperforms the classic DE algorithms with different parameter settings and some existing competitive state-of-the-art DOP approaches.

Traffic congestion has become one of the major problems of smart travel. The application of evolutionary computation (EC) for traffic signal timing optimization (TSTO) can effectively alleviate traffic congestion at a single intersection. However, while in more complicated regional traffic signal timing optimization (RTSTO) problems, the canonical EC algorithm such as particle swarm optimization (PSO) still has limitation due to population prematurity. In this paper, a multi-exemplar learning (MEL) strategy is adopted to improve the diversity of the population, so that the particles can have more opportunities to explore the search space. Furthermore, multiple traffic indicators are used in this paper to measure the comprehensive performance of the solution. Moreover, the microsimulation software is adopted to evaluate the solution to simulate the real-world intersection, making the obtained solution more practical in real-world application. Experiments are conducted to investigate the effectiveness and efficiency of MEL-PSO. The results show that the MEL-PSO algorithm is more effective and efficient than the compared algorithms on RTSTO problems.

Logistics scheduling is an important issue in nowadays smart city construction because the scheduling results can determine the efficiency of logistics distribution, and thus influence the development of logistics companies. Although many remarkable works attempted to solve the logistics scheduling problems, especially the logistics-related vehicle routing problem (VRP), most of them established the models based on Euclidean distance, which may result in suboptimal solutions due to the ignorance of road layout. That is, the optimal solution of the model may be suboptimal or even impractical when applied to the real-world situation because of the difference between the model and the real situation. To deal with this weakness, a VRP-based real traffic distance-aware logistics scheduling model that considers the road layout is established in this paper, where the real traffic distance is used as the input of the model. With the assistance of Baidu Map API, the real traffic distance between any two locations and the real traffic duration between them can be captured. In this way, a problem instance set with three scales (i.e., with 20, 30, and 40 locations) is built up for experiments. Besides, the ant colony system (ACS) is employed to solve the problem instances under the cases of using Euclidean distance, linear distance, and real traffic distance to measure the solutions. Comparison results from perspectives of both real traffic distance and real traffic duration show the better performance of solutions obtained under the case of real traffic distance.

Convolution neural network (CNN) is a kind of powerful and efficient deep learning approach that has obtained great success in many real-world applications. However, due to its complex network structure, the intertwining of hyperparameters, and the time-consuming procedure for network training, finding an efficient network configuration for CNN is a challenging yet tough work. To efficiently solve the hyperparameters setting problem, this paper proposes a distributed particle swarm optimization (DPSO) approach, which can optimize the hyperparameters to find high-performing CNNs. Compared to tedious, historical-experience-based, and personal-preference-based manual designs, the proposed DPSO approach can evolve the hyperparameters automatically and globally to obtain promising CNNs, which provides a new idea and approach for finding the global optimal hyperparameter combination. Moreover, by cooperating with the distributed computing techniques, the DPSO approach can have a considerable speedup when compared with the traditional particle swarm optimization (PSO) algorithm. Extensive experiments on widely-used image classification benchmarks have verified that the proposed DPSO approach can effectively find the CNN model with promising performance, and at the same time, has greatly reduced the computational time when compared with traditional PSO.

Sensor activity scheduling is critical for prolonging the lifetime of wireless sensor networks (WSNs). However, most existing methods assume sensors to have one fixed sensing range. Prevalence of sensors with adjustable sensing ranges posts two new challenges to the topic: 1) expanded search space, due to the rise in the number of possible activation modes and 2) more complex energy allocation, as the sensors differ in the energy consumption rate when using different sensing ranges. These two challenges make it hard to directly solve the lifetime maximization problem of WSNs with range-adjustable sensors (LM-RASs). This article proposes a neighborhood-based estimation of distribution algorithm (NEDA) to address it in a recursive manner. In NEDA, each individual represents a coverage scheme in which the sensors are selectively activated to monitor all the targets. A linear programming (LP) model is built to assign activation time to the schemes in the population so that their sum, the network lifetime, can be maximized conditioned on the current population. Using the activation time derived from LP as individual fitness, the NEDA is driven to seek coverage schemes promising for prolonging the network lifetime. The network lifetime is thus optimized by repeating the steps of the coverage scheme evolution and LP model solving. To encourage the search for diverse coverage schemes, a neighborhood sampling strategy is introduced. Besides, a heuristic repair strategy is designed to fine-tune the existing schemes for further improving the search efficiency. Experimental results on WSNs of different scales show that NEDA outperforms state-of-the-art approaches. It is also expected that NEDA can serve as a potential framework for solving other flexible LP problems that share the same structure with LM-RAS.

Data privacy and utility are two essential requirements in outsourced data storage. Traditional techniques for sensitive data protection, such as data encryption, affect the efficiency of data query and evaluation. By splitting attributes of sensitive associations, database fragmentation techniques can help protect data privacy and improve data utility. In this article, a distributed memetic algorithm (DMA) is proposed for enhancing database privacy and utility. A balanced best random distributed framework is designed to achieve high optimization efficiency. In order to enhance global search, a dynamic grouping recombination operator is proposed to aggregate and utilize evolutionary elements; two mutation operators, namely, merge and split, are designed to help arrange and create evolutionary elements; a two-dimension selection approach is designed based on the priority of privacy and utility. Furthermore, a splicing-driven local search strategy is embedded to introduce rare utility elements without violating constraints. Extensive experiments are carried out to verify the performance of the proposed DMA. Furthermore, the effectiveness of the proposed distributed framework and novel operators is verified.

Due to the population-based and iterative-based characteristics of evolutionary computation (EC) algorithms, parallel techniques have been widely used to speed up the EC algorithms. However, the parallelism usually performs in the population level where multiple populations (or subpopulations) run in parallel or in the individual level where the individuals are distributed to multiple resources. That is, different populations or different individuals can be executed simultaneously to reduce running time. However, the research into generation-level parallelism for EC algorithms has seldom been reported. In this article, we propose a new paradigm of the parallel EC algorithm by making the first attempt to parallelize the algorithm in the generation level. This idea is inspired by the industrial pipeline technique. Specifically, a kind of EC algorithm called local version particle swarm optimization (PSO) is adopted to implement a pipeline-based parallel PSO (PPPSO, i.e., P3SO). Due to the generation-level parallelism in P3SO, when some particles still perform their evolutionary operations in the current generation, some other particles can simultaneously go to the next generation to carry out the new evolutionary operations, or even go to further next generation(s). The experimental results show that the problem-solving ability of P3SO is not affected while the evolutionary speed has been substantially accelerated in a significant fashion. Therefore, generation-level parallelism is possible in EC algorithms and may have significant potential applications in time-consumption optimization problems.

Data-driven evolutionary algorithms (DDEAs) aim to utilize data and surrogates to drive optimization, which is useful and efficient when the objective function of the optimization problem is expensive or difficult to access. However, the performance of DDEAs relies on their surrogate quality and often deteriorates if the amount of available data decreases. To solve these problems, this article proposes a new DDEA framework with perturbation-based ensemble surrogates (DDEA-PES), which contain two efficient mechanisms. The first is a diverse surrogate generation method that can generate diverse surrogates through performing data perturbations on the available data. The second is a selective ensemble method that selects some of the prebuilt surrogates to form a final ensemble surrogate model. By combining these two mechanisms, the proposed DDEA-PES framework has three advantages, including larger data quantity, better data utilization, and higher surrogate accuracy. To validate the effectiveness of the proposed framework, this article provides both theoretical and experimental analyses. For the experimental comparisons, a specific DDEA-PES algorithm is developed as an instance by adopting a genetic algorithm as the optimizer and radial basis function neural networks as the base models. The experimental results on widely used benchmarks and an aerodynamic airfoil design real-world optimization problem show that the proposed DDEA-PES algorithm outperforms some state-of-the-art DDEAs. Moreover, when compared with traditional nondata-driven methods, the proposed DDEA-PES algorithm only requires about 2% computational budgets to produce competitive results.

Large-scale optimization has become a significant and challenging research topic in the evolutionary computation (EC) community. Although many improved EC algorithms have been proposed for large-scale optimization, the slow convergence in the huge search space and the trap into local optima among massive suboptima are still the challenges. Targeted to these two issues, this article proposes an adaptive granularity learning distributed particle swarm optimization (AGLDPSO) with the help of machine-learning techniques, including clustering analysis based on locality-sensitive hashing (LSH) and adaptive granularity control based on logistic regression (LR). In AGLDPSO, a master-slave multisubpopulation distributed model is adopted, where the entire population is divided into multiple subpopulations, and these subpopulations are co-evolved. Compared with other large-scale optimization algorithms with single population evolution or centralized mechanism, the multisubpopulation distributed co-evolution mechanism will fully exchange the evolutionary information among different subpopulations to further enhance the population diversity. Furthermore, we propose an adaptive granularity learning strategy (AGLS) based on LSH and LR. The AGLS is helpful to determine an appropriate subpopulation size to control the learning granularity of the distributed subpopulations in different evolutionary states to balance the exploration ability for escaping from massive suboptima and the exploitation ability for converging in the huge search space. The experimental results show that AGLDPSO performs better than or at least comparable with some other state-of-the-art large-scale optimization algorithms, even the winner of the competition on large-scale optimization, on all the 35 benchmark functions from both IEEE Congress on Evolutionary Computation (IEEE CEC2010) and IEEE CEC2013 large-scale optimization test suites.

In the last decade, many evolutionary computation (EC) algorithms with diversity enhancement have been proposed to solve large-scale optimization problems in big data era. Among them, the social learning particle swarm optimization (SLPSO) has shown good performance. However, as SLPSO uses different guidance information for different particles to maintain the diversity, it often results in slow convergence speed. Therefore, this article proposes a new region encoding scheme (RES) to extend the solution representation from a single point to a region, which can help EC algorithms evolve faster. The RES is generic for EC algorithms and is applied to SLPSO. Based on RES, a novel adaptive region search (ARS) is designed to on the one hand keep the diversity of SLPSO and on the other hand accelerate the convergence speed, forming the SLPSO with ARS (SLPSO-ARS). In SLPSO-ARS, each particle is encoded as a region so that some of the best (e.g., the top P) particles can carry out region search to search for better solutions near their current positions. The ARS strategy offers the particle a greater chance to discover the nearby optimal solutions and helps to accelerate the convergence speed of the whole population. Moreover, the region radius is adaptively controlled based on the search information. Comprehensive experiments on all the problems in both IEEE Congress on Evolutionary Computation 2010 (CEC 2010) and 2013 (CEC 2013) competitions are conducted to validate the effectiveness and efficiency of SLPSO-ARS and to investigate its important parameters and components. The experimental results show that SLPSO-ARS can achieve generally better performance than the compared algorithms.

