Internet of Things (IoT) task offloading involves conflicting objectives of energy consumption and delay. We formulate a bi-objective optimization model for a multi-UAV-assisted mobile edge computing (MEC) system, jointly optimizing resource allocation, task offloading decisions, and UAV deployment to minimize both energy consumption and delay. As the number of offloaded tasks increases, finding feasible solutions becomes more challenging. To address this, we develop an Information Feedback Evolutionary Algorithm (IFEA) that leverages feedback driven guidance to enhance the diversity and convergence of the Pareto front (PF). Simulation results show that IFEA achieves better trade offs than the other four multi-objective algorithms.

As the search space and hence the optimum vary through time, dynamic optimization problems (DOPs) bring tremendous difficulties. Changes in DOPs often manifest as diverse dynamics. Consequently, regulating individuals’ search to adapt to diverse dynamics is crucial to tackle DOPs. Besides, due to the inherent population nature in dynamic optimization algorithms (DOAs), loss of global and local diversities is a critical issue deteriorating the performance of DOAs. Faced with these difficulties, this article proposes a neural network-aided differential evolution with double Q-learning (NNDE-DQ), in which an evolutionary regulation network (ERN) is designed to maintain high global and local diversities over time and regulate individuals’ search that can adapt to diverse dynamics. NNDE-DQ first partitions the search space into multiple subspaces and in each subspace distant individuals are selected as the centers of ERN’s hidden nodes activated by radial basis function. Every input individual is mutated with two randomly selected hidden node centers from different subspaces as differential individuals, facilitating the maintenance of a high global diversity due to very distinct differential terms of the population. Moreover, each mutated individual selects a hidden node center from the subspace located by the mutated individual to undergo crossover. Due to distant hidden node centers in each subspace, a high local diversity can be maintained by individuals’ crossover. Besides, DQ is introduced to acquire ERN’s desired output by interactively estimating individuals’ state-action information, enabling ERN to learn the regulation of individuals’ search in dynamic environments and hence adapt to diverse dynamics. The experimental results demonstrate that NNDE-DQ significantly improves the performance in solving various DOPs comparing to seven state-of-the-art DOAs.

Large-scale assembly production suffers from inefficient resource allocation, difficulties in coordinating interests across workstations, and severe congestion issues due to massive scale, complex tasks, and fluctuating constraints. To address these challenges, this study proposes a resource-efficient scheduling decision-making method based on a mixture pulsation model (DMMPM). The main contributions are as follows: 1) quantitative criteria for pulsation rhythm (takt-time) consistency in assembly production are defined, and a mixture equilibrium model for multiworkstation collaborative scheduling is developed, to integrate production rhythm alignment with workforce optimization within a coalition-driven profit maximization framework; 2) a spatiotemporally constrained task-allocation method driven by theoretical allocation batches is designed, balancing interstation resource demand conflicts and production rhythm synchronization requirements; and 3) a bi-level "scheduling-collaboration" architecture is proposed, where scheduling agents generate workstation-level strategies and collaboration agents coordinate cross-workstation coalition strategies through profit distribution, thereby enabling the efficient integration of decentralized decision-making and global optimization. The mathematical model is validated using ILOG CPLEX. Compared with conventional approaches, DMMPM significantly reduces the integrated scheduling cost and demonstrates superior decision-making capability and improved control of pulsation rhythm in large-scale aircraft manufacturing scenarios.

Optimization problems in real-world applications often involve dynamic environmental changes, requiring algorithms to adapt quickly, track optimal solutions, and maintain efficiency. Existing dynamic multiobjective optimization evolutionary algorithms (DMOEAs) typically rely on fixed or limited dynamic response mechanisms, which are often insufficient to handle complex and varied dynamic environments. To overcome these limitations, this article proposes an adaptive dynamic response-based DMOEA (ADR-DMOEA), which employs a subpopulation-level adaptive mechanism to coordinate diversity-driven, prediction-driven, and memory-driven strategies. The strategy weights are dynamically adjusted according to the static optimization distance of each subpopulation, ensuring that appropriate strategies are adaptively deployed in different environments. This design overcomes the inefficiency of fixed assignments and the instability of individual-level perturbations, enabling coordinated and stable evolution. Extensive experiments on DF benchmark functions and a blast furnace (BF) ironmaking case study demonstrate that ADR-DMOEA achieves superior convergence, diversity, and robustness compared to state-of-the-art algorithms, effectively supporting real-world decision-making under dynamic conditions.

The Nearest-Better Network (NBN) is a powerful method to visualize sampled data for continuous optimization problems while preserving multiple landscape features. However, the calculation of NBN is very time-consuming, and the extension of the method to combinatorial optimization problems is challenging but very important for analyzing the algorithm’s behavior. This paper provides a straightforward theoretical derivation showing that the NBN network essentially functions as the maximum probability transition network for algorithms. This paper also presents an efficient NBN computation method with logarithmic linear time complexity to address the time-consuming issue. By applying this efficient NBN algorithm to the OneMax problem and the Traveling Salesman Problem (TSP), we have made several remarkable discoveries for the first time: The fitness landscape of OneMax exhibits neutrality, ruggedness, and modality features. The primary challenges of TSP problems are ruggedness, modality, and deception. Three state-of-the-art TSP algorithms (EAX, LKH, and NLKH) have limitations when addressing challenges related to modality and deception, respectively. LKH, based on local search operators, fails when there are deceptive solutions near global optima. EAX, which is based on a single population, can efficiently maintain diversity. However, when multiple attraction basins exist, EAX retains individuals within multiple basins simultaneously, reducing inter-basin interaction efficiency and leading to algorithm’s stagnation. NLKH improves over LKH by leveraging learned edge weights to increase the chance of reaching the global basin, but it remains vulnerable to deceptive funnels due to biased learning from underrepresented complex instances.

Prediction-based dynamic multi-objective optimization algorithms (DMOEAs) are widely used to explore the relationships of Pareto-optimal solutions (POSs) under continuous time steps, aiming to tackle dynamic multi-objective optimization problems (DMOPs). However, DMOPs with irregular POS shapes pose significant challenges to the quality of predicted solutions owing to the misaligned binding of solutions. To bridge this gap, this paper proposes a learning algorithm based on similarity identification and knowledge transfer, called SIKT-DMOEA, which comprises the following three steps. Firstly, a cluster centers-driven feedforward neural network (CCD-FNN) with global optimal binding assignment is constructed, aiming to learn the regional POS dynamics between adjacent environments. Secondly, a similarity identification technique archives valuable knowledge in historical environments and transfers it to the current environment for evolutionary acceleration. Finally, a population reconstruction strategy is presented for adaptive guidance according to the dominant property of each solution, which approximates the new POS with superior convergence and distribution. Comprehensive experiments demonstrate that SIKT-DMOEA manifests competitiveness when addressing DF test problems and one real-world application problem compared to state-of-the-art DMOEAs. SIKT-DMOEA has corroborated its capability of effectively reducing the loss of population convergence and diversity facing different patterns of environmental changes.

Dynamic multi-objective optimisation (DMO) handles optimisation problems with multiple (often conflicting) objectives in varying environments. This paper proposes vector autoregressive evolution (VARE) consisting of vector autoregression (VAR) and environment-aware hypermutation (EAH) to address environmental changes in DMO. In light of mutual dependency between decision variables in Pareto-optimal solutions, VARE builds an efficient VAR model, capturing such mutual relationship while handling dense model parameterisation with dimensionality reduction, to predict the moving solutions in dynamic environments. Additionally, VARE introduces EAH to address the blindness of existing hypermutation strategies in increasing population diversity, for scenarios where predictive approaches are unsuitable, by making hypermutation aware of the significance of environmental changes in both decision and objective spaces. A seamless integration of VAR and EAH in an environment-adaptive manner makes VARE effective to handle a variety of dynamic environments and competitive with several popular DMO algorithms, as demonstrated in extensive empirical studies. Specially, the proposed algorithm is computationally much faster than popular transfer learning based approaches while producing significantly better results.

Dynamic optimization focuses on solving problems where the search space changes over time. The multi-population method is the most widely used approach for addressing such problems. Traditional multi-population methods often lack a deep understanding of the problem’s structural characteristics, such as the boundaries of basins of attraction (BoAs), which leads to redundant searches in less promising regions. Without guidance from these structural features, most populations are regenerated randomly, resulting in inefficient exploration. Furthermore, the search range for each population remains fixed and does not adapt to the BoAs, leading to the loss of tracking for certain peaks. To address these challenges, this paper proposes a solution space partitioning based multi-population method. The algorithm partitions the solution space into subspaces and leverages historical population data to assign an uncertainty property to each subspace. It further learns the problem’s BoAs to guide populations in exploiting within the BoAs while exploring outside them. A dual-layer exclusion mechanism dynamically adjusts the search and exclusion ranges based on the BoAs, ensuring precise control, preventing overlaps, and preserving diversity. Experimental results demonstrate that the proposed algorithm significantly outperforms state-of-the-art algorithms on moving peaks benchmark, generalized moving peaks benchmark, and a real-world problem: marine magnetic compensation problem.

As an effective approximation algorithm for multi-objective jobshop scheduling, multi-objective evolutionary algorithms (MOEAs) have received extensive attention. However, maintaining a balance between the diversity and convergence of non-dominated solutions while ensuring overall convergence is an open problem in the context of solving Multi-objective Fuzzy Flexible Jobshop Scheduling Problems (MFFJSPs). To address it, we propose a new MOEA named MOEA/DCH by introducing a hierarchical estimation method, a clustering-based adaptive decomposition strategy, and a heuristic-based initialization method into a basic MOEA based on decomposition. Specifically, a hierarchical estimation method balances the convergence and diversity of non-dominant solutions by integrating Pareto dominance and scalarization function information. A clustering-based adaptive decomposition strategy is constructed to enhance the population’s ability to approximate a complex Pareto front. A heuristic-based initialization method is developed to provide high-quality initial solutions. The performance of MOEA/DCH is verified and compared with five competitive MOEAs on widely-tested benchmark datasets. Empirical results demonstrate the effectiveness of MOEA/DCH in balancing the diversity and convergence of non-dominated solutions while ensuring overall convergence.

Integrated coal mine energy systems (ICMES) generate streaming constraints where the number of active constraints fluctuates over time due to equipment switching, safety driven operations, and maintenance events. These dynamics cause abrupt contraction, expansion, or fragmentation of the feasible region. To address this challenge, we propose a federated learning (FL) variational autoencoder (VAE) evolutionary algorithm (FVE). Each constraint is mapped to an FL client so that local VAEs can learn heterogeneous constraint specific feasible subspaces as clients observe differently structured constraint data. Federated aggregation fuses these local latent models into a global generative model that adapts quickly and robustly to constraint inflow and outflow. An adaptive population correction mechanism repairs infeasible individuals, and enhanced dynamic dynamic nondominated sorting genetic algorithm-II tracks pareto front evolution under structural shifts. Comparative experiments on benchmark functions and an ICMES scheduling case demonstrate that FVE achieves faster feasibility restoration, improved convergence, and higher diversity than state-of-the-art methods. These results confirm the practicality of FVE for real-time industrial optimization under streaming constraints.

Many real-world optimization problems exhibit dynamic characteristics, posing significant challenges for traditional optimization methods. Evolutionary Dynamic Optimization Algorithms (EDOAs) have been developed to address these challenges by adapting to changing environments over time. However, the reproducibility and consistency of experimental results in the literature remain limited due to the lack of publicly available source codes and the complexity of accurately re-implementing algorithms and performance evaluation protocols. To support the community, we introduce E volutionary D ynamic O ptimization LAB oratory (EDOLAB), an open source MATLAB platform designed for both research and educational purposes. EDOLAB includes 27 EDOAs, four highly configurable benchmark generators, and a growing suite of performance indicators. The platform supports full parameter tuning, batch experiment management, parallel execution, and automated statistical comparisons—including rankings, significance testing, box plots, and performance trend visualizations over time. An educational application allows users to observe: (a) dynamic changes in a 2D problem landscape, (b) the movement of individuals in response to these changes, and (c) the ability of an algorithm to track moving optima. By providing an integrated environment for experimentation, benchmarking, and instructional use, EDOLAB promotes reproducibility, comparative analysis, and a deeper understanding of EDOAs in dynamic environments.

Flexible job shop co-scheduling problems (FJSCSPs) normally adopt single-load automated guided vehicles (AGVs) for transportation, possibly causing the waste of load capacity. To enhance the transportation efficiency, a multiload AGVs (MAGVs) that carry more than one job simultaneously within its load capacity come into use in flexible manufacturing systems (FMSs). In this scenario, transit throughput can achieve the obvious improvement without increasing the vehicle fleet size, having become more prevalent gradually. However, co-scheduling machines and MAGVs is seldom investigated, which is crucial for maximizing production efficiency due to the inherent interdependence between transporting and processing. Considering constraints on load capacity, task assignment, and transportation sequence, this co-scheduling problem is formulated by minimizing the makespan as an optimization objective. Subsequently, a collaboration–competition estimation of distribution algorithm (CCEDA) is put forward to solve the difficulties caused by the flexible sequence for pickup and delivery tasks of MAGVs. In particular, two problem-related heuristic rules for selecting AGVs and machines are designed, and then a hybrid initialization strategy is developed to produce high-quality initial individuals. To comprehensively describe the landscape of the problem, multiple probability models are established by learning the elite solutions, and then a collaboration–competition mechanism adaptively samples using different models to maintain the high-efficiency exploration. Furthermore, a local search based on variable neighborhood is introduced to enhance the exploitation in promising regions. The experimental results on 30 instances expose that the proposed algorithm outperforms the other state-of-the-art algorithms significantly. Also, the analysis on the impact of AGV load capacity on production confirms that its increase effectively reduces the makespan, thereby demonstrating the practical value of MAGVs.

Recently, machine learning-embedded large-scale multiobjective evolutionary algorithms (LMOEAs) have shown great promise in solving large-scale multiobjective optimization problems (LMOPs). However, the fast convergence of the population to the true Pareto-optimal front (POF) and even distribution of the obtained Pareto-optimal solutions (POSs) on the POF are not adequately considered when tackling an LMOP. Besides, existing LMOEAs typically pair solutions with a matching rule and employ a network to learn the evolution pattern among the obtained solution pairs. It is difficult to learn various evolution patterns through a simple network, which hinders the collaboration of different patterns for enhancing the search capability. Facing such difficulties, this article proposes an LMOEA with multipattern learning and collaboration (LMOEA-MLC), where a single-hidden-layer multioutput network (SMN) is established to learn inductive and hybrid evolution patterns. Specifically, two inductive ones can be learned with the solution pairs built by two matching rules toward fast convergence and even distribution, respectively. Moreover, the solution pairs considering the fusion of the two inductive ones are collected, enabling SMN to learn a hybrid one and thus making a tradeoff between fast convergence and even distribution. Besides, the learned evolution patterns collaborate to enhance the search capability due to the distinct patterns. To enhance learning speed, SMN’s parameters are updated by an incremental random vector functional link (IRVFL). In our experiments, comprehensive comparisons with eight state-of-the-art LMOEAs demonstrate the significant performance improvement of LMOEA-MLC in handling LMOPs.

The presence of constraints often leads to the formation of narrow and fragmented feasible regions within the search region, presenting significant challenges for optimization problem-solving. This paper introduces a novel approach, Feasible Regions Identification based on Historical Solutions (FRIHS), designed to address these challenges. FRIHS leverages previously evaluated solutions to partition the search region into ε-feasible and ε-infeasible regions. Additionally, by analyzing the correlations among constraints, they are reformulated as auxiliary objectives, effectively transforming the constrained optimization problem into a constrained multi-objective optimization problem. The method employs the classical evolutionary algorithm Differential Evolution and the multi-objective method NSGA-III to search the most promising feasible regions. The effectiveness of FRIHS is evaluated through a comparative analysis with five advanced constraint-handling algorithms across a benchmark test suite. Experimental results indicate that the proposed approach demonstrates competitive performance on the test problems.

The Reentrant Flexible Flow Shop Scheduling Problem (RFFSP) involves multiple repetitions of job processing in the production system, which leads to higher scheduling complexity. To solve the RFFSP, this paper proposes a Reinforcement Learning- enhanced Genetic Algorithm (RL-GA). First, a model for the RFFSP is established with the goal of minimizing the total delay time. Then, based on the characteristics of the RFFSP, a machine selection and operation selection (MSOS) encoding scheme is designed. Finally, to address the issue of genetic algorithms getting stuck in local optima and having poor local search capabilities, a reinforcement learning-based method for selecting crossover and mutation strategies is proposed. This allows the algorithm to adaptively choose more suitable crossover and mutation strategies during the iteration process. The proposed method is validated by comparing it with five other scheduling algorithms, demonstrating an improvement in the algorithm's performance

In this paper, a multi-strategy improved African Vulture Optimization Algorithm (MIAVOA) is proposed address the drawback of premature convergence of the African Vulture Optimization Algorithm (AVOA). Firstly, the gaussian quasi reflection-based learning strategy is introduced, which improves the vulture initial population’s randomness and diversity. Then, the adaptive control strategy is used to enhance the search ability of the algorithm and avoid premature convergence. Furthermore, the elite candidate pooling strategy is designed in the exploitation phase, which expands the discovery fields for the optimal solution and reinforces the ability to escape from local optima. Finally, the formula of starvation factor is modified to balance the exploitative and explorative abilities of algorithm. MIAVOA is compared with seven state-of-the-art meta-heuristics on CEC 2022 and 23 classical test functions. It is observed that the proposed algorithm significant outperforms the other compared algorithms in terms of convergence and accuracy on the majority of benchmark functions. In addition, four engineering design problems and mobile robot path planning problem are utilized to evaluate the performance of MIAVOA. The experimental results demonstrate MIAVOA is effective and can achieve better applicability in real-world scenarios.

Fitness landscape analysis (FLA) is quite important in evolutionary computation. In this article, we propose a novel FLA method, the nearest-better network (NBN), which uses the nearest-better relationship to simplify the original fitness landscape of continuous optimization problems. We introduce an efficient algorithm to calculate NBN for continuous problems. We also propose four numerical measurements and a 3-D visualization method based on NBN. Experiments show that compared to the other main FLA methods, the four numerical measurements proposed here can effectively measure the four intended features: 1) neutrality; 2) ruggedness; 3) modality; and 4) Basin of Attraction, respectively, and common features of the fitness landscape can be maintained in 3-D NBN visualization, regardless of the scale of the problem. NBN also provides a view of how algorithms search in high-dimensional problems with the help of the 3-D NBN visualization.

Dynamic multiobjective evolutionary algorithms (DMOEAs) have gained great popularity in dealing with the dynamic multiobjective optimization problems (DMOPs). However, the existing studies have difficulties in tackling DMOPs subject to (dynamic) constraints. In this article, we propose a prediction and weak coevolutionary multiobjective optimization algorithm (PWDCMO) to handle the dynamic constrained multiobjective optimization problems (DCMOPs), where a prediction strategy is employed to forecast potential optimal regions under the new environment, with a weak coevolutionary constrained multiobjective optimization (CCMO) as the optimizer aiming at balancing exploration and convergence. The proposed method is compared with the four popular dynamic constrained multiobjective evolutionary algorithms (DCMOEAs) on six test instances from two various test suites with their convergence and the overall performance being discussed. Furthermore, the performance of the proposed prediction strategy is also investigated to observe its impact on the final results. Additionally, the PWDCMO is employed in the optimization of an integrated coal mine energy system (ICMES) to validate the proficiency in addressing real world problems. Experimental results demonstrate the superiority of PWDCMO.

Balancing objectives and constraints is challenging in addressing constrained multiobjective optimization problems (CMOPs). Existing methods may have limitations in handling various CMOPs due to the complex geometries of the Pareto front (PF). And the complexity arises from the constraints that narrow the feasible region. Categorizing problems based on their geometric characteristics facilitates facing this challenge. For this purpose, this article proposes a novel constrained multiobjective optimization framework with detection and supervision phases, called COEA-DAS. The framework categorizes the problems into four types based on the overlap between the obtained approximate unconstrained PF (UPF) and constrained PF (CPF) to guide the coevolution of the two populations. In the detection phase, the detection population approaches the UPF ignoring the constraints. The main population is guided by the detection population to cross infeasible barriers and approximate the CPF. In the supervision phase, specialized evolutionary mechanisms are designed for each possible problem type. The detection population maintains evolution to assist the main population in spreading along the CPF. Meanwhile, the supervision strategy is conducted to reevaluate the problem types based on the evolutionary state of the populations. This idea of balancing constraints and objectives based on the type of problem provides a novel approach for more effectively addressing the CMOPs. Experimental results indicate that the proposed algorithm performs better or more competitively on 57 benchmark problems and 12 real-world CMOPs compared with eight state-of-the-art algorithms.

In the post-pandemic era, more manufacturers have expedited the shift from centralized to distributed manufacturing to enhance supply chain resilience. Along with this, the distributed shop floor scheduling problem has attracted much attention from academia, one of which is the distributed flexible job-shop scheduling problem (DFJSP). Nonetheless, the majority of research on DFJSPs overlooks crucial real-world necessities, such as multi-objective decision making and preventive maintenance (PM). Thus, this article suggests a multi-objective DFJSP with PM (DFJSP/PM) as a new variant of the DFJSP. The aim is to achieve a trade-off between production and maintenance to minimize the makespan, maintenance cost, and energy consumption. To this end, we establish a mathematical model and then customize a learning-assisted bi-population evolutionary algorithm (LBPEA) to solve it. In LBPEA, a novel encoding mechanism is proposed to initialize the population randomly. Then, a neighborhood search heuristic is designed to enhance the population’s quality. To balance the convergence and diversity of the population, a bi-population evolution idea is introduced during the environmental selection. Besides, a two-stage local search (LS) process is adaptively triggered to balance the allocation of computational resources between exploration and exploitation. At the first stage, a reinforcement learning mechanism is employed to intelligently select LS operators to adjust either the operations’ sequence or assignment to different factories and machines, while the second stage is to adjust the number and placement of maintenance decisions. Experimental results show that LBPEA has excellent performance in terms of convergence and diversity when solving the proposed multi-objective DFJSP/PM.

Most existing dynamic multi-objective evolutionary algorithms (DMOEAs) have been designed to handle dynamic multi-objective optimization problems (DMOPs) with regular environmental changes. However, they often overlook scenarios where environmental changes are irregular and less predictable. Recently, knowledge transfer has been proposed as a novel paradigm for solving DMOPs. Despite this, most transfer strategies only consider transferring knowledge obtained from the previous environment while ignoring significant differences that may exist between adjacent environments due to irregular changes. To address these issues, this paper proposes a novel knowledge transfer strategy based on a Gaussian mixture model (denoted as KTMM) for solving DMOPs with irregular changes. In particular, an adaptive Gaussian mixture model is designed to capture the knowledge of historical environments, which is then transferred to generate an initial population for the new environment. Additionally, a new method for controlling irregular changes is introduced into widely-used benchmarks to form the DMOP benchmark with irregular changes. Our proposed KTMM is compared with six state-of-the-art DMOEAs on several benchmark problems with irregular changes. Experimental results demonstrate the superiority of our proposed method in most test instances and in a real-world problem.

Data stream clustering can be performed to discover the patterns underlying continuously arriving sequences of data. A number of data stream clustering algorithms for finding clusters in arbitrary shapes and handling outliers, such as density-based clustering algorithms, have been proposed. However, these algorithms are often limited in their ability to construct and merge microclusters by measuring the Euclidean distances between high-dimensional data objects, e.g., transferring valuable knowledge from historical landmark windows to the current landmark window, and exploiting evolving subspace structures adaptively. We propose an online sparse representation clustering (OSRC) method to learn an affinity matrix for evaluating the relationships among high-dimensional data objects in evolving data streams. We first introduce a low-dimensional projection (LDP) into sparse representation to adaptively reduce the potential negative influence associated with the noise and redundancy contained in high-dimensional data. Then, we take advantage of the -norm optimization technique to choose the appropriate number of representative data objects and form a specific dictionary for sparse representation. The specific dictionary is integrated into sparse representation to adaptively exploit the evolving subspace structures of the high-dimensional data objects. Moreover, the data object representatives from the current landmark window can transfer valuable knowledge to the next landmark window. The experimental results based on a synthetic dataset and six benchmark datasets validate the effectiveness of the proposed method compared to that of state-of-the-art methods for data stream clustering.