The key challenge of expensive optimization problems (EOP) is that evaluating the true fitness value of the solution is computationally expensive. A common method to deal with this issue is to seek for a less expensive surrogate model to replace the original expensive objective function. However, this method also brings in model approximation error. To efficiently solve the EOP, a novel scale-adaptive fitness evaluation (SAFE) method is proposed in this article to directly evaluate the true fitness value of the solution on the original objective function. To reduce the computational cost, the SAFE method uses a set of evaluation methods (EM) with different accuracy scales to cooperatively complete the fitness evaluation process. The basic idea is to adopt the low-accuracy scale EM to fast locate promising regions and utilize the high-accuracy scale EM to refine the solution accuracy. To this aim, two EM switch strategies are proposed in the SAFE method to adaptively control the multiple EMs according to different evolutionary stages and search requirements. Moreover, a neighbor best-based evaluation (NBE) strategy is also put forward to evaluate the solution according to its nearest high-quality evaluated solution, which can further reduce computational cost. Extensive experiments are carried out on the case study of crowdshipping scheduling problem in the smart city to verify the effectiveness and efficiency of the proposed SAFE method, and to investigate the effects of the two EM switch strategies and the NBE strategy. Experimental results show that the proposed SAFE method achieves better solution quality than some baseline and state-of-the-art algorithms, indicating an efficient method for solving EOP with a better balance between solution accuracy and computational cost.

The airline crew rostering problem (CRP) is significant for balancing the workload of crew and for improving the satisfaction rate of crew’s preferences, which is related to the fairness and satisfaction of crew. However, most existing work considers only one objective on fairness or satisfaction. In this study, we propose a new practical model for CRP that takes both fairness and satisfaction into account simultaneously. To solve the multi-objective CRP efficiently, we develop an ant colony system (ACS) algorithm based on the multiple populations for multiple objectives (MPMO) framework, termed multi-objective ACS (MOACS). The main contributions of MOACS lie in three aspects. Firstly, two ant colonies are utilized to optimize fairness and satisfaction objectives, respectively. Secondly, a new hybrid complementary heuristic strategy with three kinds of heuristic information schemes is proposed to avoid ant colonies focusing only on their own objectives. Ant colonies randomly choose one of the three schemes to help explore the Pareto front (PF) sufficiently. Thirdly, a local search strategy with two types of local search respectively for fairness and satisfaction is designed to further approach the global PF. The MOACS is applied to seven real-world monthly CRPs with different sizes from a major North-American airline. Experimental results show that MOACS generally outperforms the greedy algorithm and some other popular multi-objective optimization algorithms, especially on large-scale instances.

In the greedy selection operator of differential evolution (DE), the trial solution will be selected into the new population only if it is better than the original target solution. Otherwise, the generated solution is simply eliminated. However, in most cases, these eliminated solutions may still be promising, and it will waste the computing resources to directly ignore them. Especially for the large-scale global optimization (LSGO) problems, it is important to make full use of all generated solutions and to enhance the population diversity in the limited fitness evaluation budget. To address this issue, an adaptive population DE, termed as APDE, is proposed with dual control strategy. Firstly, a population increasing (pop-inc) strategy is proposed for giving the opportunity to the generated trial solutions to survive in the population even though they are not good enough. Secondly, to avoid the gradual expansion of the population due to the pop-inc strategy, a population decreasing (pop-dec) strategy is proposed based on the “degradation value” designed for solutions. In the end of every iteration, if the degradation value of a solution is large, it represents the solution has a worse fitness value or has no improvement for a long time, and this solution will be deleted. In this way, the population size can be kept within a certain range. The test functions in CEC'2013 on LSGO are used to verify the performance of APDE. The experiment shows that APDE generally outperforms the original DE and two state-of-the-art LSGO algorithms.

Multimodal optimization problems (MMOPs) target to locate multiple global optima simultaneously, which require the algorithms not only can maintain the population diversity to locate the global optima as many as possible, but also can ensure the convergence on each found optimal region to refine the solutions as high accuracy as possible. Aiming to these two goals and to efficiently deal with MMOPs, an adaptive guidance-based differential evolution (AGDE) with archive strategy is proposed in this paper, including three novel components. Firstly, an adaptive mutation strategy (AMS) is introduced, which guides the current individual to move towards the peak that is closest to itself. Secondly, an iterative feedback archive (IFA) strategy is used to store the global optima of the population in every iteration. Thirdly, a Gaussian disturbance-based elite learning (GDEL) strategy is performed on the archive to refine the accuracy of the solutions. The AMS strategy helps to locate more peaks, while the IFA and GDEL strategies help to maintain the found solutions and refine their accuracy. The performance of AGDE is tested on 20 widely used multimodal benchmark functions of CEC'2013. The experimental results of AGDE are competitive with the results obtained by the state-of-the-art multimodal algorithms.

Genetic algorithm (GA) is a widely used probabilistic search optimization algorithm. In the GA, selection is an important operator to guarantee the quality of solution. Therefore, the behavior of selection operator makes a great effect on the performance of the algorithm. This paper designs a new and efficient selection operator for GA base on the idea of promotion competition. This operator simulates the rule and process of promotion competition to protect the well perform chromosomes and eliminates poor chromosomes. This is a fundamental but significant research issue in GA that may be adopted into any existing GA variants to replace any other selection operators. We design four types of experiments to comprehensively verify the behavior of the proposed promotion selection operator, by comparing it with five other existing and commonly used selection operators. The results show that promotion selection operator has a general good performance in enhancing GA in terms of solution quality, convergence speed, and running time.

Multimodal optimization problems (MMOPs) require the algorithm to locate multiple global optima and also achieve a certain accuracy on the found optima. When applying particle swarm optimization (PSO) to solve MMOPs, a fixed population communication topology may not be sufficient to handle these two requirements simultaneously. In this paper, a novel PSO with hybrid ring topology, termed HRTPSO, is proposed for MMOPs. In the early evolutionary process of HRTPSO, a sparse topology is constructed to enhance the population diversity to help locate multiple optima, while in the later evolutionary process of HRTPSO, the population communication topology is switched to a relatively dense topology for improving the convergence efficiency on the found optima. The switch of topology is controlled by a threshold and its effect is also analyzed in this paper. Experimental results on the 20 multimodal functions in CEC'2013 benchmark set show that HRTPSO has better performance than the other six multimodal optimization algorithms.

With the rapid development of Industry 5.0 and mobile devices, the research of mobile crowdsensing networks has become an important research focus. Task allocation is an important research content that can inspire crowd workers to participate in crowd tasks and provide truthful sensed data in mobile crowdsourcing systems. However, how to inspire crowd workers to participate in crowd tasks and provide truthful sensed data still has many challenges. In this article, based on the Markov model and collaborative filtering model, the similarities, trajectory prediction, dwell time, and trust degree are considered to propose the Markov and Collaborative filtering-based Task Recommendation (MCTR) model. Then, based on the Walrasian equilibrium, the optimum solution is researched to maximize the social welfare of mobile crowdsourcing systems. Finally, the comparison experiments are carried out to evaluate the performance of the proposed multiobjective optimization and the Markov-based task allocation with other methods. Through comparison experiments, the efficiency and adaptation of mobile crowdsourcing systems could be improved by the proposed task allocation.

Cloud workflow scheduling is a significant topic in both commercial and industrial applications. However, the growing scale of workflow has made such a scheduling problem increasingly challenging. Many current algorithms often deal with small- or medium-scale problems (e.g., less than 1000 tasks) and face difficulties in providing satisfactory solutions when dealing with the large-scale problems, due to the curse of dimensionality. To this aim, this article proposes a dynamic group learning distributed particle swarm optimization (DGLDPSO) for large-scale optimization and extends it for the large-scale cloud workflow scheduling. DGLDPSO is efficient for large-scale optimization due to its following two advantages. First, the entire population is divided into many groups, and these groups are coevolved by using the master-slave multigroup distributed model, forming a distributed PSO (DPSO) to enhance the algorithm diversity. Second, a dynamic group learning (DGL) strategy is adopted for DPSO to balance diversity and convergence. When applied DGLDPSO into the large-scale cloud workflow scheduling, an adaptive renumber strategy (ARS) is further developed to make solutions relate to the resource characteristic and to make the searching behavior meaningful rather than aimless. Experiments are conducted on the large-scale benchmark functions set and the large-scale cloud workflow scheduling instances to further investigate the performance of DGLDPSO. The comparison results show that DGLDPSO is better than or at least comparable to other state-of-the-art large-scale optimization algorithms and workflow scheduling algorithms.

There are two common challenges in particle swarm optimization (PSO) research, that is, selecting proper exemplars and designing an efficient learning model for a particle. In this article, we propose a triple archives PSO (TAPSO), in which particles in three archives are used to deal with the above two challenges. First, particles who have better fitness (i.e., elites) are recorded in one archive while other particles who offer faster progress, called profiteers in this article, are saved in another archive. Second, when breeding each dimension of a potential exemplar for a particle, we choose a pair of elite and profiteer from corresponding archives as two parents to generate the dimension value by ordinary genetic operators. Third, each particle carries out a specific learning model according to the fitness of its potential exemplars. Furthermore, there is no acceleration coefficient in TAPSO aiming to simplify the learning models. Finally, if an exemplar has excellent performance, it will be regarded as an outstanding exemplar and saved in the third archive, which can be reused by inferior particles aiming to enhance the exploitation and to save computing resources. The experimental results and comparisons between TAPSO and other eight PSOs on 30 benchmark functions and four real applications suggest that TAPSO attains very promising performance in different types of functions, contributing to both higher solution accuracy and faster convergence speed. Furthermore, the effectiveness and efficiency of these new proposed strategies are discussed based on extensive experiments.