Dynamic multiobjective optimization problems (DMOPs) are characterized by multiple objectives that change over time in varying environments. More specifically, environmental changes can be described as various dynamics. However, it is difficult for existing dynamic multiobjective algorithms (DMOAs) to handle DMOPs due to their inability to learn in different environments to guide the search. Besides, solving DMOPs is typically an online task, requiring low computational cost of a DMOA. To address the above challenges, we propose a particle search guidance network (PSGN), capable of directing individuals' search actions, including learning target selection and acceleration coefficient control. PSGN can learn the actions that should be taken in each environment through rewarding or punishing the network by reinforcement learning. Thus, PSGN is capable of tackling DMOPs of various dynamics. Additionally, we efficiently adjust PSGN hidden nodes and update the output weights in an incremental learning way, enabling PSGN to direct particle search at a low computational cost. We compare the proposed PSGN with seven state-of-the-art algorithms, and the excellent performance of PSGN verifies that it can handle DMOPs of various dynamics in a computationally very efficient way.

Dynamic constrained multiobjective optimization involves irregular changes in the distribution of the true Pareto-optimal fronts, drastic changes in the feasible region caused by constraints, and the movement directions and magnitudes of the optimal distance variables due to diverse changing environments. To solve these problems, we propose a multi-population evolution based dynamic constrained multiobjective optimization algorithm. In this algorithm, we design a tribe classification operator to divide the population into different tribes according to a feasibility check and the objective values, which is beneficial for driving the population toward the feasible region and Pareto-optimal fronts. Meanwhile, a population selection strategy is proposed to identify promising solutions from tribes and exploit them to update the population. The optimal values of the distance variables vary differently with dynamic environments, thus, we design a dynamic response strategy for solutions in different tribes that estimates their distances to approach the Pareto-optimal fronts and regenerates a promising population when detecting environmental changes. In addition, a scalable generator is designed to simulate diverse movement directions and magnitudes of the optimal distance variables in real-world problems under dynamic environments, obtaining a set of improved test problems. Experimental results show the effectiveness of test problems, and the proposed algorithm is impressively competitive with several chosen state-of-the-art competitors.

Dynamic constrained multiobjective optimization problems (DCMOPs) abound in real-world applications and gain increasing attention in the evolutionary computation community. To evaluate the capability of an algorithm in solving DCMOPs, artificial test problems play a fundamental role. Nevertheless, some characteristics of real-world scenarios are not fully considered in the previous test suites, such as time-varying size, location and shape of feasible regions, the controllable change severity, as well as small feasible regions. Therefore, we develop the generators of objective functions and constraints to facilitate the systematic design of DCMOPs, and then a novel test suite consisting of nine benchmarks, termed as DCP, is put forward. To solve these problems, a dynamic constrained multiobjective evolutionary algorithm with a two-stage diversity compensation strategy (TDCEA) is proposed. Some initial individuals are randomly generated to replace historical ones in the first stage, improving the global diversity. In the second stage, the increment between center points of Pareto sets in the past two environments is calculated and employed to adaptively disturb solutions, forming an initial population with good diversity for the new environment. Intensive experiments show that the proposed test problems enable a good understanding of strengths and weaknesses of algorithms, and TDCEA outperforms other state-of-the-art comparative ones, achieving promising performance in tackling DCMOPs.

In recent years, researchers have made significant progress in handling dynamic multiobjective optimization problems (DMOPs), particularly for environmental changes with predictable characteristics. However, little attention has been paid to DMOPs with stochastic changes. It may be difficult for existing dynamic multiobjective evolutionary algorithms (DMOEAs) to effectively handle this kind of DMOPs because most DMOEAs assume that environmental changes follow regular patterns and consecutive environments are similar. This article presents a Mahalanobis distance-based approach (MDA) to deal with DMOPs with stochastic changes. Specifically, we make an all-sided assessment of search environments via Mahalanobis distance on saved information to learn the relationship between the new environment and historical ones. Afterward, a change response strategy applies the learning to the new environment to accelerate the convergence and maintain the diversity of the population. Besides, the change degree is considered for all decision variables to alleviate the impact of stochastic changes on the evolving population. An MDA has been tested on stochastic DMOPs with two to four objectives. The results show that MDA performs significantly better than the other latest algorithms in this article, suggesting that MDA is effective for DMOPs with stochastic changes.

Location-routing problems (LRPs) widely exist in logistics activities. For the biomass waste collection, there is a recognized need for novel models to locate the collection facilities and plan the vehicle routes. So far most location-routing models fall into the cost-driven-only category. However, comprehensive objectives are required in the specific context, such as time-dependent pollution and speed- and load-related emission. Furthermore, LRPs are hierarchical by nature, containing the facility location problems (strategic level) and the vehicle routing problems (VRPs) (tactical level). Existing studies in this field usually adopt computational intelligence methods directly without decomposing the problem. This can be inefficient especially when multiple objectives are applied. Motivated by these, we develop a novel multiobjective optimization model for the LRP for biomass waste collection. To solve this model, we explore the way to tailor evolutionary algorithms to the hierarchical structure. We develop adapted versions of two commonly used evolutionary algorithms: 1) the genetic algorithm and 2) the ant colony optimization algorithm. For the genetic algorithm, we divide the population by the strategic level decisions, so that each subpopulation has a fixed location plan, breaking the LRP down into many multidepot VRPs. For the ant colony optimization, we use an additional pheromone vector to track the good decisions on the location level, and segregate the pheromones related to different satellite depots to avoid misleading information. Thus, the problem degenerates into VRP. Experimental results show that our proposed methods have better performances on the LRP for biomass waste collection.

Maintaining the diversity of the decision space is of great significance in multimodal multiobjective optimization problems (MMOPs). Since the traditional Pareto-dominance-based algorithms prioritize the convergence of individuals by the Pareto-dominated sorting, it will face a phenomenon that a large number of well-distributed individuals could be dominated by other well-converged individuals during the optimization of MMOPs. To solve this problem, we propose a dynamic-niching-based Pareto domination, called DNPD, which adds a dynamic niche to constrain the tranditional Pareto dominantion to achieve a balance of convergence and diversity of population in the decision space. In the early stage of the algorithm, the smaller niche makes the algorithm retain a large number of well-distributed individuals. In the later stage of the algorithm, the dynamically increased niche accelerates the convergence of the population. DNPD can be integrated into the Pareto-dominance-based algorithms to solve MMOPs. Experimental results show that the DNPD performs well on MMF and IDMP series benchmark functions after comparing the original algorithm with the original algorithm combined with the DNPD.

In science and engineering, multiobjective optimization problems (MOPs) usually contain multiple complex constraints, which poses a significant challenge in obtaining the optimal solution. This article aims to solve the challenges brought by multiple complex constraints. First, this article analyzes the relationship between single-constrained Pareto front (SCPF) and their common Pareto front (PF) subconstrained PF (SubCPF). Next, we discussed the SCPF, SubCPF, and unconstraint PF (UPF)’s help to solve constraining PF (CPF). Then, further discusses what kind of cooperation should be used between multiple populations constrained multiobjective optimization algorithm (CMOEA) to better deal with multiconstrained MOPs (mCMOPs). At the same time, based on the discussion in this article, we propose a new multipopulation CMOEA called MCCMO, which uses a new cooperation mechanism. MCCMO uses C+2 (C is the number of constraints) populations to find the UPF, SCPF, and SubCPF at an appropriate time. Furthermore, MCCMO uses the newly proposed activation dormancy detection (ADD) to accelerate the optimization process and uses the proposed combine occasion detection (COD) to find the appropriate time to find the SubCPF. The performance on 32 mCMOPs and real-world mCMOPs shows that our algorithm can obtain competitive solutions on MOPs with multiple constraints.

Incomplete multiview data are collected from multiple sources or characterized by multiple modalities, where the features of some samples or some views may be missing. Incomplete multiview clustering (IMVC) aims to partition the data into different groups by taking full advantage of the complementary information from multiple incomplete views. Most existing methods based on matrix factorization or subspace learning attempt to recover the missing views or perform imputation of the missing features to improve clustering performance. However, this problem is intractable due to a lack of prior knowledge, e.g., label information or data distribution, especially when the missing views or features are completely damaged. In this article, we proposed an augmented sparse representation (ASR) method for IMVC. We first introduce a discriminative sparse representation learning (DSRL) model, which learns the sparse representations of multiple views as applied to measure the similarity of the existing features. The DSRL model explores complementary and consistent information by integrating the sparse regularization item and a consensus regularization item, respectively. Simultaneously, it learns a discriminative dictionary from the original samples. The sparsity constrained optimization problem in the DSRL model can be efficiently solved by the alternating direction method of multipliers (ADMM). Then, we present a similarity fusion scheme, namely, a sparsity augmented fusion of sparse representations, to obtain a sparsity augmented similarity matrix across different views for spectral clustering. Experimental results on several datasets demonstrate the effectiveness of the proposed ASR method for IMVC.

This article focuses on multitask selective maintenance (SM) for multistate complex systems, with the goal of selecting subsets of feasible maintenance actions on multitask systems simultaneously due to limited resources. For each task, system characteristic comprises of various configurations, such as series, parallel, bridge, and complex, Weibull distribution, and multiple states; maintenance characteristic includes perfect maintenance, imperfect maintenance (IM), and minimal repair. Considering these realistic issues, this article introduces a reliability evaluation approach, including Markov chain, universal generating function, and IM age reduction model. The challenge of solving such kind of problems lies not only in the reliability estimation, but also in the solution method. Since it is the first time to solve the multitask SM problem, this article tailors a novel multifactorial evolutionary algorithm, with an improved associate mating. In our algorithm, a similarity-based task selection mechanism tries to determine the intensity between intertask self-evolution and intertask knowledge transfer, based on the relatedness between tasks; a feedback-based task transfer mechanism adjusts the transfer intensity, with regard to convergence and diversity. Numerical experiments verify the effectiveness of the proposed method compared with the original one.

In dynamic optimization problems (DOPs), environmental changes can be characterized as various dynamics. Faced with different dynamics, existing dynamic optimization algorithms (DOAs) are difficult to tackle, because they are incapable of learning in each environment to control the search. Besides, diversity loss is a critical issue in solving DOPs. Maintaining a high-diversity over dynamic environments is reasonable as it can address such an issue automatically. In this article, we propose a particle search control network (PSCN) to maintain a high-diversity over time and control two key search actions of each input individual, i.e., locating the local learning target and adjusting the local acceleration coefficient. Specifically, PSCN adequately considers the diversity to generate subpopulations located by hidden node centers, where each center is assessed by significance-based criteria and distance-based criteria. The former enable a small intrasubpopulation distance and a big search scope (subpopulation width) for each subpopulation, while the latter make each center distant from other existing centers. In each subpopulation, the best-found position is selected as the local learning target. In the output layer, PSCN determines the action of adjusting the local acceleration coefficient of each individual. Reinforcement learning is introduced to obtain the desired output of PSCN, enabling the network to control the search by learning in different iterations of each environment. The experimental results especially performance comparisons with eight state-of-the-art DOAs demonstrate that PSCN brings significant improvements in performance of solving DOPs.

Environmental selection is an important process in multi-objective evolutionary algorithms (MOEAs). As the evolution progresses, the number of non-dominated solutions increases. This paper is focused on selecting a subset from excess non-dominated solutions for evolutionary or the final output. However, traditional selection methods in classical MOEAs encounter difficulties when dealing with candidate solutions that possess irregular topologies. Although the distance-based subset selection methods are not sensitive to the topologies of the candidate points, they have significant room for reducing computational complexity. In order to address the above issues, a subspace selection method is proposed in this paper. It partitions the objective space into multiple subspaces that have comparable volumes and shapes. The maximal minimum distance of each solution is considered to ensure that the sparsest solution is always chosen first. To save computational costs, only the solutions in the neighboring subspaces are taken into account. The experimental results demonstrate that the proposed subspace selection method outperforms classical selection methods in solving problems with various shapes of the Pareto front.

With increasing people who suffer from diet-related diseases, providing suggestions for personal daily nutrient-dense intake is highly expected. However, current dietary nutrition models are less precise, and dietary nutrition optimizers usually fail to give satisfactory solutions. Therefore, we construct a constrained many-objective nutrition model with more precise nutrient assessments and a scalable constrained many-objective benchmark set. This test suite has great flexibility in evaluating algorithms' performance on high dimensional search and objective spaces with some feasible region fragments. We also propose a kd-tree based dynamic constrained many-objective evolutionary algorithm to search for customized food combinations according to personal daily consumption and intake preference. Experiments show that our algorithm has better diversity maintenance ability in high dimension space.

Uncertainty is a practical issue in system design optimization because some characteristics of components, such as reliability and cost, cannot be determined precisely in many situations. Considering the imprecise characteristics of components, few works have focused on the multi-objective optimization for the redundancy allocation due to the challenges of comparing multi intervals. To tackle the issue, a novel angle-based bi- objective redundancy allocation algorithm is proposed in this study, introducing three original contributions: 1) An angle-based interval crowding distance (ICA) is especially designed for effective performance and reduced computational time; 2) Two techniques are applied to tackle the problem: An elite selection for mutation is presented for generating better offsprings; A penalty-guided constraint handling technique is introduced for converting the problem into an unconstrained one. 3) Since a set of optimal solutions is obtained by the proposed method and no preference on uncertainties is provided, this paper proposes a novel knee interval method to help DMs make a decision. To be specific, the proposed ICA can describe the distribution of the whole population intuitively and effectively, considering not only the angle between two compared individuals but also the angle range of the interval values. The computational results from two typical experiments demonstrate that the proposed algorithm is more efficient than other state-of-the-art algorithms, generating Pareto sets with less repeating individuals, stronger convergence, wider distribution, less imprecision, and reduced computational time. Note to Practitioners—This article is motivated by two practical problems in multi-objective redundancy allocation in presence of interval uncertainty: First, this paper tries to solve the multi-objective redundancy allocation problem with the imprecise characteristics of components, which is rarely considered in the field of reliability optimization design. Second, the calculation of the crowding distance needs extra time cost and is less efficient. To tackle this issue, an interval crowding angle is especially designed, considering not only the angle between two compared individuals, but also the angle range of the interval values. The proposed method can be embedded in most multi-objective interval evolutionary algorithms to compute the diversity of the individuals. The goal of this study is to allocate the economy and high-reliable components for practitioners. The computational results verify its effectiveness and efficiency. Besides, in many cases the practitioners know only few or no preferences, this paper proposes a knee point analysis of interval values that allows practitioners to select the optimal solution with large hypervolume and less imprecision among a set of solutions.

Data streams are a potentially unbounded sequence of data objects, and the clustering of such data is an effective way of identifying their underlying patterns. Existing data stream clustering algorithms face two critical issues: 1) evaluating the relationship among data objects with individual landmark windows of fixed size and 2) passing useful knowledge from previous landmark windows to the current landmark window. Based on sparse representation techniques, this article proposes a two-stage sparse representation clustering (TSSRC) method. The novelty of the proposed TSSRC algorithm comes from evaluating the effective relationship among data objects in the landmark windows with an accurate number of clusters. First, the proposed algorithm evaluates the relationship among data objects using sparse representation techniques. The dictionary and sparse representations are iteratively updated by solving a convex optimization problem. Second, the proposed TSSRC algorithm presents a dictionary initialization strategy that seeks representative data objects by making full use of the sparse representation results. This efficiently passes previously learned knowledge to the current landmark window over time. Moreover, the convergence and sparse stability of TSSRC can be theoretically guaranteed in continuous landmark windows under certain conditions. Experimental results on benchmark datasets demonstrate the effectiveness and robustness of TSSRC.

In traditional data stream mining, classification models are typically trained on labeled samples from a single source. However, in real-world scenarios, obtaining accurate labels is very hard and expensive, especially, when multiple data streams are concurrently sampled from an environment or the same process. To address this issue, multistream classification is proposed, in which a data stream with biased labels (called the source stream) is leveraged to train a suitable model for prediction over another stream with unlabeled samples (called the target stream). Despite the growing research in this field, previous multistream classification methods are mostly designed for single-source stream scenarios. However, various source streams contain diverse data distributions, providing more valuable information for building a more accurate model. In addition, previous works construct classification models in the original shared feature space, ignoring the effect of redundant or low-quality features on the classification performance. This may produce inefficient knowledge transfer across streams. In view of this, a reduced-space multistream classification based on multiobjective evolutionary optimization is proposed in this article. First, a multiobjective evolutionary optimization is employed to seek the most valuable feature subset shared in the source and target domains, with the purpose of narrowing the distribution difference between source and target streams. Following that, a Gaussian mixture model-based weighting mechanism for source samples is presented. More especially, two drift adaptation methods are proposed to address asynchronous drift. Experimental results on benchmark datasets show that the proposed method outperforms other comparative methods on classification accuracy and G-mean.

There are usually multiple constraints in constrained multiobjective optimization. Those constraints reduce the feasible area of the constrained multiobjective optimization problems (CMOPs) and make it difficult for current multiobjective optimization algorithms (CMOEAs) to obtain satisfactory feasible solutions. In order to solve this problem, this article studies the relationship between constraints, then obtains the priority between constraints according to the relationship between the pareto front (PF) of the single constraint and their common PF. Meanwhile, this article proposes a multistage CMOEA and applies this priority, which can save computing resources while helping the algorithm converge. The proposed algorithm completely abandons the feasibility in the early stage to better explore the objective space, and obtains the priority of constraints according to the relationship. Then, the algorithm evaluates a single constraint in the medium stage to further explore the objective space according to this priority, and abandons the evaluation of some less important constraints according to the relationship to save the evaluation times. At the end stage of the algorithm, the feasibility will be fully considered to improve the quality of the solutions obtained in the first two stages, and finally get the solutions with good convergence, feasibility, and diversity. The results on five CMOP suites and three real-world CMOPs show that the algorithm proposed in this article can have strong competitiveness in existing constrained multiobjective optimization.

Although evolutionary computing (EC) methods are stochastic optimization methods, it is usually difficult to find the global optimum by restarting the methods when the population converges to a local optimum. A major reason is that many optimization problems have basins of attraction (BoAs) that differ widely in shape and size, and the population always prefers to converge toward BoAs that are easy to search. Although heuristic restart based on tabu search is a theoretically feasible idea to solve this problem, existing EC methods with heuristic restart are difficult to avoid repetitive search results while maintaining search efficiency. This article tries to overcome the dilemma by online learning the BoAs and proposes a search mode called history-guided hill exploration (HGHE). In the search mode, evaluated solutions are used to help separate the search space into hill regions which correspond to the BoAs, and a classical EC method is used to locate the optimum in each hill region. An instance algorithm for continuous optimization named HGHE differential evolution (HGHE-DE) is proposed to verify the effectiveness of HGHE. Experimental results prove that HGHE-DE can continuously discover unidentified BoAs and locate optima in identified BoAs.

In large-scale multiobjective optimization, too many decision variables hinder the convergence search of evolutionary algorithms. Reducing the search range of the decision space will significantly alleviate this puzzle. With this in mind, this article proposes a fuzzy decision variables framework for large-scale multiobjective optimization. The framework divides the entire evolutionary process into two main stages: 1) fuzzy evolution and 2) precise evolution. In fuzzy evolution, we blur the decision variables of the original solution to reduce the search range of the evolutionary algorithm in the decision space so that the evolutionary population can quickly converge. The degree of fuzzification gradually decreases with the evolutionary process. Once the population approximately converges, the framework will turn to precise evolution. In precise evolution, the actual decision variables of the solution are directly optimized to increase the diversity of the population so as to be closer to the true Pareto optimal front. Finally, this article embeds some representative algorithms into the proposed framework and verifies the framework’s effectiveness through comparative experiments on various large-scale multiobjective problems with 500 to 5000 decision variables. The experimental results show that in large-scale multiobjective optimization, the framework proposed in this article can significantly improve the performance and computational efficiency of multiobjective optimization algorithms.

Ensemble techniques are a powerful method for recognising and reacting to changes in non-stationary data. However, most researches into dynamic classification with ensembles assume that the true class label of each incoming point is available or easily obtained. This is unrealistic in most practical applications, especially in high-velocity streams where manually labeling each point is prohibitively expensive. To address this challenge, this paper proposes an algorithm, named Clustering and One-Class Classification Ensemble Learning (COCEL), which incorporates a stream clustering algorithm and an ensemble of one-class classifiers with active learning, for classification in dynamic data streams. The method exploits the intuitive relationship between clusters and one-class classifiers to cope with a small training set (or no training set) and improve with experience, self-modifying its internal state to cope with changes in the data stream. The proposed method is evaluated on synthetic data streams exhibiting concept evolution and concept drift and a collection of high-velocity real data streams where manually labeling each incoming point is infeasible or expensive and labor intensive. Finally, a comparative evaluation with peer stream classification ensembles shows that COCEL can achieve superior or comparative accuracy while typically requiring less than 0.01% of the stream labels.

Due to the capability of effectively learning intrinsic structures from high-dimensional data, techniques based on sparse representation have begun to display an impressive impact on several fields, such as image processing, computer vision, and pattern recognition. Learning sparse representations isoften computationally expensive due to the iterative computations needed to solve convex optimization problems in which the number of iterations is unknown before convergence. Moreover, most sparse representation algorithms focus only on determining the final sparse representation results and ignore the changes in the sparsity ratio (SR) during iterative computations. In this article, two algorithms are proposed to learn sparse representations based on locality-constrained linear representation learning with probabilistic simplex constraints. Specifically, the first algorithm, called approximated local linear representation (ALLR), obtains a closed-form solution from individual locality-constrained sparse representations. The second algorithm, called ALLR with symmetric constraints (ALLRSC), further obtains a symmetric sparse representation result with a limited number of computations; notably, the sparsity and convergence of sparse representations can be guaranteed based on theoretical analysis. The steady decline in the SR during iterative computations is a critical factor in practical applications. Experimental results based on public datasets demonstrate that the proposed algorithms perform better than several state-of-the-art algorithms for learning with high-dimensional data.

In complex optimization problems, learning where to search is a difficult but critical decision for all search algorithms. Evolutionary computation methods also encounter a dilemma about where to explore or exploit. In this paper, a Monte-Carlo tree is constructed to guide evolutionary algorithms to search multiple promising regions simultaneously. In the Monte-Carlo tree model, a root node that contains all historical solutions represents the whole solution space. In each node of the tree, with k-means clustering method to partition solutions into different groups, group labels of the solutions are used to train support vector regression, which can learn a boundary to partition a region into different sub-regions. According to state values of nodes, reproduction operators of evolutionary algorithms are strengthened by selecting solutions in the most promising regions. From experimental results on multimodal problems, the proposed algorithm shows a competitive performance, which also indicates a great potential for applications to other kinds of optimization problems.

The main challenge in studying constrained multi-objective optimization problems (CMOPs) is reasonably balancing convergence, diversity, and feasibility. One of the most successful solutions to this challenge is the co-evolutionary frame-work, an algorithm in which multiple populations cooperate and complement each other, with different but interdependent populations addressing different but related problems. However, the effectiveness of existing algorithms for information exchange between various populations is not apparent. This paper proposes a new algorithm named SDKT using population state detection and knowledge transfer. The method has dual stages (i.e., knowledge acquisition and knowledge reception) and dual populations. Specifically, by restarting the strategy, these two populations (i.e., mainPop and auxPop) first explore more feasible regions with and without constraints. Then, in the knowledge receiving stage, ma i nPop and auxPop provide effective information to promote each other's approach to constrained PF (CPF) and unconstrained PF (UPF), respectively. Extensive experiments on three well-known test suites and three real-world problem studies fully demonstrate that SDKT is more competitive than five state-of-the-art constrained multi-objective evolutionary algorithms.