Due to the increasing complexity of optimization problems, distributed differential evolution (DDE) has become a promising approach for global optimization. However, similar to the centralized algorithms, DDE also faces the difficulty of strategies' selection and parameters' setting. To deal with such problems effectively, this article proposes an adaptive DDE (ADDE) to relieve the sensitivity of strategies and parameters. In ADDE, three populations called exploration population, exploitation population, and balance population are co-evolved concurrently by using the master-slave multipopulation distributed framework. Different populations will adaptively choose their suitable mutation strategies based on the evolutionary state estimation to make full use of the feedback information from both individuals and the whole corresponding population. Besides, the historical successful experience and best solution improvement are collected and used to adaptively update the individual parameters (amplification factor F and crossover rate CR) and population parameter (population size N), respectively. The performance of ADDE is evaluated on all 30 widely used benchmark functions from the CEC 2014 test suite and all 22 widely used real-world application problems from the CEC 2011 test suite. The experimental results show that ADDE has great superiority compared with the other state-of-the-art DDE and adaptive differential evolution variants.

Supply chain network design (SCND) is a complicated constrained optimization problem that plays a significant role in the business management. This article extends the SCND model to a large-scale SCND with uncertainties (LUSCND), which is more practical but also more challenging. However, it is difficult for traditional approaches to obtain the feasible solutions in the large-scale search space within the limited time. This article proposes a cooperative coevolutionary bare-bones particle swarm optimization (CCBBPSO) with function independent decomposition (FID), called CCBBPSO-FID, for a multiperiod three-echelon LUSCND problem. For the large-scale issue, binary encoding of the original model is converted to integer encoding for dimensionality reduction, and a novel FID is designed to efficiently decompose the problem. For obtaining the feasible solutions, two repair methods are designed to repair the infeasible solutions that appear frequently in the LUSCND problem. A step translation method is proposed to deal with the variables out of bounds, and a labeled reposition operator with adaptive probabilities is designed to repair the infeasible solutions that violate the constraints. Experiments are conducted on 405 instances with three different scales. The results show that CCBBPSO-FID has an evident superiority over contestant algorithms.

The multimodal optimization problem (MMOP) requires the algorithm to find multiple global optima of the problem simultaneously. In order to solve MMOP efficiently, a novel differential evolution (DE) algorithm based on the local binary pattern (LBP) is proposed in this paper. The LBP makes use of the neighbors' information for extracting relevant pattern information, so as to identify the multiple regions of interests, which is similar to finding multiple peaks in MMOP. Inspired by the principle of LBP, this paper proposes an LBP-based adaptive DE (LBPADE) algorithm. It enables the LBP operator to form multiple niches, and further to locate multiple peak regions in MMOP. Moreover, based on the LBP niching information, we develop a niching and global interaction (NGI) mutation strategy and an adaptive parameter strategy (APS) to fully search the niching areas and maintain multiple peak regions. The proposed NGI mutation strategy incorporates information from both the niching and the global areas for effective exploration, while APS adjusts the parameters of each individual based on its own LBP information and guides the individual to the promising direction. The proposed LBPADE algorithm is evaluated on the extensive MMOPs test functions. The experimental results show that LBPADE outperforms or at least remains competitive with some state-of-the-art algorithms.

Locating more peaks and refining the solution accuracy on the found peaks are two challenging issues in solving multimodal optimization problems (MMOPs). To deal with these two challenges, a distributed individuals differential evolution (DIDE) algorithm is proposed in this article based on a distributed individuals for multiple peaks (DIMP) framework and two novel mechanisms. First, the DIMP framework provides sufficient diversity by letting each individual act as a distributed unit to track a peak. Based on the DIMP framework, each individual uses a virtual population controlled by an adaptive range adjustment strategy to explore the search space sufficiently for locating a peak and then gradually approach it. Second, the two novel mechanisms named lifetime mechanism and elite learning mechanism (ELM) cooperate with the DIMP framework. The lifetime mechanism is inspired by the natural phenomenon that every organism will gradually age and has a limited lifespan. When an individual runs out of its lifetime and also has good fitness, it is regarded as an elite solution and will be added to an archive. Then the individual restarts a new lifetime, so as to bring further diversity to locate more peaks. The ELM is proposed to refine the accuracy of those elite solutions in the archive, being efficient in dealing with the solution accuracy issue on the found peaks. The experimental results on 20 multimodal benchmark test functions show that the proposed DIDE algorithm has generally better or competitive performance compared with the state-of-the-art multimodal optimization algorithms.

By efficiently building and exploiting surrogates, data-driven evolutionary algorithms (DDEAs) can be very helpful in solving expensive and computationally intensive problems. However, they still often suffer from two difficulties. First, many existing methods for building a single ad hoc surrogate are suitable for some special problems but may not work well on some other problems. Second, the optimization accuracy of DDEAs deteriorates if available data are not enough for building accurate surrogates, which is common in expensive optimization problems. To this end, this article proposes a novel DDEA with two efficient components. First, a boosting strategy (BS) is proposed for self-aware model managements, which can iteratively build and combine surrogates to obtain suitable surrogate models for different problems. Second, a localized data generation (LDG) method is proposed to generate synthetic data to alleviate data shortage and increase data quantity, which is achieved by approximating fitness through data positions. By integrating the BS and the LDG, the BDDEA-LDG algorithm is able to improve model accuracy and data quantity at the same time automatically according to the problems at hand. Besides, a tradeoff is empirically considered to strike a better balance between the effectiveness of surrogates and the time cost for building them. The experimental results show that the proposed BDDEA-LDG algorithm can generally outperform both traditional methods without surrogates and other state-of-the-art DDEA son widely used benchmarks and an arterial traffic signal timing real-world optimization problem. Furthermore, the proposed BDDEA-LDG algorithm can use only about 2% computational budgets of traditional methods for producing competitive results.

Niching techniques have been widely incorporated into evolutionary algorithms (EAs) for solving multimodal optimization problems (MMOPs). However, most of the existing niching techniques are either sensitive to the niching parameters or require extra fitness evaluations (FEs) to maintain the niche detection accuracy. In this paper, we propose a new automatic niching technique based on the affinity propagation clustering (APC) and design a novel niching differential evolution (DE) algorithm, termed as automatic niching DE (ANDE), for solving MMOPs. In the proposed ANDE algorithm, APC acts as a parameter-free automatic niching method that does not need to predefine the number of clusters or the cluster size. Also, it can facilitate locating multiple peaks without extra FEs. Furthermore, the ANDE algorithm is enhanced by a contour prediction approach (CPA) and a two-level local search (TLLS) strategy. First, the CPA is a predictive search strategy. It exploits the individual distribution information in each niche to estimate the contour landscape, and then predicts the rough position of the potential peak to help accelerate the convergence speed. Second, the TLLS is a solution refine strategy to further increase the solution accuracy after the CPA roughly predicting the peaks. Compared with the other state-of-the-art DE and non-DE multimodal algorithms, even the winner of competition on multimodal optimization, the experimental results on 20 widely used benchmark functions illustrate the superiority of the proposed ANDE algorithm.

Automatic itinerary planning is a crucial and challenging issue in tourism. This paper proposes a novel automatic planning method to suggest multiple itineraries that satisfy the specific demands of tourists. First, a multiple-itinerary planning model is developed, which provides three customized goals for a tourist to choose and supports generating multiple D -day trips. The model makes fewer assumptions than the literature works did, while it provides more flexibility to the tourists. Then, based on the multiple-itinerary planning model, we design a niching genetic evolution approach to accomplish the automatic itinerary planning task. The genetic evolution approach guarantees a high search efficiency, while the niching strategy facilitates maintaining the population diversity. Consequently, the resultant algorithm can finally provide a number of diverse and superior solutions. Experimental results on real-world datasets show that our proposed algorithm not only outperforms state-of-the-art methods in considering different user-specified goals, but it is also capable of generating a set of diverse itineraries for the tourist to select. Additional experiments further verify the scalability of the proposed algorithm in terms of the problem size and the optimization objective.

As a powerful measure to alleviate greenhouse gas emissions and global warming issue, new energy vehicle (NEV) has aroused extensive attention from the whole society in recent years. In the past few decades, many studies have been conducted on the dispatch of traditional fuel-driven vehicles. As a means of transportation, NEV has the characteristics of fuel-driven vehicles, but the dispatch is different because of its unique refueling manner. With the popularization of NEV, its unique dispatch research is imminent. This paper comprehensively considers electricity and charging piles during the NEV dispatch (NEVD) process. An NEVD framework containing a novel dispatch model is proposed, which elaborates the application service of NEV. To the best of our knowledge, this study is the first to combine NEVD with service system. Based on the formulated model, an efficient ant colony system (EACS) approach enhanced by pre-selection strategy and local pruning strategy is designed to dispatch NEVs to passengers. Experiments are carried out to investigate the applicable scenarios of ACS-based algorithms. The results verify that the proposed EACS algorithm is an effective and efficient approach to solve the NEVD problem.

In dynamic optimization problems (DOPs), as the environment changes through time, the optima also dynamically change. How to adapt to the dynamic environment and quickly find the optima in all environments is a challenging issue in solving DOPs. Usually, a new environment is strongly relevant to its previous environment. If we know how it changes from the previous environment to the new one, then we can transfer the information of the previous environment, e.g., past solutions, to get new promising information of the new environment, e.g., new high-quality solutions. Thus, in this paper, we propose a neural network (NN)-based information transfer method, named NNIT, to learn the transfer model of environment changes by NN and then use the learned model to reuse the past solutions. When the environment changes, NNIT first collects the solutions from both the previous environment and the new environment and then uses an NN to learn the transfer model from these solutions. After that, the NN is used to transfer the past solutions to new promising solutions for assisting the optimization in the new environment. The proposed NNIT can be incorporated into population-based evolutionary algorithms (EAs) to solve DOPs. Several typical state-of-the-art EAs for DOPs are selected for comprehensive study and evaluated using the widely used moving peaks benchmark. The experimental results show that the proposed NNIT is promising and can accelerate algorithm convergence.