Data stream clustering provides valuable insights into the evolving patterns of long sequences of continuously generated data objects. Most existing clustering methods focus on single-view data streams. In this paper, we propose a multi-view representation learning (MVRL) method for multi-view clustering of data streams. We first introduce an integrated representation learning model to learn a fused sparse affinity matrix across multiple views for spectral clustering. Motivated by the optimization procedure of the integrated representation learning model, we propose three consecutive stages: collaborative representation, the construction of individual global affinity matrices using a mapping function, and the calculation of a fused sparse affinity matrix using Euclidean projection. These stages allow the effective capture of the global and local structures of high-dimensional data objects. Moreover, each stage has a closed-form solution, which determines the upper bound of the computational cost and memory consumption. We then employ the construction residuals of the collaborative representation to adaptively update a dynamic set, which is used to preserve the representative data objects. The dynamic set efficiently transfers previously learned useful knowledge to the arriving data objects. Extensive experimental results on multi-view data stream datasets demonstrate the effectiveness of the proposed MVRL method.

Change is one of the biggest challenges in dynamic stream mining. From a data-mining perspective, adaptingand trackingchange is desirable in order to understand how and why change has occurred. Clustering, a form of unsupervised learning, can be used to identify the underlying patterns in a stream. Density-based clustering identifies clusters as areas of high density separated by areas of low density. This paper proposes a Multi-Density Stream Clustering (MDSC) algorithm to address these two problems; the multi-density problem and the problem of discovering and tracking changes in a dynamic stream. MDSC consists of two on-line components; discovered, labelled clusters and an outlier buffer. Incoming points are assigned to a live cluster or passed to the outlier buffer. New clusters are discovered in the buffer using an ant-inspired swarm intelligence approach. The newly discovered cluster is uniquely labelled and added to the set of live clusters. Processed data is subject to an ageing function and will disappear when it is no longer relevant. MDSC is shown to perform favourably to state-of-the-art peer stream-clustering algorithms on a range of real and synthetic data-streams. Experimental results suggest that MDSC can discover qualitatively useful patterns while being scalable and robust to noise.

Multiview subspace clustering is one of the most widely used methods for exploiting the internal structures of multiview data. Most previous studies have performed the task of learning multiview representations by individually constructing an affinity matrix for each view without simultaneously exploiting the intrinsic characteristics of multiview data. In this article, we propose a multiview low-rank representation (MLRR) method to comprehensively discover the correlation of multiview data for multiview subspace clustering. MLRR considers symmetric low-rank representations (LRRs) to be an approximately linear spatial transformation under the new base, that is, the multiview data themselves, to fully exploit the angular information of the principal directions of LRRs, which is adopted to construct an affinity matrix for multiview subspace clustering, under a symmetric condition. MLRR takes full advantage of LRR techniques and a diversity regularization term to exploit the diversity and consistency of multiple views, respectively, and this method simultaneously imposes a symmetry constraint on LRRs. Hence, the angular information of the principal directions of rows is consistent with that of columns in symmetric LRRs. The MLRR model can be efficiently calculated by solving a convex optimization problem. Moreover, we present an intuitive fusion strategy for symmetric LRRs from the perspective of spectral clustering to obtain a compact representation, which can be shared by multiple views and comprehensively represents the intrinsic features of multiview data. Finally, the experimental results based on benchmark datasets demonstrate the effectiveness and robustness of MLRR compared with several state-of-the-art multiview subspace clustering algorithms.

In recent years, dynamic multiobjective optimization problems (DMOPs) have drawn increasing interest. Many dynamic multiobjective evolutionary algorithms (DMOEAs) have been put forward to solve DMOPs mainly by incorporating diversity introduction or prediction approaches with conventional multiobjective evolutionary algorithms. Maintaining a good balance of population diversity and convergence is critical to the performance of DMOEAs. To address the above issue, a DMOEA based on decision variable classification (DMOEA-DVC) is proposed in this article. DMOEA-DVC divides the decision variables into two and three different groups in static optimization and changes response stages, respectively. In static optimization, two different crossover operators are used for the two decision variable groups to accelerate the convergence while maintaining good diversity. In change response, DMOEA-DVC reinitializes the three decision variable groups by maintenance, prediction, and diversity introduction strategies, respectively. DMOEA-DVC is compared with the other six state-of-the-art DMOEAs on 33 benchmark DMOPs. The experimental results demonstrate that the overall performance of the DMOEA-DVC is superior or comparable to that of the compared algorithms.

This article proposes an adaptive localized decision variable analysis approach under the decomposition-based framework to solve the large-scale multiobjective and many-objective optimization problems (MaOPs). Its main idea is to incorporate the guidance of reference vectors into the control variable analysis and optimize the decision variables using an adaptive strategy. Especially, in the control variable analysis, for each search direction, the convergence relevance degree of each decision variable is measured by a projection-based detection method. In the decision variable optimization, the grouped decision variables are optimized with an adaptive scalarization strategy, which is able to adaptively balance the convergence and diversity of the solutions in the objective space. The proposed algorithm is evaluated with a suite of test problems with 2-10 objectives and 200-1000 variables. Experimental results validate the effectiveness and efficiency of the proposed algorithm on the large-scale multiobjective and MaOPs.

The performance of decomposition-based algorithms is sensitive to the Pareto front shapes since their reference vectors preset in advance are not always adaptable to various problem characteristics with no a priori knowledge. For this issue, this article proposes an adaptive reference vector reinforcement learning (RVRL) approach to decomposition-based algorithms for industrial copper burdening optimization. The proposed approach involves two main operations, that is: 1) a reinforcement learning (RL) operation and 2) a reference point sampling operation. Given the fact that the states of reference vectors interact with the landscape environment (quite often), the RL operation treats the reference vector adaption process as an RL task, where each reference vector learns from the environmental feedback and selects optimal actions for gradually fitting the problem characteristics. Accordingly, the reference point sampling operation uses estimation-of-distribution learning models to sample new reference points. Finally, the resultant algorithm is applied to handle the proposed industrial copper burdening problem. For this problem, an adaptive penalty function and a soft constraint-based relaxing approach are used to handle complex constraints. Experimental results on both benchmark problems and real-world instances verify the competitiveness and effectiveness of the proposed algorithm.

Patient stratification has been studied widely to tackle subtype diagnosis problems for effective treatment. Due to the dimensionality curse and poor interpretability of data, there is always a long-lasting challenge in constructing a stratification model with high diagnostic ability and good generalization. To address these problems, this article proposes two novel evolutionary multiobjective clustering algorithms with ensemble (NSGA-II-ECFE and MOEA/D-ECFE) with four cluster validity indices used as the objective functions. First, an effective ensemble construction method is developed to enrich the ensemble diversity. After that, an ensemble clustering fitness evaluation (ECFE) method is proposed to evaluate the ensembles by measuring the consensus clustering under those four objective functions. To generate the consensus clustering, ECFE exploits the hybrid co-association matrix from the ensembles and then dynamically selects the suitable clustering algorithm on that matrix. Multiple experiments have been conducted to demonstrate the effectiveness of the proposed algorithm in comparison with seven clustering algorithms, twelve ensemble clustering approaches, and two multiobjective clustering algorithms on 55 synthetic datasets and 35 real patient stratification datasets. The experimental results demonstrate the competitive edges of the proposed algorithms over those compared methods. Furthermore, the proposed algorithm is applied to extend its advantages by identifying cancer subtypes from five cancer-related single-cell RNA-seq datasets.

Genetic algorithms (GAs) have been widely applied in Steiner tree optimization problems. However, as the core operation, existing crossover operators for tree-based GAs suffer from producing illegal offspring trees. Therefore, some global link information must be adopted to ensure the connectivity of the offspring, which incurs heavy computation. To address this problem, this article proposes a new crossover mechanism, called leaf crossover (LC), which generates legal offspring by just exchanging partial parent chromosomes, requiring neither the global network link information, encoding/decoding nor repair operations. Our simulation study indicates that GAs with LC outperform GAs with existing crossover mechanisms in terms of not only producing better solutions but also converging faster in networks of varying sizes.

The decomposition-based evolutionary algorithm (MOEA/D) has attained excellent performance in solving optimization problems involving multiple conflicting objectives. However, the Pareto-optimal front (POF) of many multiobjective optimization problems (MOPs) has irregular properties, which weakens the performance of MOEA/D. To address this issue, we devise a dynamic transfer reference point-oriented MOEA/D with local objective-space knowledge (DTR-MOEA/D). The design principle is based on three original and rigorous mechanisms. First, the individuals are projected onto a line segment (two-objective case) or a 3-D plane (three-objective case) after being normalized in the objective space. The line segment or the plane is divided into three different regions: 1) the central region; 2) the middle region; and 3) the edge region. Second, a dynamic transfer criterion of the reference point is developed based on the population density relationships in different regions. Third, a strategy of population diversity enhancement guided by local objective-space knowledge is adopted to improve the diversity of the population. Finally, the experimental results conducted on 16 benchmark MOPs and eight modified MOPs with irregular POF shapes verify that the proposed DTR-MOEA/D has attained a strong competitiveness compared with other representative algorithms.

Mobile edge computing (MEC) is an emerging computing paradigm that decreases the computing time and extends the lifespan of user equipments (UEs). In MEC, the computational tasks are offloaded from UEs to the base station (BS) at the edge of the network for processing. However, MEC cannot cope with environments where there are no BS or where communication facilities have been destroyed. In this paper, we study the problem of minimizing the energy consumption of UAV equipped with MEC servers as a mobile base station to serve users. The problem involves user offloading decision, UAV location and allocation with computational resources, and is a hybrid optimization problem with continuous and discrete variables. To address this problem, we propose a hybrid nature-inspired optimization algorithm (HNIO) and its version for discrete optimization, where HNIO incorporates mutation and population diversity detection mechanisms to boost its global optimization capability, and we design a probabilistic selection-based coding strategy for the discrete optimization version. The experimental study is conducted based on ten cases with different numbers of UEs. Comparing HNIO with several other state-of-the-art optimization algorithms, it is concluded from the Friedman and Wilcoxon’s test of the experimental results that HNIO shows better precision and stability in nine out of the ten cases with higher number of UEs.

Single-cell RNA sequencing is a transformative technology that enables us to study the heterogeneity of the tissue at the cellular level. Clustering is used as the key computational approach to group cells under the transcriptome profiles from single-cell RNA-seq data. However, accurate identification of distinct cell types is facing the challenge of high dimensionality, and it could cause uninformative clusters when clustering is directly applied on the original transcriptome. To address such challenge, an evolutionary multiobjective deep clustering (EMDC) algorithm is proposed to identify single-cell RNA-seq data in this study. First, EMDC removes redundant and irrelevant genes by applying the differential gene expression analysis to identify differentially expressed genes across biological conditions. After that, a deep autoencoder is proposed to project the high-dimensional data into different low-dimensional nonlinear embedding subspaces under different bottleneck layers. Then, the basic clustering algorithm is applied in those nonlinear embedding subspaces to generate some basic clustering results to produce the cluster ensemble. To lessen the unnecessary cost produced by those clusterings in the ensemble, the multiobjective evolutionary optimization is designed to prune the basic clustering results in the ensemble, unleashing its cell type discovery performance under three objective functions. Multiple experiments have been conducted on 30 synthetic single-cell RNA-seq datasets and six real single-cell RNA-seq datasets, which reveal that EMDC outperforms eight other clustering methods and three multiobjective optimization algorithms in cell type identification. In addition, we have conducted extensive comparisons to effectively demonstrate the impact of each component in our proposed EMDC.

Modeling dynamic multi-objective optimization problems (DMOPs) has been one of the most challenging tasks in the field of dynamic evolutionary optimization. Based on the analysis of the existing DMOPs, several features widely existed in real-world applications are not taken into account: different objectives may have different function models and variables to be optimized; and the number of conflicting variables should be independent from the number of objectives; the time-linkage property is not considered. In order to overcome the above issues, a novel framework for constructing DMOPs is proposed, where all objectives can be designed independently, and the number of the conflicting variables can be tuned by users. Moreover, it is easy to add new dynamic features to this framework. Several classical dynamic multi-objective optimization algorithms are tested on four scenarios, results show that these characteristics are challenging for the existing algorithms.