The aircraft arrival scheduling (AAS) problem is an important issue in airport management that requires well-designed scheduling approaches to help improve the operating efficiency of airports. However, most of the existing approaches are based on a single runway while the multi-runway situation is more common and more complex in reality. In order to solve the multi-runway AAS (MRAAS) problem, this paper proposes a receding horizon control (RHC) based two-level ant colony system (ACS) approach. The RHC divides the problem with receding time windows. Therefore, the number of aircraft considered in each RHC stage is reduced, so that the ACS algorithm can endure less computational burden and search for good scheduling sufficiently. Moreover, in each RHC stage to schedule the aircraft, a two-level scheduling strategy is proposed to assist the ACS to deal with the multi-runway difficulty. During the first level scheduling, the ACS algorithm schedules aircraft based on a single runway. Then in the second level scheduling, we assign the aircraft to real multi-runways based on both the obtained sequence of the first level scheduling and the real occupancy condition of each runway. We have conducted experiments based on case study and compared the results with first come first serve (FCFS) approach, showing the feasibility as well as the higher performance of the proposed RHC-ACS-MRAAS approach.

In outsourcing data storage, privacy and utility are significant concerns. Techniques such as data encryption can protect the privacy of sensitive information but affect the efficiency of data usage accordingly. By splitting attributes of sensitive associations, database fragmentation can protect data privacy. In the meantime, data utility can be improved through grouping data of high affinity. In this paper, a benefit-driven genetic algorithm is proposed to achieve a better balance between privacy and utility for database fragmentation. To integrate useful fragmentation information in different solutions, a matching strategy is designed. Two benefit-driven operators for mutation and improvement are proposed to construct valuable fragments and rearrange elements. The experimental results show that the proposed benefit-driven genetic algorithm is competitive when compared with existing approaches in database fragmentation.

Mobile crowdsourcing is an emerging crowdsourcing paradigm, which generates large-scale sensing tasks and sensing data. One of the major issues in mobile crowdsourcing is how to maximize social welfare through selecting appropriate sensing tasks for crowd workers and selecting appropriate workers for sensing tasks such that it can improve the effectiveness and efficiency of mobile crowdsourcing. This paper proposes an incentive mechanism to maximize social welfare for mobile crowdsourcing and, respectively, investigates worker-centric task selection and platform-centric worker selection. This paper applies an optimization algorithm in task selection for mobile crowdsourcing systems. A discrete particle swarm optimization (DPSO) algorithm for worker-centric task selection is designed to maximize the utilities of workers. In addition, a platform-centric worker selection method, which integrates multiattribute auction and two-stage auction, is proposed to maximize the utility of the platform. The performance of the proposed incentive mechanism is evaluated through experiments. The experimental results show that the proposed incentive mechanism can improve the efficiency and truthfulness of mobile crowdsourcing effectively.

Cloud workflow scheduling is significantly challenging due to not only the large scale of workflow but also the elasticity and heterogeneity of cloud resources. Moreover, the pricing model of clouds makes the execution time and execution cost two critical issues in the scheduling. This paper models the cloud workflow scheduling as a multiobjective optimization problem that optimizes both execution time and execution cost. A novel multiobjective ant colony system based on a co-evolutionary multiple populations for multiple objectives framework is proposed, which adopts two colonies to deal with these two objectives, respectively. Moreover, the proposed approach incorporates with the following three novel designs to efficiently deal with the multiobjective challenges: 1) a new pheromone update rule based on a set of nondominated solutions from a global archive to guide each colony to search its optimization objective sufficiently; 2) a complementary heuristic strategy to avoid a colony only focusing on its corresponding single optimization objective, cooperating with the pheromone update rule to balance the search of both objectives; and 3) an elite study strategy to improve the solution quality of the global archive to help further approach the global Pareto front. Experimental simulations are conducted on five types of real-world scientific workflows and consider the properties of Amazon EC2 cloud platform. The experimental results show that the proposed algorithm performs better than both some state-of-the-art multiobjective optimization approaches and the constrained optimization approaches.

Parallel test assembly has long been an important yet challenging topic in educational assessment. Cognitive diagnosis models (CDMs) are a new class of assessment models and have drawn increasing attention for being able to measure examinees' ability in detail. However, few studies have been devoted to the parallel test assembly problem in CDMs (CDM-PTA). To fill the gap, this paper models CDM-PTA as a subset-based bi-objective combinatorial optimization problem. Given an item bank, it aims to find a required number of tests that achieve optimal but balanced diagnostic performance, while satisfying important practical requests in the aspects of test length, item type distribution, and overlapping proportion. A set-based multiobjective particle swarm optimizer based on decomposition (S-MOPSO/D) is proposed to solve the problem. To coordinate with the property of CDM-PTA, S-MOPSO/D utilizes an assignment-based representation scheme and a constructive learning strategy. Through this, promising solutions can be built efficiently based on useful assignment patterns learned from personal and collective search experience on neighboring scalar problems. A heuristic constraint handling strategy is also developed to further enhance the search efficiency. Experimental results in comparison with three representative approaches validate that the proposed algorithm is effective and efficient.

The application of multiobjective evolutionary algorithms to many-objective optimization problems often faces challenges in terms of diversity and convergence. On the one hand, with a limited population size, it is difficult for an algorithm to cover different parts of the whole Pareto front (PF) in a large objective space. The algorithm tends to concentrate only on limited areas. On the other hand, as the number of objectives increases, solutions easily have poor values on some objectives, which can be regarded as poor bottleneck objectives that restrict solutions' convergence to the PF. Thus, we propose a coevolutionary particle swarm optimization with a bottleneck objective learning (BOL) strategy for many-objective optimization. In the proposed algorithm, multiple swarms coevolve in distributed fashion to maintain diversity for approximating different parts of the whole PF, and a novel BOL strategy is developed to improve convergence on all objectives. In addition, we develop a solution reproduction procedure with both an elitist learning strategy (ELS) and a juncture learning strategy (JLS) to improve the quality of archived solutions. The ELS helps the algorithm to jump out of local PFs, and the JLS helps to reach out to the missing areas of the PF that are easily missed by the swarms. The performance of the proposed algorithm is evaluated using two widely used test suites with different numbers of objectives. Experimental results show that the proposed algorithm compares favorably with six other state-of-the-art algorithms on many-objective optimization.

As the mutation strategy and algorithmic parameters in differential evolution (DE) are sensitive to the problems being solved, a hot research topic is to adaptively control the strategy and parameters according to the requirements of the problem. In the literature, most adaptive DE use either historical experiences of the population or heuristic information of the individuals to promote adaptation. In this paper, we develop a novel variant of adaptive DE, utilizing both the historical experience and heuristic information for the adaptation. In this novel historical and heuristic DE (HHDE), each individual dynamically adjusts its mutation strategy and associated parameters not only by learning from previous successful experience of the whole population, but also according to heuristic information related with its own current state. These help the algorithm select a more suitable mutation strategy and determinate better parameters for each individual in different evolutionary stages. The performance of the proposed HHDE is extensively evaluated on 30 benchmark functions with different dimensions. Experimental results confirm the competitiveness of the proposed algorithm to a number of DE variants.

Differential evolution (DE) is a simple and efficient evolutionary algorithm for global optimization. In distributed differential evolution (DDE), the population is divided into several sub-populations and each sub-population evolves independently for enhancing algorithmic performance. Through sharing elite individuals between sub-populations, effective information is spread. However, the information exchanged through individuals is still too limited. To address this issue, a competition-based strategy is proposed in this paper to achieve comprehensive interaction between sub-populations. Two operators named opposition-invasion and cross-invasion are designed to realize the invasion from good performing sub-populations to bad performing subpopulations. By utilizing opposite invading sub-population, the search efficiency at promising regions is improved by opposition-invasion. In cross-invasion, information from both invading and invaded sub-populations is combined and population diversity is maintained. Moreover, the proposed algorithm is implemented in a parallel master-slave manner. Extensive experiments are conducted on 15 widely used large-scale benchmark functions. Experimental results demonstrate that the proposed competition-based DDE (DDE-CB) could achieve competitive or even better performance compared with several state-of-the-art DDE algorithms. The effect of proposed competition-based strategy cooperation with well-known DDE variants is also verified.

The arrival of the era of “big data” has witnessed an urgent need of finding a proper algorithm for large scale optimization. Hence, this paper proposes a competitive swarm optimizer with dynamic grouping (CSO-DG) for large scale optimization. In CSO-DG, particles are separated into many groups to search for different regions of the large landscape. Moreover, the size of the group (the number of particles in each group) changes dynamically to control the swarm competitive strength, so as to balance the convergence and diversity. We also investigate the influences of different group sizes on different problems, and then propose a size range for the dynamic change bounds. By using multiple groups, only the worst particle in each group will be updated by learning from the best particle in the same group and the mean position of the whole swarm. This is helpful to save fitness evaluations. This way, the algorithm is able to work well in high-dimensional optimization. The experimental results show that CSO-DG exhibits a competitive performance than other state-of-the-art algorithms on 20 benchmark functions (CEC`2010) for large scale optimization.

Nowadays, large-scale optimization problems are ubiquitous in many research fields. To deal with such problems efficiently, this paper proposes a distributed differential evolution with adaptive mergence and split (DDE-AMS) on subpopulations. The novel mergence and split operators are designed to make full use of limited population resource, which is important for large-scale optimization. They are adaptively performed based on the performance of the subpopulations. During the evolution, once a subpopulation finds a promising region, the current worst performing subpopulation will merge into it. If the merged subpopulation could not continuously provide competitive solutions, it will be split in half. In this way, the number of subpopulations is adaptively adjusted and better performing subpopulations obtain more individuals. Thus, population resource can be adaptively arranged for subpopulations during the evolution. Moreover, the proposed algorithm is implemented with a parallel master-slave manner. Extensive experiments are conducted on 20 widely used large-scale benchmark functions. Experimental results demonstrate that the proposed DDE-AMS could achieve competitive or even better performance compared with several state-of-the-art algorithms. The effects of DDE-AMS components, adaptive behavior, scalability, and parameter sensitivity are also studied. Finally, we investigate the speedup ratios of DDE-AMS with different computation resources.

Virtual machine placement (VMP) and energy efficiency are significant topics in cloud computing research. In this paper, evolutionary computing is applied to VMP to minimize the number of active physical servers, so as to schedule underutilized servers to save energy. Inspired by the promising performance of the ant colony system (ACS) algorithm for combinatorial problems, an ACS-based approach is developed to achieve the VMP goal. Coupled with order exchange and migration (OEM) local search techniques, the resultant algorithm is termed an OEMACS. It effectively minimizes the number of active servers used for the assignment of virtual machines (VMs) from a global optimization perspective through a novel strategy for pheromone deposition which guides the artificial ants toward promising solutions that group candidate VMs together. The OEMACS is applied to a variety of VMP problems with differing VM sizes in cloud environments of homogenous and heterogeneous servers. The results show that the OEMACS generally outperforms conventional heuristic and other evolutionary-based approaches, especially on VMP with bottleneck resource characteristics, and offers significant savings of energy and more efficient use of different resources.

Multimodal optimization problem (MMOP), which targets at searching for multiple optimal solutions simultaneously, is one of the most challenging problems for optimization. There are two general goals for solving MMOPs. One is to maintain population diversity so as to locate global optima as many as possible, while the other is to increase the accuracy of the solutions found. To achieve these two goals, a novel dual-strategy differential evolution (DSDE) with affinity propagation clustering (APC) is proposed in this paper. The novelties and advantages of DSDE include the following three aspects. First, a dual-strategy mutation scheme is designed to balance exploration and exploitation in generating offspring. Second, an adaptive selection mechanism based on APC is proposed to choose diverse individuals from different optimal regions for locating as many peaks as possible. Third, an archive technique is applied to detect and protect stagnated and converged individuals. These individuals are stored in the archive to preserve the found promising solutions and are reinitialized for exploring more new areas. The experimental results show that the proposed DSDE algorithm is better than or at least comparable to the state-of-the-art multimodal algorithms when evaluated on the benchmark problems from CEC2013, in terms of locating more global optima, obtaining higher accuracy solution, and converging with faster speed.

Virtual network embedding (VNE), which is a significant problem in cloud computing, has gained much attention among many researchers recently. Due to the NP-hardness of VNE, the existing solvers are either inefficient or inaccurate. This paper develops a novel algorithm based on the ant colony system (ACS). To solve the VNE problem, the algorithm structure concentrates on the link mapping from virtual network to substrate network. Particularly, for a specific virtual network request, we first sort the embedding sequence of virtual nodes according to their link resources. Then, ACS is used to embed the virtual nodes onto substrate nodes according the sorted sequence, while the virtual links are mapped via a shortest path strategy for the embedded nodes. For the first time, we propose a link resource heuristic information and incorporate it into the search process of ACS. The link resource heuristic information has two significant effects, one is to make virtual nodes tend to be embedded on the substrate nodes that cost less bandwidth, and the other is to confirm the connectivity of the substrate nodes that embed the virtual nodes. The proposed algorithm improves the optimization performance of VNE when compared with a few existing algorithms, while it substantially reduces the cost of time.

Clustering ensemble approaches usually have more accurate, robust and stable results than traditional single clustering approaches. However, clustering ensemble can still be improved in the following aspects: (1) improve the diversity of subspaces; (2) employ probabilistic latent clustering; (3) adopt the internal latent factor analysis before the consensus function. Therefore, we propose a new clustering ensemble framework. Specifically, we analysis the original data via Jensen-Shannon divergence distribution, and then soft subspaces are generated according to the corresponding fuzzy matrix. Next, the probabilistic latent semantic analysis clustering algorithm is employed to perform clustering in each soft subspace. The final clustering performance is improved due to the reason that the latent factor model is applied to fusion matrix. Compared with traditional single and ensemble clustering algorithms, our framework achieves superior performances on 12 real-world datasets.

The virtual networking embedding (VNE) problem is a core issue in network virtualization. This is also a challenging problem as it contains different kinds of constraints, and its complexity becomes even higher in an online VNE problem with thousands of virtual network (VN) requests. In this paper, we proposed an ant colony system based VNE algorithm, called ACS-VNE, for the online VNE problem. The benefits of ACS-VNE are threefold. First, it is an ACS based algorithm so it can take full advantage of the dynamically changing heuristic information and pheromone to improve the quality of a solution. Second, different from previous work that only considers the resource of nodes in node mapping phase, we take the distance message related to links into consideration so that we can reduce the cost of VN requests. The last but not least, the algorithm tries to reduce the cost for every single VN and it helps to increase the possibility of accepting more future VN requests. The proposed method is tested on both the single VN request VNE problem and the online VNE problem. Experimental results show that the proposed algorithm outperforms some previous approaches in terms of average revenue and acceptance ratio, and the results also have a relatively low cost.

Existing differential evolution (DE) algorithms often face two challenges. The first is that the optimization performance is significantly affected by the ad hoc configurations of operators and parameters for different problems. The second is the long runtime for real-world problems whose fitness evaluations are often expensive. Aiming at solving these two problems, this paper develops a novel double-layered heterogeneous DE algorithm and realizes it in cloud computing distributed environment. In the first layer, different populations with various parameters and/or operators run concurrently and adaptively migrate to deliver robust solutions by making the best use of performance differences among multiple populations. In the second layer, a set of cloud virtual machines run in parallel to evaluate fitness of corresponding populations, reducing computational costs as offered by cloud. Experimental results on a set of benchmark problems with different search requirements and a case study with expensive design evaluations have shown that the proposed algorithm offers generally improved performance and reduced computational time, compared with not only conventional and a number of state-of-the-art DE variants, but also a number of other distributed DE and high-performing evolutionary algorithms. The speedup is significant especially on expensive problems, offering high potential in a broad range of real-world applications.

Many real-world optimization problems encounter the presence of uncertainties. Dynamic optimization is a class of problems whose fitness functions vary through time. For these problems, evolutionary algorithm is expected to adapt to the changing environments immediately and find the best solution accurately. Besides, most of the environmental changes may not be too drastic in real-world applications, which indicates the evolutionary information in the past may be helpful for finding the optimum solution in the new environment. As a result, effective reuse of historical evolutionary information is necessary, since it leads a faster convergence after a change has occurred. This paper develops an orthogonal learning particle swarm optimization (OLPSO) with the variable relocation strategy (VRS) to solve the dynamic optimization problem (DOP). The proposed OLPSO-VRS algorithm has two advantages as follows. First and foremost, the orthogonal learning strategy guides particles to fly in better directions by constructing a much promising and efficient exemplar, which can achieve a balance between fast convergence and population diversity. Furthermore, the VRS collects historical information in the stable search stage and then reuse such information to guide the particle variable relocation once the search environment has changed. This operation enables the algorithm to quickly shift to the new promising regions in the changing fitness landscape. We evaluated OLPSO-VRS on several dynamic benchmark problems and compared with several state-of-the-art dynamic algorithms. The results show that OLPSO-VRS obtains very competitive results and enjoys a statistically superior performance on most problems.

Multimodal optimization problem always has several peaks that are all optima of the problem. A promising approach to deal with such kind of problem should locate the peaks as many as possible (e.g., all the peaks) and should obtain high accuracy in each peak. The species-based particle swarm optimization (SPSO) divides the population into several subpopulations. Each subpopulation is gathered around a neighborhood best called species seed within the radius r, trying to locate different peaks. It does well in some low-dimensional multimodal optimization problems. However, the parameter r, which is associated with the efficiency and the accuracy of the algorithm, must be specified by the users. This makes SPSO very difficult for users to determine how much the parameter r should be. In this paper, a method of adaptively choosing radius r in SPSO is proposed, termed as adaptive SPSO (ASPSO). The experimental results show that the performance of ASPSO is more effective and accurate than standard SPSO in dealing with low-dimensional multimodal optimization problems.

This paper studies the optimization problem of topological active net (TAN), which is often seen in image segmentation and shape modeling. A TAN is a topological structure containing many nodes, whose positions must be optimized while a predefined topology needs to be maintained. TAN optimization is often time-consuming and even constructing a single solution is hard to do. Such a problem is usually approached by a "best improvement local search" (BILS) algorithm based on deterministic search (DS), which is inefficient because it spends too much efforts in nonpromising probing. In this paper, we propose the use of micro-differential evolution (DE) to replace DS in BILS for improved directional guidance. The resultant algorithm is termed deBILS. Its micro-population efficiently utilizes historical information for potentially promising search directions and hence improves efficiency in probing. Results show that deBILS can probe promising neighborhoods for each node of a TAN. Experimental tests verify that deBILS offers substantially higher search speed and solution quality not only than ordinary BILS, but also the genetic algorithm and scatter search algorithm.

Decomposition-based multiobjective evolutionary algorithms (MOEAs) have been studied a lot and have been widely and successfully used in practice. However, there are no related theoretical studies on this kind of MOEAs. In this paper, we theoretically analyze the MOEAs based on decomposition. First, we analyze the runtime complexity with two basic simple instances. In both cases the Pareto front have oneto-one map to the decomposed subproblems or not. Second, we analyze the runtime complexity on two difficult instances with bad neighborhood relations in fitness space or decision space. Our studies show that: 1) in certain cases, polynomialsized evenly distributed weight parameters-based decomposition cannot map each point in a polynomial sized Pareto front to a subproblem; 2) an ideal serialized algorithm can be very efficient on some simple instances; 3) the standard MOEA based on decomposition can benefit a runtime cut of a constant fraction from its neighborhood coevolution scheme; and 4) the standard MOEA based on decomposition performs well on difficult instances because both the Pareto domination-based and the scalar subproblem-based search schemes are combined in a proper way.

In recent years, multiobjective immune algorithms (MOIAs) have shown promising performance in solving multiobjective optimization problems (MOPs). However, basic MOIAs only use a single hypermutation operation to evolve individuals, which may induce some difficulties in tackling complicated MOPs. In this paper, we propose a novel hybrid evolutionary framework for MOIAs, in which the cloned individuals are divided into several subpopulations and then evolved using different evolutionary strategies. An example of this hybrid framework is implemented, in which simulated binary crossover and differential evolution with polynomial mutation are adopted. A fine-grained selection mechanism and a novel elitism sharing strategy are also adopted for performance enhancement. Various comparative experiments are conducted on 28 test MOPs and our empirical results validate the effectiveness and competitiveness of our proposed algorithm in solving MOPs of different types.