In evolutionary algorithms, how to effectively select interactive solutions for generating offspring is a challenging problem. Though many operators are proposed, most of them select interactive solutions (parents) randomly, having no specificity for the features of landscapes in various problems. To address this issue, this paper proposes a reinforcement-learning-based evolutionary algorithm to select solutions within the approximated basin of attraction. In the algorithm, the solution space is partitioned by the k-dimensional tree, and features of subspaces are approximated with respect to two aspects: objective values and uncertainties. Accordingly, two reinforcement learning (RL) systems are constructed to determine where to search: the objective-based RL exploits basins of attraction (clustered subspaces) and the uncertainty-based RL explores subspaces that have been searched comparatively less. Experiments are conducted on widely used benchmark functions, demonstrating that the algorithm outperforms three other popular multimodal optimization algorithms.

Computer aided diagnosis for mammogram images have seen positive results through the usage of deep learning architectures. However, limited sample sizes for the target datasets might prevent the usage of a deep learning model under real world scenarios. The usage of unlabeled data to improve the accuracy of the model can be an approach to tackle the lack of target data. Moreover, important model attributes for the medical domain as model uncertainty might be improved through the usage of unlabeled data. Therefore, in this work we explore the impact of using unlabeled data through the implementation of a recent approach known as MixMatch, for mammogram images. We evaluate the improvement on accuracy and uncertainty of the model using popular and simple approaches to estimate uncertainty. For this aim, we propose the usage of the uncertainty balanced accuracy metric.

In video-based point cloud compression (V-PCC), one geometry video and one color video are generated from a dynamic point cloud. Then, the two videos are compressed independently using a state-of-the-art video coder. In the Moving Picture Experts Group (MPEG) V-PCC test model, the quantization parameters for a given group of frames are constrained according to a fixed offset rule. For example, for the low-delay configuration, the difference between the quantization parameters of the first frame and the quantization parameters of the following frames in the same group is zero by default. We show that the rate-distortion performance of the V-PCC test model can be improved by lifting this constraint and considering the ratedistortion optimization problem as a multi-variable constrained combinatorial optimization problem where the variables are the quantization parameters of all frames. To solve the optimization problem, we use a variant of the differential evolution algorithm. Experimental results for the low-delay configuration show that our method can achieve a Bjøntegaard delta bitrate of up to -43.04% and more accurate rate control (average bitrate error to the target bitrate of 0.45% vs. 10.75%) compared to the state-of- the-art method, which optimizes the rate-distortion performance subject to the test model default offset rule. We also show that our optimization strategy can be used to improve the rate-distortion performance of two-dimensional video coders.

Objectives optimization and constraints satisfaction are two equally important goals to solve constrained many-objective optimization problems (CMaOPs). However, most existing studies for CMaOPs can be classified as feasibility-driven-constrained many-objective evolutionary algorithms (CMaOEAs), and they always give priority to satisfy constraints, while ignoring the maintenance of the population diversity for dealing with conflicting objectives. Consequently, the population may be pushed toward some locally feasible optimal or locally infeasible areas in the high-dimensional objective space. To alleviate this issue, this article presents a problem transformation technique, which transforms a CMaOP into a dynamic CMaOP (DCMaOP) for handling constraints and optimizing objectives simultaneously, to help the population cross the large and discrete infeasible regions. The well-known reference-point-based NSGA-III is tailored under the problem transformation model to solve CMaOPs, namely, DCNSGA-III. In this article, ε -feasible solutions play an important role in the proposed algorithm. To this end, in DCNSGA-III, a mating selection mechanism and an environmental selection operator are designed to generate and choose high-quality ε -feasible offspring solutions, respectively. The proposed algorithm is evaluated on a series of benchmark CMaOPs with three, five, eight, ten, and 15 objectives and compared against six state-of-the-art CMaOEAs. The experimental results indicate that the proposed algorithm is highly competitive for solving CMaOPs.

Robust optimization Over Time (ROOT) is a new method of solving Dynamic optimization Problems in respect to choosing a robust solution, that would last over a number of environment changes, rather than the approach that chooses the optimal solution at every change. ROOT methods currently show that ROOT can be solved by predicting an individual fitness for a number of future environment changes. In this work, a benchmark problem based on the Modified Moving Peaks Benchmark (MMPB) is proposed that includes an attractor heuristic, that guides optima to a determined location in the environment, resulting in a more predictable optimum. We study a number of time series forecasting methods to test different prediction methods of future fitness values in a ROOT method. Four time series regression techniques are considered as the prediction method: Linear and Quadratic Regression, an Autoregressive model, and Support Vector Regression. We find that there is not much difference in choosing a simple Linear Regression to more advanced prediction methods. We also suggest that current benchmark problems that cannot be predicted will deceive the optimizer and ROOT framework as the peaks may move using a random walk. Results show an improvement in comparison with MMPB used in most ROOT studies.

Some real-world optimization problems involve multiple decision makers holding different positions, each of whom has multiple conflicting objectives. These problems are defined as multiparty multiobjective optimization problems (MPMOPs). Although evolutionary multiobjective optimization has been widely studied for many years, little attention has been paid to multiparty multiobjective optimization in the field of evolutionary computation. In this paper, a class of MPMOPs, that is, MPMOPs having common Pareto optimal solutions, is addressed. A benchmark for MPMOPs, obtained by modifying an existing dynamic multiobjective optimization benchmark, is provided, and a multiparty multiobjective evolutionary algorithm to find the common Pareto optimal set is proposed. The results of experiments conducted using the benchmark show that the proposed multiparty multiobjective evolutionary algorithm is effective.

The explosion in the number of electric vehicles (EVs) has had a significant impact on the energy systems and structures of cities. Large-scale EVs inevitably increase the load on the grid, while uncoordinated vehicle to Grid (V2G) technologies pose challenges to the stability and security of the grid. This paper introduces a global intelligent method to find optimal cooperation charging/discharging strategies for EVs to minimize the operation cost. EVs aggregates co-ordinate the energy information and needs of all EVs and use real-time pricing based on micro-grid loads to influence EV charge-discharge behavior. Particle swarm optimization (PSO) is introduced to solve the EV scheduling problem. This study also discusses the negative impact on the energy system of different strategies for charging EVs. Simulation shows that this smart charging strategy and improved PSO can effectively decrease the operation cost of EVs and reduce the load for each micro-grid.

Coronavirus (Covid-19) is spreading fast, infecting people through contact in various forms including droplets from sneezing and coughing. Therefore, the detection of infected subjects in an early, quick and cheap manner is urgent. Currently available tests are scarce and limited to people in danger of serious illness. The application of deep learning to chest X- ray images for Covid-19 detection is an attractive approach. However, this technology usually relies on the availability of large labelled datasets, a requirement hard to meet in the context of a virus outbreak. To overcome this challenge, a semi-supervised deep learning model using both labelled and unlabelled data is proposed. We develop and test a semi-supervised deep learning framework based on the Mix Match architecture to classify chest X-rays into Covid-19, pneumonia and healthy cases. The presented approach was calibrated using two publicly available datasets. The results show an accuracy increase of around 15% under low labelled / unlabelled data ratio. This indicates that our semi-supervised framework can help improve performance levels towards Covid-19 detection when the amount of high-quality labelled data is scarce. Also, we introduce a semi-supervised deep learning boost coefficient which is meant to ease the scalability of our approach and performance comparison.

Photostimulable Phosphor Plates are commonly used in digital X-ray imaging for dentistry. During its usage, these plates get damaged, influencing the diagnosis performance and confidence of the dentistry professional. We propose a deep learning based classifier to discard or extend the use of photostimulable phosphor (PSP) plates based on their physical damage. The system automatically assesses, for the first time in the literature, when dentists should discard their plates. To validate our methodology, an in-house dataset is built on 25 PSP artifact masks (Carestream, CS 7600) digitally superimposed over 100 Complementary Metal-oxide-semiconductor (CMOS) periapical images (Carestream, RVG 6200) with known radiologic interpretations. From these 2500 images, unique subsets of 100 images were evaluated by 25 dentists to find periapical inflammatory lesions on the tooth. Doctors' opinion on whether the plates should be discarded or not was also collected. State-of-the-art deep convolutional networks were tested using fivefold cross validation, yielding classification accuracies from 87% to almost 89%. Specifically, InceptionV3 and Resnet50 obtained the best performances with statistical significance. Qualitative heat-maps showed that such models can identify and employ artifacts to decide on whether to discard the PSP plate or not. This work intends to be the base line for future works related to the automatic PSP plate assessment.

Population-based evolutionary algorithms have great potential to handle multiobjective optimisation problems . However, the performance of these algorithms depends largely on problem characteristics. There is a need to improve these algorithms for wide applicability. References, often specified by the decision maker’s preference in different forms, are very effective to boost the performance of algorithms. This paper proposes a novel framework for effective use of references to strengthen algorithms. This framework considers references as search targets which can be adjusted based on the information collected during the search. The proposed framework is combined with new strategies, such as reference adaptation and adaptive local mating, to solve different types of problems. The proposed algorithm is compared with state-of-the-arts on a wide range of problems with diverse characteristics. The comparison and extensive sensitivity analysis demonstrate that the proposed algorithm is competitive and robust across different types of problems studied in this paper.

Dynamic multiobjective optimization (DMO) has gained increasing attention in recent years. Test problems are of great importance in order to facilitate the development of advanced algorithms that can handle dynamic environments well. However, many of the existing dynamic multiobjective test problems have not been rigorously constructed and analyzed, which may induce some unexpected bias when they are used for algorithmic analysis. In this paper, some of these biases are identified after a review of widely used test problems. These include poor scalability of objectives and, more important, problematic overemphasis of static properties rather than dynamics making it difficult to draw accurate conclusion about the strengths and weaknesses of the algorithms studied. A diverse set of dynamics and features is then highlighted that a good test suite should have. We further develop a scalable continuous test suite, which includes a number of dynamics or features that have been rarely considered in literature but frequently occur in real life. It is demonstrated with empirical studies that the proposed test suite is more challenging to the DMO algorithms found in the literature. The test suite can also test algorithms in ways that existing test suites cannot.

To promote research on dynamic constrained multiobjective optimization, we first propose a group of generic test problems with challenging characteristics, including different modes of the true Pareto front (e.g., convexity-concavity and connectedness-disconnectedness) and the changing feasible region. Subsequently, motivated by the challenges presented by dynamism and constraints, we design a dynamic constrained multiobjective optimization algorithm with a nondominated solution selection operator, a mating selection strategy, a population selection operator, a change detection method, and a change response strategy. The designed nondominated solution selection operator can obtain a nondominated population with diversity when the environment changes. The mating selection strategy and population selection operator can adaptively handle infeasible solutions. If a change is detected, the proposed change response strategy reuses some portion of the old solutions in combination with randomly generated solutions to reinitialize the population, and a steady-state update method is designed to improve the retained previous solutions. The experimental results show that the proposed test problems can be used to clearly distinguish the performance of algorithms, and that the proposed algorithm is very competitive for solving dynamic constrained multiobjective optimization problems in comparison with state-of-the-art algorithms.

Dynamic interval multiobjective optimization problems (DI-MOPs) are very common in real-world applications. However, there are few evolutionary algorithms (EAs) that are suitable for tackling DI-MOPs up to date. A framework of dynamic interval multiobjective cooperative co-evolutionary optimization based on the interval similarity is presented in this paper to handle DI-MOPs. In the framework, a strategy for decomposing decision variables is first proposed, through which all the decision variables are divided into two groups according to the interval similarity between each decision variable and interval parameters. Following that, two subpopulations are utilized to cooperatively optimize decision variables in the two groups. Furthermore, two response strategies, i.e., a strategy based on the change intensity and a random mutation strategy, are employed to rapidly track the changing Pareto front of the optimization problem. The proposed algorithm is applied to eight benchmark optimization instances as well as a multiperiod portfolio selection problem and compared with five state-of-the-art EAs. The experimental results reveal that the proposed algorithm is very competitive on most optimization instances.