Operating mode scheduling is crucial for the lifetime of wireless sensor networks (WSNs). However, the growing scale of networks has made such a scheduling problem more challenging, as existing set cover and evolutionary algorithms become unable to provide satisfactory efficiency due to the curse of dimensionality. In this paper, a Kuhn–Munkres (KM) parallel genetic algorithm is developed to solve the set cover problem and is applied to the lifetime maximization of large-scale WSNs. The proposed algorithm schedules the sensors into a number of disjoint complete cover sets and activates them in batch for energy conservation. It uses a divide-and-conquer strategy of dimensionality reduction, and the polynomial KM algorithm a are hence adopted to splice the feasible solutions obtained in each subarea to enhance the search efficiency substantially. To further improve global efficiency, a redundant-trend sensor schedule strategy was developed. Additionally, we meliorate the evaluation function through penalizing incomplete cover sets, which speeds up convergence. Eight types of experiments are conducted on a distributed platform to test and inform the effectiveness of the proposed algorithm. The results show that it offers promising performance in terms of the convergence rate, solution quality, and success rate.

Cloud computing resources scheduling is significant for executing the workflows in cloud platform because it relates to both the execution time and execution cost. In order to take both the time and cost into consideration, Rodriguez and Buyya have proposed a cost-minimization and deadline-constrained workflow scheduling model on cloud computing. Their model has great applicability but the solution of their particle swarm optimization (PSO) approach is not good enough and cannot meet a tight deadline condition. In this paper, we propose a genetic algorithm (GA) approach to solve this model. In order to tackle with the tight deadline condition, a dynamic objective strategy is further proposed to let GA focus on optimize the execution time objective to meet the deadline constraint when the feasible solution hasn't been obtained. After obtaining a feasible solution, the GA focuses on optimizing the execution cost within the deadline constraint. Therefore, the proposed dynamic objective GA (DOGA) has adaptive ability to the search environment to different objectives. We have conduct extensive experiments based on workflows with different scales and different cloud resources. Experimental results show that DOGA can find better solution with smaller cost than PSO does on different scheduling scales and different deadline conditions. DOGA approach is more applicable to be used in commercial activities.

Cloud computing offers unprecedented capacity to execute large-scale workflows in the “era of big data”. In 2014, a cost-minimization and deadline-constrained workflow scheduling (CMDCWS) model is firstly proposed by Rodriguez and Buyya, which is applicable for the business need of cloud computing that a workflow task should be finished by minimizing the execute cost within a deadline constraint. As scheduling cloud computing resources for workflow is an NP-hard problem, Rodriguez and Buyya proposed to use particle swarm optimization (PSO) to solve the CMDCWS problem. In traditional PSO for CMDCWS, each dimension in the particle position stands for each task and the value of the corresponding dimension stands for the index of the cloud resource that executes this task. However, this may have drawback because the value of each dimension does not relate to the resource characteristic but is only a meaningless index number. Therefore the learning behaviors among the particles do not make sense because learning from index number may not lead to better position. In this paper, we present a resource renumber strategy to encode the particle position and design a renumber PSO (RNPSO) for CMDCWS. In RNPSO, all the resources are re-ordered and re-numbered according to their computational ability, i.e., the cost per unit time. By this, the values of particle position can make sense and the positions difference between the well-performed and poorly-performed particles can guide poorly-performed particle to promising region. We conduct experiments on test cases with small, middle, and large scales to compare the performance of PSO and RNPSO. The results show that the resource renumber strategy is promising for enhancing the PSO performance.

Particle swarm optimization (PSO) is originally designed to solve continuous optimization problems. Recently, lots of improved PSO variants with different features have been proposed, such as Adaptive particle swarm optimization (APSO), Orthogonal Learning particle swarm optimization (OLPSO) and Comprehensive Learning particle swarm optimization (CLPSO). In order to find out whether these PSOs have any particular difficulties or preference and whether one of them would outperform the others on a majority of the tested problems, we analyze the performance of different PSOs on various tested problems. In this paper, we evaluate the performance of APSO, OLPSO, and CLPSO on more complex benchmark functions. The comparison is performed on a large amount of real-parameter optimization problems, including the CEC 2005 and the CEC 2014 benchmark functions. Finally, we find out that the OLPSO achieves higher solution quality than the other two PSOs on most problems based on the simulation results on benchmark functions.

Differential evolution (DE) is an efficient and powerful population-based stochastic evolutionary algorithm, which evolves according to the differential between individuals. The success of DE in obtaining the optima of a specific problem depends greatly on the choice of mutation strategies and control parameter values. Good parameters lead the individuals towards optima successfully. The increasing of the success rate (the ratio of entering the next generation successfully) of population can speed up the searching. Adaptive DE incorporates success-history or population-state based parameter adaptation. However, sometimes poor parameters may improve individual with small probability and are regarded as successful parameters. The poor parameters may mislead the parameter control. So, in this paper, we propose a novel approach to distinguish between good and poor parameters in successful parameters. In order to speed up the convergence of algorithm and find more "good" parameters, we propose a dichotomy adaptive DE (DADE), in which the successful parameters are divided into two parts and only the part with higher success rate is used for parameter adaptation control. Simulation results show that DADE is competitive to other classic or adaptive DE algorithms on a set of benchmark problem and IEEE CEC 2014 test suite.

Existing multiobjective evolutionary algorithms (MOEAs) tackle a multiobjective problem either as a whole or as several decomposed single-objective sub-problems. Though the problem decomposition approach generally converges faster through optimizing all the sub-problems simultaneously, there are two issues not fully addressed, i.e., distribution of solutions often depends on a priori problem decomposition, and the lack of population diversity among sub-problems. In this paper, a MOEA with double-level archives is developed. The algorithm takes advantages of both the multiobjective-problem-level and the sub-problem-level approaches by introducing two types of archives, i.e., the global archive and the sub-archive. In each generation, self-reproduction with the global archive and cross-reproduction between the global archive and sub-archives both breed new individuals. The global archive and sub-archives communicate through cross-reproduction, and are updated using the reproduced individuals. Such a framework thus retains fast convergence, and at the same time handles solution distribution along Pareto front (PF) with scalability. To test the performance of the proposed algorithm, experiments are conducted on both the widely used benchmarks and a set of truly disconnected problems. The results verify that, compared with state-of-the-art MOEAs, the proposed algorithm offers competitive advantages in distance to the PF, solution coverage, and search speed.

Utilizing cumulative correlation information already existing in an evolutionary process, this paper proposes a predictive approach to the reproduction mechanism of new individuals for differential evolution (DE) algorithms. DE uses a distributed model (DM) to generate new individuals, which is relatively explorative, whilst evolution strategy (ES) uses a centralized model (CM) to generate offspring, which through adaptation retains a convergence momentum. This paper adopts a key feature in the CM of a covariance matrix adaptation ES, the cumulatively learned evolution path (EP), to formulate a new evolutionary algorithm (EA) framework, termed DEEP, standing for DE with an EP. Without mechanistically combining two CM and DM based algorithms together, the DEEP framework offers advantages of both a DM and a CM and hence substantially enhances performance. Under this architecture, a self-adaptation mechanism can be built inherently in a DEEP algorithm, easing the task of predetermining algorithm control parameters. Two DEEP variants are developed and illustrated in the paper. Experiments on the CEC'13 test suites and two practical problems demonstrate that the DEEP algorithms offer promising results, compared with the original DEs and other relevant state-of-the-art EAs.

This paper proposes to solve the dynamic optimization problem (DOP) by using an adaptive particle swarm optimization (APSO) algorithm with an variable relocation strategy (VRS). The VRS based APSO algorithm (APSO/VRS) has the following two advantages when solving DOP. Firstly, by using the APSO optimizing framework, the algorithm benefits from the fast optimization speed due to the adaptive parameter control. More importantly, the adaptive parameter and operator in APSO make the algorithm fast respond to the environment changes of DOP. Secondly, VRS was reported in the literature to help dynamic evolutionary algorithm (DEA) to relocate the individual position in promising region when environment changes. Therefore, the modified VRS used in APSO can collect historical information in the stability stage and use such information to guide the particle variable relocation in the change stage. We evaluated both APSO and APSO/VRS on several dynamic benchmark problems and compared with two state-of-the-art DEAs and DEA that also used the VRS. The results show that both APSO and APSO/VRS can obtain very competitive results on these problems, and APSO/VRS outperforms others on most of the test cases.

Cloud computing provides resources as services in pay-as-you-go mode to customers by using virtualization technology. As virtual machine (VM) is hosted on physical server, great energy is consumed by maintaining the servers in data center. More physical servers means more energy consumption and more money cost. Therefore, the VM placement (VMP) problem is significant in cloud computing. This paper proposes an approach based on ant colony optimization (ACO) to solve the VMP problem, named as ACO-VMP, so as to effectively use the physical resources and to reduce the number of running physical servers. The number of physical servers is the same as the number of the VMs at the beginning. Then the ACO approach tries to reduce the physical server one by one. We evaluate the performance of the proposed ACO-VMP approach in solving VMP with the number of VMs being up to 600. Experimental results compared with the ones obtained by the first-fit decreasing (FFD) algorithm show that ACO-VMP can solve VMP more efficiently to reduce the number of physical servers significantly, especially when the number of VMs is large.

The performance of a multimodal evolutionary algorithm is highly sensitive to the setting of population size. This paper introduces a generic archive technique to reduce the importance of properly setting the population size parameter. The proposed archive technique contains two components: subpopulation identification and convergence detection. The first component is used to identify subpopulations in a number of individuals while the second one is used to determine whether a subpopulation is converged. By using the two components, converged subpopulations are identified, and then, individuals in the converged subpopulations are stored in an external archive and re-initialized to search for other optima. We integrate the archive technique with several state-of-the-art PSO-based multimodal algorithms. Experiments are carried out on a recently proposed multimodal problem set to investigate the effect of the archive technique. The experimental results show that the proposed method can reduce the influence of the population size parameter and improve the performance of multimodal algorithms.

The performance of differential evolution (DE) largely depends on its mutation strategy and control parameters. In this paper, we propose an adaptive DE (ADE) algorithm with a new mutation strategy DE/lbest/1 and a two-level adaptive parameter control scheme. The DE/lbest/1 strategy is a variant of the greedy DE/best/1 strategy. However, the population is mutated under the guide of multiple locally best individuals in DE/lbest/1 instead of one globally best individual in DE/best/1. This strategy is beneficial to the balance between fast convergence and population diversity. The two-level adaptive parameter control scheme is implemented mainly in two steps. In the first step, the population-level parameters Fp and CRp for the whole population are adaptively controlled according to the optimization states, namely, the exploration state and the exploitation state in each generation. These optimization states are estimated by measuring the population distribution. Then, the individual-level parameters Fi and CRi for each individual are generated by adjusting the population-level parameters. The adjustment is based on considering the individual's fitness value and its distance from the globally best individual. This way, the parameters can be adapted to not only the overall state of the population but also the characteristics of different individuals. The performance of the proposed ADE is evaluated on a suite of benchmark functions. Experimental results show that ADE generally outperforms four state-of-the-art DE variants on different kinds of optimization problems. The effects of ADE components, parameter properties of ADE, search behavior of ADE, and parameter sensitivity of ADE are also studied. Finally, we investigate the capability of ADE for solving three real-world optimization problems.