This paper proposes a new prediction-based dynamic multiobjective optimization (PBDMO) method, which combines a new prediction-based reaction mechanism and a popular regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA) for solving dynamic multiobjective optimization problems. Whenever a change is detected, PBDMO reacts effectively to it by generating three subpopulations based on different strategies. The first subpopulation is created by moving nondominated individuals using a simple linear prediction model with different step sizes. The second subpopulation consists of some individuals generated by a novel sampling strategy to improve population convergence as well as distribution. The third subpopulation comprises some individuals generated using a shrinking strategy based on the probability distribution of variables. These subpopulations are tailored to form a population for the new environment. The experimental results carried out on a variety of bi- and three-objective benchmark functions demonstrate that the proposed technique has competitive performance compared with some state-of-the-art algorithms.

This paper proposes a general algorithm framework for solving dynamic sequence optimization problems (DSOPs). The framework adapts a novel genetic learning (GL) algorithm to dynamic environments via a clustering-based multi-population strategy with a memory scheme, namely, multi-population GL (MPGL). The framework is instantiated for a 3D dynamic shortest path problem, which is developed in this paper. Experimental comparison studies show that MPGL is able to quickly adapt to new environments and it outperforms several ant colony optimization variants.

The energy management of the microgrid (MG) with electric vehicles (EVs) is a large-scale optimization problem where the goal should take into account the performance and economic benefits of the power system while meeting the travel needs of EVs. Due to the development of vehicle to grid (V2G) technologies and demand response (DR), the relationship between EVs and MG becomes currently closer, which leads to a more complex situation. Therefore, the relationship of interest between MG and EVs has to be clarified to improve the performance of MG and EVs to achieve a win-win situation. This paper proposes a two-tier energy management strategy that considers the benefits for both MG and EVs. The first layer ensures the performance of the MG, while the second layer reduces the charging cost from the perspective of the car owners. In addition, based on the existence of uncertain parameters, mixed type variables and nonlinear constraints in the optimization problem, the differential evolution, stochastic search and greedy algorithm are used to analyze and find the optimal solution. Simulation results verify the effectiveness of the proposed strategy and solutions, which benefit both the MG and EV owners.

Radio frequency identification technology (RFID) is widely used in identity authentication and payment, and it also becomes an indispensable part of daily life. Cloud-based RFID systems have broad application prospects, and can be provided as a service to individuals or organisations. For example, RFID cards can be used for cash-less payment, physical access control, temporary rights and identification in cloud environment. When an RFID card is used, there is a wireless transaction between the card and its reader, which could be attacked by several methods, including a relay attack. Relay attacks are difficult to completely prevent and a serious threat to RFID systems security. An attacker could use limited resources to build up this kind of attack and may need little knowledge of the underlying protocol. In recent years, researchers have proposed solutions using second channels to resist relay attack, such as using environmental measurements including noise, light and temperature. This paper describes research on the defence techniques for relay attacks in cloudbased RFID systems. The cloud-based architecture for RFID systems typically consists of RFID tags, card readers (fixed or mobile) and cloud-based server functionality.

Environmental changes are traditionally considered intrinsic in evolutionary dynamic optimization. However, by ignoring that changes can instead be induced, we are ignoring that environmental changes can be eventually beneficial. To investigate the impact of artificial changes on the optimization speed up, we propose a framework for inducing artificial changes in any pseudo-Boolean or continuous optimization in this paper. Seven types of changes can be induced. Knowing when and how the changes occur allows us to design new strategies for evolutionary algorithms. Through computational experiments and illustrative examples, the impact of introducing changes in the optimization process is investigated. Experimental results indicate that changing the environments according to the proposed framework can lead to higher speed up, but not for all problems and change types. The best performance was obtained by change types that introduce plateaus and/or modify the gradient of regions of the fitness landscape around the current best solution. By doing this, the evolutionary dynamics is modified, eventually allowing the population to escape faster from local optima and reach new zones of the fitness landscape. Given a pseudo-Boolean or continuous optimization static problem, the proposed framework can be used to dynamically change the problem to speed up the optimization.

A data stream is a continuously arriving sequence of data and clustering data streams requires additional considerations to traditional clustering. A stream is potentially unbounded, data points arrive online and each data point can be examined only once. This imposes limitations on available memory and processing time. Furthermore, streams can be noisy and the number of clusters in the data and their statistical properties can change over time. This paper presents an online, bio-inspired approach to clustering dynamic data streams. The proposed ant colony stream clustering (ACSC) algorithm is a density-based clustering algorithm, whereby clusters are identified as high-density areas of the feature space separated by low-density areas. ACSC identifies clusters as groups of micro-clusters. The tumbling window model is used to read a stream and rough clusters are incrementally formed during a single pass of a window. A stochastic method is employed to find these rough clusters, this is shown to significantly speeding up the algorithm with only a minor cost to performance, as compared to a deterministic approach. The rough clusters are then refined using a method inspired by the observed sorting behavior of ants. Ants pick-up and drop items based on the similarity with the surrounding items. Artificial ants sort clusters by probabilistically picking and dropping micro-clusters based on local density and local similarity. Clusters are summarized using their constituent micro-clusters and these summary statistics are stored offline. Experimental results show that the clustering quality of ACSC is scalable, robust to noise and favorable to leading ant clustering and stream-clustering algorithms. It also requires fewer parameters and less computational time.

In this paper, a novel multiobjective evolutionary algorithm (MOEA/CT) is proposed to better manage convergence and distribution of solutions when MOEAs are used for solving multiobjective optimization problems. The coordinate transformation strategy, an external archive update strategy, and a diversity maintenance strategy are proposed in MOEA/CT. The coordinate transformation strategy in the objective space is designed to find more efficient solutions that can accelerate the convergence process. Based on the coordinate transformation strategy, a novel update strategy and diversity maintenance approach for selecting nondominated solutions from the external archive set are integrated in MOEA/CT for getting better distribution of the solutions. The proposed MOEA/CT is compared with eight state-of-art algorithms on six biobjective and seven tri-objective test problems. In terms of four performance metrics, the comparative experimental results demonstrate that MOEA/CT outperforms the other eight competitors and it can achieve solutions with better distribution and better convergence to the Pareto front. In addition, parameter sensitivity analysis is provided to investigate the effect of a key parameter in MOEA/CT; the proposed three strategies are also studied individually to investigate their contribution to MOEA/CT; the performance analysis along with the capacity of external archive is given to clearly make the influence in MOEA/CT; finally, the scalability performance of MOEA/CT is investigated and compared with five notable many-objective evolutionary algorithms on the DTLZ and WFG test suites with 5, 8, 10, and 15 objectives.

The performance of many nature-inspired optimization algorithms (NIOAs) depends strongly on their implemented coordinate system. However, the commonly used coordinate system is fixed and not well suited for different function landscapes, NIOAs thus might not search efficiently. To overcome this shortcoming, in this paper we propose a framework, named ACoS, to adaptively tune the coordinate systems in NIOAs. In ACoS, an Eigen coordinate system is established by making use of the cumulative population distribution information, which can be obtained based on a covariance matrix adaptation strategy and an additional archiving mechanism. Since the population distribution information can reflect the features of the function landscape to some extent, NIOAs in the Eigen coordinate system have the capability to identify the modality of the function landscape. In addition, the Eigen coordinate system is coupled with the original coordinate system, and they are selected according to a probability vector. The probability vector aims to determine the selection ratio of each coordinate system for each individual, and is adaptively updated based on the collected information from the offspring. ACoS has been applied to two of the most popular paradigms of NIOAs, i.e., particle swarm optimization and differential evolution, for solving 30 test functions with 30D and 50D at the 2014 IEEE Congress on Evolutionary Computation. The experimental studies demonstrate its effectiveness.

For expensive constrained optimization problems (ECOPs), the computation of objective function and constraints is very time-consuming. This paper proposes a novel global and local surrogate-assisted differential evolution (DE) for solving ECOPs with inequality constraints. The proposed method consists of two main phases: 1) global surrogate-assisted phase and 2) local surrogate-assisted phase. In the global surrogate-assisted phase, DE serves as the search engine to produce multiple trial vectors. Afterward, the generalized regression neural network is used to evaluate these trial vectors. In order to select the best candidate from these trial vectors, two rules are combined. The first is the feasibility rule, which at first guides the population toward the feasible region, and then toward the optimal solution. In addition, the second rule puts more emphasis on the solution with the highest predicted uncertainty, and thus alleviates the inaccuracy of the surrogates. In the local surrogate-assisted phase, the interior point method coupled with radial basis function is utilized to refine each individual in the population. During the evolution, the global surrogate-assisted phase has the capability to promptly locate the promising region and the local surrogate-assisted phase is able to speed up the convergence. Therefore, by combining these two important elements, the number of fitness evaluations can be reduced remarkably. The proposed method has been tested on numerous benchmark test functions from three test suites and two real-world cases. The experimental results demonstrate that the performance of the proposed method is better than that of other state-of-the-art methods.

Dynamic multiobjective optimisation deals with multiobjective problems whose objective functions, search spaces, or constraints are time-varying during the optimisation process. Due to wide presence in real-world applications, dynamic multiobjective problems (DMOPs) have been increasingly studied in recent years. Whilst most studies concentrated on DMOPs with only two objectives, there is little work on more objectives. This paper presents an empirical investigation of evolutionary algorithms for three-objective dynamic problems. Experimental studies show that all the evolutionary algorithms tested in this paper encounter performance degradedness to some extent. Amongst these algorithms, the multipopulation based change handling mechanism is generally more robust for a larger number of objectives, but has difficulty in deal with time-varying deceptive characteristics.

Task scheduling is one of the most difficult problems in grid computing systems. Therefore, various studies have been proposed to present methods which provide efficient schedules. Meta-heuristic approaches are among the methods which have proven their efficiency in this domain. However, the literature shows that hybridizing two or more meta-heuristics can improve performance to a greater extent than stand-alone algorithms as the new high-level algorithm will inherit the best features of the hybridized algorithms. In this paper, a loosely coupled hybrid meta-heuristic algorithm is proposed for solving the static independent task scheduling problem in grid computing. It combines ant colony optimization and variable neighborhood search, where the former operates first and whose output is subsequently improved by the latter. The experimental results show that the proposed algorithm achieves better task-machine mapping in terms of minimizing makespan than other selected approaches from the literature.

Multiobjective optimisation in dynamic environments is challenging due to the presence of dynamics in the problems in question. Whilst much progress has been made in benchmarks and algorithm design for dynamic multiobjective optimisation, there is a lack of work on the detectability of environmental changes and how this affects the performance of evolutionary algorithms. This is not intentionally left blank but due to the unavailability of suitable test cases to study. To bridge the gap, this work presents several scenarios where environmental changes are less likely to be detected. Our experimental studies suggest that the less detectable environments pose a big challenge to evolutionary algorithms.

Decomposition-based multiobjective evolutionary algorithms (MOEAs) have received increasing research interests due to their high performance for solving multiobjective optimization problems. However, scalarizing functions (SFs), which play a crucial role in balancing diversity and convergence in these kinds of algorithms, have not been fully investigated. This paper is mainly devoted to presenting two new SFs and analyzing their effect in decomposition-based MOEAs. Additionally, we come up with an efficient framework for decomposition-based MOEAs based on the proposed SFs and some new strategies. Extensive experimental studies have demonstrated the effectiveness of the proposed SFs and algorithm.

Studying the search behavior of evolutionary many-objective optimization is an important, but challenging issue. Existing studies rely mainly on the use of performance indicators which, however, not only encounter increasing difficulties with the number of objectives, but also fail to provide the visual information of the evolutionary search. In this paper, we propose a class of scalable test problems, called multiline distance minimization problem (ML-DMP), which are used to visually examine the behavior of many-objective search. Two key characteristics of the ML-DMP problem are: 1) its Pareto optimal solutions lie in a regular polygon in the 2-D decision space and 2) these solutions are similar (in the sense of Euclidean geometry) to their images in the high-dimensional objective space. This allows a straightforward understanding of the distribution of the objective vector set (e.g., its uniformity and coverage over the Pareto front) via observing the solution set in the 2-D decision space. Fifteen well-established algorithms have been investigated on three types of ten ML-DMP problem instances. Weakness has been revealed across classic multiobjective algorithms (such as Pareto-based, decomposition-based, and indicator-based algorithms) and even state-of-the-art algorithms designed especially for many-objective optimization. This, together with some interesting observations from the experimental studies, suggests that the proposed ML-DMP may also be used as a benchmark function to challenge the search ability of optimization algorithms.