The TSP problem is considered as classical discrete optimization grouping problem, which is widely used in practice, but it is real a difficult NP problem. Simultaneously differential evolution (DE) algorithm has been proven to be a powerful optimization algorithm. Since the mutation process of DE contains a series of arithmetic operators operating on continuous space, few algorithms based on DE solve this problem nicely and the advantages of DE in continuous space cannot be used to solve TSP. To take full advantages of the strengths of DE, this paper proposes a set-based DE (S-DE) which completely follows the procedure of the original DE. We present a representation scheme to characterize the discrete problem space and by redefining its basic concept and all related operators in mutation, DE can operate directly on the original set space of the discrete optimization problems instead of performing a space transformation. In that way, the searching features of DE in continuous space is kept. In experiment, we test the performance of our proposed S-DE and the results show it is very promising.

Nurse rostering is a non-deterministic polynomial problem with many constraints. In the literature, a number of heuristic approaches have been proposed, but few of them can achieve satisfying performance on both solution quality and search speed. Inspired by the successful experience of ant colony optimization (ACO) on many highly-constrained problems, this paper proposed an ant colony optimization approach termed ACO-NR for solving the nurse rostering problem. First, the search space of the nurse rostering problem is remodeled as a graph, with each solution corresponding to a path on the graph. Then a heuristic function is designed to guide the path construction behavior of ACO-NR. The heuristic information comes not only from the static information defined by the problem-dependent knowledge, but also from the dynamic information generated by the solution construction procedure. A penalty function is defined to help ACO-NR handle problem constraints. Experimental results on 52 benchmark instances show that the proposed ACO-NR can achieve better performance than classic nurse rostering algorithms.

Human being is the most intelligent organism in the world and the brainstorming process popularly used by them has been demonstrated to be a significant and promising way to create great ideas for problem solving. Brain storm optimization (BSO) is a new kind of swarm intelligence algorithm inspired by human being creative problem solving process. BSO transplants the brainstorming process in human being into optimization algorithm design and gains successes. BSO generally uses the grouping, replacing, and creating operators to produce ideas as many as possible to approach the problem solution generation by generation. In these operators, BSO involves mainly three control parameters named: (1) p_replce to control the replacing operator; (2) p_one to control the creating operator to create new ideas between one cluster and two clusters; and (3) p_center (p_one_center and p_two_center) to control using cluster center or random idea to create new idea. In this paper, we make investigations on these parameters to see how they affect the performance of BSO. More importantly, a new BSO variant designed according to the investigation results is proposed and its performance is evaluated.

Traditional multiobjective evolutionary algorithms (MOEAs) consider multiple objectives as a whole when solving multiobjective optimization problems (MOPs). However, this consideration may cause difficulty to assign fitness to individuals because different objectives often conflict with each other. In order to avoid this difficulty, this paper proposes a novel coevolutionary technique named multiple populations for multiple objectives (MPMO) when developing MOEAs. The novelty of MPMO is that it provides a simple and straightforward way to solve MOPs by letting each population correspond with only one objective. This way, the fitness assignment problem can be addressed because the individuals' fitness in each population can be assigned by the corresponding objective. MPMO is a general technique that each population can use existing optimization algorithms. In this paper, particle swarm optimization (PSO) is adopted for each population, and coevolutionary multiswarm PSO (CMPSO) is developed based on the MPMO technique. Furthermore, CMPSO is novel and effective by using an external shared archive for different populations to exchange search information and by using two novel designs to enhance the performance. One design is to modify the velocity update equation to use the search information found by different populations to approximate the whole Pareto front (PF) fast. The other design is to use an elitist learning strategy for the archive update to bring in diversity to avoid local PFs. CMPSO is comprehensively tested on different sets of benchmark problems with different characteristics and is compared with some state-of-the-art algorithms. The results show that CMPSO has superior performance in solving these different sets of MOPs.

In nature, almost every organism ages and has a limited lifespan. Aging has been explored by biologists to be an important mechanism for maintaining diversity. In a social animal colony, aging makes the old leader of the colony become weak, providing opportunities for the other individuals to challenge the leadership position. Inspired by this natural phenomenon, this paper transplants the aging mechanism to particle swarm optimization (PSO) and proposes a PSO with an aging leader and challengers (ALC-PSO). ALC-PSO is designed to overcome the problem of premature convergence without significantly impairing the fast-converging feature of PSO. It is characterized by assigning the leader of the swarm with a growing age and a lifespan, and allowing the other individuals to challenge the leadership when the leader becomes aged. The lifespan of the leader is adaptively tuned according to the leader's leading power. If a leader shows strong leading power, it lives longer to attract the swarm toward better positions. Otherwise, if a leader fails to improve the swarm and gets old, new particles emerge to challenge and claim the leadership, which brings in diversity. In this way, the concept “aging” in ALC-PSO actually serves as a challenging mechanism for promoting a suitable leader to lead the swarm. The algorithm is experimentally validated on 17 benchmark functions. Its high performance is confirmed by comparing with eight popular PSO variants.

Brain storm optimization (BSO) is a new kind of swarm intelligence algorithm inspired by human creative problem solving process. Human being is the most intelligent organism in the world and the brainstorming process popularly used by them has been demonstrated to be a significant and promising way to create great ideas for problem solving. BSO transplants the brainstorming process in human being into optimization algorithm design and gains successes. BSO generally uses the grouping, replacing, and creating operators to produce ideas as many as possible to approach the problem global optimum generation by generation. In this paper, we propose two novel designs to enhance the conventional BSO performance. The first design of the modified BSO (MBSO) is that it uses a simple grouping method (SGM) in the grouping operator instead of the clustering method to reduce the algorithm computational burden. The second design is that MBSO uses a novel idea difference strategy (IDS) in the creating operator instead of the Gaussian random strategy. The IDS not only contains open minded element to avoid the ideas being trapped by local optima, but also can match the search environment to create better new ideas for problem solving. Experiments have been conducted to illustrate the effectiveness and efficiency of the MBSO algorithm. Moreover, the contributions of SGM and IDS are investigated to show how and why MBSO can perform better than BSO.

Developing techniques for optimal allocation of limited resources to a set of activities has received increasing attention in recent years. In this paper, an efficient resource allocation scheme based on particle swarm optimization (PSO) is developed. Different from many existing evolutionary algorithms for solving resource allocation problems (RAPs), this PSO algorithm incorporates a novel representation of each particle in the population and a comprehensive learning strategy for the PSO search process. The novelty of this representation lies in that the position of each particle is represented by a pair of points, one on each side of the constraint hyper-plane in the problem space. The line joining these two points intersects the constraint hyper-plane and their intersection point indicates a feasible solution. With the evaluation value of the feasible solution used as the fitness value of the particle, such a representation provides an effective way to ensure the equality resource constraints in RAPs are met. Without the distraction of infeasible solutions, the particle thus searches the space smoothly. In addition, particles search for optimal solutions by learning from themselves and their neighborhood using the comprehensive learning strategy, helping prevent premature convergence and improve the solution quality for multimodal problems. This new algorithm is shown to be applicable to both single-objective and multiobjective RAPs, with performance validated by a number of benchmarks and by a real-world bed capacity planning problem. Experimental results verify the effectiveness and efficiency of the proposed algorithm.

The rapid development of radio frequency identification (RFID) technology creates the challenge of optimal deployment of an RFID network. The RFID network planning (RNP) problem involves many constraints and objectives and has been proven to be NP-hard. The use of evolutionary computation (EC) and swarm intelligence (SI) for solving RNP has gained significant attention in the literature, but the algorithms proposed have seen difficulties in adjusting the number of readers deployed in the network. However, the number of deployed readers has an enormous impact on the network complexity and cost. In this paper, we develop a novel particle swarm optimization (PSO) algorithm with a tentative reader elimination (TRE) operator to deal with RNP. The TRE operator tentatively deletes readers during the search process of PSO and is able to recover the deleted readers after a few generations if the deletion lowers tag coverage. By using TRE, the proposed algorithm is capable of adaptively adjusting the number of readers used in order to improve the overall performance of RFID network. Moreover, a mutation operator is embedded into the algorithm to improve the success rate of TRE. In the experiment, six RNP benchmarks and a real-world RFID working scenario are tested and four algorithms are implemented and compared. Experimental results show that the proposed algorithm is capable of achieving higher coverage and using fewer readers than the other algorithms.

Power electronic circuit (PEC) always consists of a number of components such as resistors, capacitors, and inductors which have to be optimized in order to obtain good circuit performance. In current studies, the search ranges of these components are always pre-defined carefully by expert designers, making it difficult for practical applications. In this paper, the search space is freely set to the commonly used ranges and an efficient orthogonal learning particle swarm optimization (OLPSO) is applied to optimally design the PEC with such search space. OLPSO uses an orthogonal learning (OL) strategy for PSO to discover useful information that lies in the personal historical best experience and the neighborhood's best experience via orthogonal experimental design. Therefore, OLPSO can construct a more promising and efficient exemplar to guide particle to fly better towards the global optimal region. OLPSO is implemented to optimize the design of a buck regulator in PEC. The optimized results are compared with those obtained by using a genetic algorithm (GA) approach and those obtained by using PSO with traditional learning strategy. Results show that the OLPSO algorithm is more promising in the design and optimization of the PEC with large search space. Moreover, the simulations results demonstrate the advantages of OLPSO by showing that the circuit optimized by OLPSO exhibits better startup and large-signal disturbance performance when compared with the one optimized by GA.

Particle swarm optimization (PSO) relies on its learning strategy to guide its search direction. Traditionally, each particle utilizes its historical best experience and its neighborhood's best experience through linear summation. Such a learning strategy is easy to use, but is inefficient when searching in complex problem spaces. Hence, designing learning strategies that can utilize previous search information (experience) more efficiently has become one of the most salient and active PSO research topics. In this paper, we proposes an orthogonal learning (OL) strategy for PSO to discover more useful information that lies in the above two experiences via orthogonal experimental design. We name this PSO as orthogonal learning particle swarm optimization (OLPSO). The OL strategy can guide particles to fly in better directions by constructing a much promising and efficient exemplar. The OL strategy can be applied to PSO with any topological structure. In this paper, it is applied to both global and local versions of PSO, yielding the OLPSO-G and OLPSO-L algorithms, respectively. This new learning strategy and the new algorithms are tested on a set of 16 benchmark functions, and are compared with other PSO algorithms and some state of the art evolutionary algorithms. The experimental results illustrate the effectiveness and efficiency of the proposed learning strategy and algorithms. The comparisons show that OLPSO significantly improves the performance of PSO, offering faster global convergence, higher solution quality, and stronger robustness.

Decisions for admission scheduling in hospitals are a class of optimization problems constrained by many factors. Instead of scheduling the admission of patients directly, this paper proposes a genetic algorithm (GA) designed for the optimization of a long-term admission strategy for the ophthalmology department in hospitals. For the optimization of admission strategy, we devise a coding scheme of strategies and define the objective functions for two objectives: efficiency and fairness. The proposed algorithm utilizes historical data of the hospital for evaluation of chromosomes. Experiments are conducted on several cases, and the strategy optimized by the proposed GA is compared with the first come first serve (FCFS) strategy and the greedy strategy. Experimental results show that strategies optimized by the proposed algorithm outperform FCFS and the greedy strategy.

Differential evolution (DE) is an effective and efficient optimization algorithm that has been successfully applied to many problems. However, the DE performance significantly depends on the elaborate settings of its parameters. Designers of DE usually spend great efforts to find proper parameter settings because good parameter values usually vary with different problems. In order to enhance the efficiency and robustness of DE, this paper proposes a novel DE algorithm, PLADE, which uses the learning mechanism in particle swarm optimization (PSO), termed as PSO-Learning (PL) strategy, to adaptively control the DE parameters. PLADE encodes the DE parameters into each individual and evolve the parameters during the evolutionary process. The individuals that achieve good fitness and survive in the evolution imply good parameter settings, the poor individuals use the PL strategy to let their parameters learn from the parameters in the good individuals. With such a PL based parameter self-adaptation strategy, PLADE can evolve the parameters to better values and can adapt the parameters to match the requirements of different evolutionary states and different optimization problems. PLADE is tested by six benchmark functions with unimodal and multimodal characteristics. Experimental results show that PLADE not only outperforms conventional DE with fixed parameter settings, in terms of solution quality, convergence speed, and algorithm reliability, but also is better than or at least comparable to some other state-of-the-art adaptive DE variants.

This paper proposes a parallel particle swarm optimization (PPSO) to solve the multiobjective optimization problems (MOP). PPSO makes the use of the parallel characteristic of the PSO algorithm to deal with the multiple objectives issue of the MOP. PPSO uses as many swarms as the number of the objectives in the MOP and lets each swarm optimize only one of the objectives. These swarms work in parallel and each swarm can use a standard PSO or any other improved PSO variants to solve a single objective problem. PPSO has advantages on the following two aspects. First, as each swarm focus on optimizing only one objective, PPSO can avoid the difficulty of fitness assignment because the particles can be evaluated like in the single objective optimization problem. Second, as different swarms optimize different objectives, PPSO can maintain the population diversity to make a throughout search along the whole Pareto front to obtain nondominated solutions as many as possible. The performance of PPSO is tested on a set of benchmark problems complicated Pareto sets in CEC2009. The experimental results compared with those obtained by the state-of-the-art algorithms demonstrate the effectiveness and efficiency of PPSO, showing the good performance of PPSO in solving the MOP with complicated Pareto sets.

The aircraft arrival sequencing and scheduling (ASS) problem is a salient problem in air traffic control (ATC), which proves to be nondeterministic polynomial (NP) hard. This paper formulates the ASS problem in the form of a permutation problem and proposes a new solution framework that makes the first attempt at using an ant colony system (ACS) algorithm based on the receding horizon control (RHC) to solve it. The resultant RHC-improved ACS algorithm for the ASS problem (termed the RHC-ACS-ASS algorithm) is robust, effective, and efficient, not only due to that the ACS algorithm has a strong global search ability and has been proven to be suitable for these kinds of NP-hard problems but also due to that the RHC technique can divide the problem with receding time windows to reduce the computational burden and enhance the solution's quality. The RHC-ACS-ASS algorithm is extensively tested on the cases from the literatures and the cases randomly generated. Comprehensive investigations are also made for the evaluation of the influences of ACS and RHC parameters on the performance of the algorithm. Moreover, the proposed algorithm is further enhanced by using a two-opt exchange heuristic local search. Experimental results verify that the proposed RHC-ACS-ASS algorithm generally outperforms ordinary ACS without using the RHC technique and genetic algorithms (GAs) in solving the ASS problems and offers high robustness, effectiveness, and efficiency.

This paper proposes a PSO-FFPP algorithm based on the particle swarm optimization (PSO) framework to solve the flight frequency programming problem (FFPP). The FFPP is to determine the flight frequency for each type of aircraft on each flight route. This problem is fundamental to an airline's operational planning because it affects the airline's profit and market share greatly. The FFPP can be formulated as an integer programming problem with constraints that is very suitable to be solved by the PSO algorithm. The proposed PSO-FFPP algorithm codes the decision variables of the FFPP with real number to represent the potential solutions and defines the optimization objective as a maximization problem for the airlines profit. A constraints handling method that combines the ideas of feasible solution preserving and infeasible solution rejection is developed. This method avoids the expense of infeasibility repair or penalty, making the algorithm simple to use and easy to extend. An integer handing process is also devised to round the real number to the nearest valid integer before feasibility check and function evaluation. This process maintains the search tendency of the PSO algorithm and can help to search in a promising region for the global optimum. The feasibility of the proposed algorithm is demonstrated and compared with the Monte Carlo method and the enumeration method on a simulation case with promising results. Experiments are also conducted to investigate the factors that affect the solution quality and computational time.

The aircraft arrival sequencing and scheduling (ASS) problem is one of the most significant problems in the air traffic control (ATC). This paper makes the first attempt to design an ant colony system (ACS) based approach to solve this NP-hard problem. In order to reduce the computational effort of the optimization process, the receding horizon control (RHC) strategy is integrated into the ACS to divide the optimization process into several sub-processes and solve them one by one. This strategy can reduce the problem scale in each sub-optimization process, resulting in lighter computational effort and higher quality solution for the whole problem. Experiments are conducted to demonstrate the effectiveness and efficiency of the proposed RHC based ACS algorithm for the ASS problem (RHC-ACS-ASS). Simulation results show that the RHC-ACS-ASS not only outperforms the GA based approaches, but also the ACS based approach without using the RHC strategy.

This paper proposes an information share mechanism into particle swarm optimization (PSO) in order to use all the useful information of the swarm to prevent premature convergence. The particle in traditional PSO uses only the information from its personal best position and the neighborhood's best position. This mechanism is not with sufficient search information and therefore the algorithm is easy to be trapped into local optima. In the proposed information share PSO (ISPSO), all the particles post their best search information to a share device and any particle can read the information on the device and use the information provided by any other particle to help enhance its search ability. Therefore, the ISPSO can use the whole swarm's information to guide the flying direction. The ISPSO has been applied to optimize multimodal functions, and the experimental results demonstrate that the ISPSO can yield better performance when is compared with the traditional and some other improved PSOs.

This paper proposes an orthogonal learning particle swarm optimization (OLPSO) by designing an orthogonal learning (OL) strategy through the orthogonal experimental design (OED) method. The OL strategy takes the dimensions of the problem as the orthogonal experimental factors. The levels of each dimension (factor) are the two choices of the personal best position and the neighborhood's best position. By orthogonally combining the two learning exemplars, the useful information can be discovered, preserved and utilized to construct an efficient exemplar to guide the particle to fly in a more promising direction towards the global optimum. The effectiveness and efficiency of the OL strategy is demonstrated on a set of benchmark functions by comparing the PSOs with and without OL strategy. The OL strategy improves the PSO algorithm in terms of higher quality solution and faster convergence speed.

An adaptive particle swarm optimization (APSO) that features better search efficiency than classical particle swarm optimization (PSO) is presented. More importantly, it can perform a global search over the entire search space with faster convergence speed. The APSO consists of two main steps. First, by evaluating the population distribution and particle fitness, a real-time evolutionary state estimation procedure is performed to identify one of the following four defined evolutionary states, including exploration, exploitation, convergence, and jumping out in each generation. It enables the automatic control of inertia weight, acceleration coefficients, and other algorithmic parameters at run time to improve the search efficiency and convergence speed. Then, an elitist learning strategy is performed when the evolutionary state is classified as convergence state. The strategy will act on the globally best particle to jump out of the likely local optima. The APSO has comprehensively been evaluated on 12 unimodal and multimodal benchmark functions. The effects of parameter adaptation and elitist learning will be studied. Results show that APSO substantially enhances the performance of the PSO paradigm in terms of convergence speed, global optimality, solution accuracy, and algorithm reliability. As APSO introduces two new parameters to the PSO paradigm only, it does not introduce an additional design or implementation complexity.

Research into setting the values of the acceleration coefficients c1and c2in Particle Swarm Optimization (PSO) is one of the most significant and promising areas in evolutionary computation. Parameters c1and c2in PSO indicate the “self-cognitive” and “social-influence” components which are important for the ability to explore and converge respectively. Instead of using fixed value of c1and c2with 2.0, this paper presents the use of clustering analysis to adaptively adjust the value of these two parameters in PSO. By applying the K-means algorithm, distribution of the population in the search space is clustered in each generation. An adaptive system which is based on considering the relative size of the cluster containing the best particle and the one containing the worst particle is used to adjust the values of c1and c2. The proposed method has been applied to optimize multidimensional mathematical functions, and the simulation results demonstrate that the proposed method performs with a faster convergence rate and better solutions when compared with the methods with fixed values of c1and c2.