This paper presents a differential evolution algorithm with a new encoding mechanism for efficiently solving the optimal layout of the wind farm, with the aim of maximizing the power output. In the modeling of the wind farm, the wake effects among different wind turbines are considered and the Weibull distribution is employed to estimate the wind speed distribution. In the process of evolution, a new encoding mechanism for the locations of wind turbines is designed based on the characteristics of the wind farm layout. This encoding mechanism is the first attempt to treat the location of each wind turbine as an individual. As a result, the whole population represents a layout. Compared with the traditional encoding, the advantages of this encoding mechanism are twofold: 1) the dimension of the search space is reduced to two, and 2) a crucial parameter (i.e., the population size) is eliminated. In addition, differential evolution serves as the search engine and the caching technique is adopted to enhance the computational efficiency. The comparative analysis between the proposed method and seven other state-of-the-art methods is conducted based on two wind scenarios. The experimental results indicate that the proposed method is able to obtain the best overall performance, in terms of the power output and execution time.

Density based methods have been shown to be an effective approach for clustering non-stationary data streams. The number of clusters does not need to be known a priori and density methods are robust to noise and changes in the statistical properties of the data. However, most density approaches require sensitive, data dependent parameters. These parameters greatly affect the clustering performance and in a dynamic stream a good set of parameters at time t are not necessarily the best at time t+1. Furthermore, these parameters are global and so restrict the algorithm to finding clusters of the same density. In this paper, we propose a density based algorithm with adaptive parameters which are local to each discovered cluster. The algorithm, denoted Ant Colony Multi-Density Clustering (ACMDC), uses artificial ants to form nests in dense areas of the data. As the ants move between nests, their collective memory is stored in the form of pheromone trails. Clusters are identified as groups of similar nests. The proposed algorithm is evaluated across a number of synthetic data streams containing overlapping and embedded multi-density clusters. The performance of the algorithm is shown to be favourable to a leading density based stream-clustering algorithm despite requiring no tunable parameters.

Dynamic multiobjective optimization (DMO) has received growing research interest in recent years since many real-world optimization problems appear to not only have multiple objectives that conflict with each other but also change over time. The time-varying characteristics of these DMO problems (DMOPs) pose new challenges to evolutionary algorithms. Considering the importance of a representative and diverse set of benchmark functions for DMO, in this paper, we propose a new benchmark generator that is able to tune a number of challenging characteristics, including mixed Pareto-optimal front (convexity-concavity), nonmonotonic and time-varying variable-linkages, mixed types of changes, and randomness in type change, which have rarely or not been considered or tested in the literature. A test suite of ten instances with different dynamic features is produced from the generator in this paper. Additionally, a few new performance measures are proposed to evaluate algorithms for DMOPs with different characteristics. Six representative multiobjective evolutionary algorithms from the literature are investigated based on the proposed DMO test suite and performance measures. The experimental results facilitate a better understanding of strengths and weaknesses of these compared algorithms for DMOPs.

For a dynamic traveling salesman problem (DTSP), the weights (or traveling times) between two cities (or nodes) may be subject to changes. Ant colony optimization (ACO) algorithms have proved to be powerful methods to tackle such problems due to their adaptation capabilities. It has been shown that the integration of local search operators can significantly improve the performance of ACO. In this paper, a memetic ACO algorithm, where a local search operator (called unstring and string) is integrated into ACO, is proposed to address DTSPs. The best solution from ACO is passed to the local search operator, which removes and inserts cities in such a way that improves the solution quality. The proposed memetic ACO algorithm is designed to address both symmetric and asymmetric DTSPs. The experimental results show the efficiency of the proposed memetic algorithm for addressing DTSPs in comparison with other state-of-the-art algorithms.

Due to the fact that a nonlinear equation system (NES) may contain multiple optimal solutions, solving NESs is one of the most important challenges in numerical computation. When applying evolutionary algorithms to solve NESs, two issues should be considered: 1) how to transform an NES into a kind of optimization problem and 2) how to develop an optimization algorithm to solve the transformed optimization problem. In this paper, we tackle the first issue by transforming an NES into a weighted biobjective optimization problem. By the above transformation, not only do all the optimal solutions of an original NES become the Pareto optimal solutions of the transformed biobjective optimization problem, but also their images are different points on a linear Pareto front in the objective space. In addition, we suggest an adaptive multiobjective differential evolution, the goal of which is to effectively locate the Pareto optimal solutions of the transformed biobjective optimization problem. Once these solutions are found, the optimal solutions of the original NES can also be obtained correspondingly. By combining the weighted biobjective transformation technique with the adaptive multiobjective differential evolution, we propose a generic framework for the simultaneous locating of multiple optimal solutions of NESs. Comprehensive experiments on 38 NESs with various features have demonstrated that our framework provides very competitive overall performance compared with several state-of-the-art methods.

This paper presents a new algorithm, called steady-state and generational evolutionary algorithm, which combines the fast and steadily tracking ability of steady-state algorithms and good diversity preservation of generational algorithms, for handling dynamic multiobjective optimization. Unlike most existing approaches for dynamic multiobjective optimization, the proposed algorithm detects environmental changes and responds to them in a steady-state manner. If a change is detected, it reuses a portion of outdated solutions with good distribution and relocates a number of solutions close to the new Pareto front based on the information collected from previous environments and the new environment. This way, the algorithm can quickly adapt to changing environments and thus is expected to provide a good tracking ability. The proposed algorithm is tested on a number of bi- and three-objective benchmark problems with different dynamic characteristics and difficulties. Experimental results show that the proposed algorithm is very competitive for dynamic multiobjective optimization in comparison with state-of-the-art methods.

While Pareto-based multiobjective optimization algorithms continue to show effectiveness for a wide range of practical problems that involve mostly two or three objectives, their limited application for many-objective problems, due to the increasing proportion of nondominated solutions and the lack of sufficient selection pressure, has also been gradually recognized. In this paper, we revive an early developed and computationally expensive strength Pareto-based evolutionary algorithm by introducing an efficient reference direction-based density estimator, a new fitness assignment scheme, and a new environmental selection strategy, for handling both multiobjective and many-objective problems. The performance of the proposed algorithm is validated and compared with some state-of-the-art algorithms on a number of test problems. Experimental studies demonstrate that the proposed method shows very competitive performance on both multiobjective and many-objective problems considered in this paper. Besides, our extensive investigations and discussions reveal an interesting finding, that is, diversity-first-and-convergence-second selection strategies may have great potential to deal with many-objective optimization.

In many real-world engineering applications, a uniform design needs to be conducted in a constrained experimental domain that includes linear/nonlinear and inequality/equality constraints. In general, these constraints make the constrained experimental domain small and irregular in the decision space. Therefore, it is difficult for current methods to produce a predefined number of samples and make the samples distribute uniformly in the constrained experimental domain. This paper presents a two-phase differential evolution for uniform designs in constrained experimental domains. In the first phase, considering the constraint violation as the fitness function, a clustering DE is proposed to guide the population toward the constrained experimental domain from different directions promptly. As a result, a predefined number of samples can be obtained in the constrained experimental domain. In the second phase, maximizing the minimum Euclidean distance among samples is treated as another fitness function. By optimizing this fitness function, the samples produced in the first phase can be scattered uniformly in the constrained experimental domain. The performance of the proposed method has been tested and compared with another state-of-the-art method. Experimental results suggest that our method is significantly better than the compared method in the uniform designs of a new type of automotive crash box and five benchmark test problems. Moreover, the proposed method could be considered as a general and promising framework for other uniform designs in constrained experimental domains.

Minimizing the ongoing impact of train delays has benefits to both the users of the railway system and the railway stakeholders. However, the efficient rescheduling of trains after a perturbation is a complex real-world problem. The complexity is compounded by the fact that the problem may be both dynamic and multi-objective. The aim of this research is to investigate the ability of ant colony optimization algorithms to solve a simulated dynamic multi-objective railway rescheduling problem and, in the process, to attempt to identify the features of the algorithms that enable them to cope with a multi-objective problem that is also dynamic. Results showed that, when the changes in the problem are large and frequent, retaining the archive of non-dominated solution between changes and updating the pheromones to reflect the new environment play an important role in enabling the algorithms to perform well on this dynamic multi-objective railway rescheduling problem.

The multiobjective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multiobjective optimization problem into a number of single-objective problems and solves them collaboratively. Since its introduction, MOEA/D has gained increasing research interest and has become a benchmark for validating new designed algorithms. Despite that, some recent studies have revealed that MOEA/D faces some difficulties to solve problems with complicated characteristics. In this paper, we study the influence of the penalty-based boundary intersection (PBI) approach, one of the most popular decomposition approaches used in MOEA/D, on individuals' convergence and diversity, showing that the fixed same penalty value for all the subproblems is not very sensible. Based on this observation, we propose to use adaptive penalty values to enhance the balance between population convergence and diversity. Experimental studies show that the proposed adaptive PBI can generally improve the performance of the original PBI when solving the problems considered in this paper.

Solving constrained multiobjective optimization problems is one of the most challenging areas in the evolutionary computation research community. To solve a constrained multiobjective optimization problem, an algorithm should tackle the objective functions and the constraints simultaneously. As a result, many constraint-handling techniques have been proposed. However, most of the existing constraint-handling techniques are developed to solve test instances (e.g., CTPs) with low dimension and large feasible region. On the other hand, experimental comparisons on different constraint-handling techniques remain scarce. In view of these two issues, in this paper we first construct 18 test instances, each of which exhibits different properties. Afterward, we choose three representative constraint-handling techniques and combine them with nondominated sorting genetic algorithm II to study the performance difference on various conditions. By the experimental studies, we point out the advantages and disadvantages of different constraint-handling techniques.

Differential Evolution (DE) is a popular paradigm of evolutionary algorithms, which has been successfully applied to solve different kinds of optimization problems. To design an effective DE, it is necessary to consider different requirements of the exploration and exploitation at different evolutionary stages. Motivated by this consideration, a new DE with a two-stage optimization mechanism, called TSDE, has been proposed in this paper. In TSDE, based on the number of fitness evaluations, the whole evolutionary process is divided into two stages, namely the former stage and the latter stage. TSDE focuses on improving the search ability in the former stage and emphasizes the convergence in the latter stage. Hence, different trial vector generation strategies have been utilized at different stages. TSDE has been tested on 25 benchmark test functions from IEEE CEC2005 and 30 benchmark test functions from IEEE CEC2014. The experimental results suggest that TSDE performs better than four other state-of-the-art DE variants.

In this paper, the effect of the population size on the performance of the MAX-MIN ant system for dynamic optimization problems (DOPs) is investigated. DOPs are generated with the dynamic benchmark generator for permutation-encoded problems. In particular, the empirical study investigates: a) possible dependencies of the population size parameter with the dynamic properties of DOPs; b) the effect of the population size with the problem size of the DOP; and c) whether a larger population size with less algorithmic iterations performs better than a smaller population size with more algorithmic iterations given the same computational budget for each environmental change. Our study shows that the population size is sensitive to the magnitude of change of the DOP and less sensitive to the frequency of change and the problem size. It also shows that a longer duration in terms of algorithmic iterations results in a better performance.

Train rescheduling after a perturbation is a challenging task and is an important concern of the railway industry as delayed trains can lead to large fines, disgruntled customers and loss of revenue. Sometimes not just one delay but several unrelated delays can occur in a short space of time which makes the problem even more challenging. In addition, the problem is a dynamic one that changes over time for, as trains are waiting to be rescheduled at the junction, more timetabled trains will be arriving, which will change the nature of the problem. The aim of this research is to investigate the application of several different ant colony optimization (ACO) algorithms to the problem of a dynamic train delay scenario with multiple delays. The algorithms not only resequence the trains at the junction but also resequence the trains at the stations, which is considered to be a first step towards expanding the problem to consider a larger area of the railway network. The results show that, in this dynamic rescheduling problem, ACO algorithms with a memory cope with dynamic changes better than an ACO algorithm that uses only pheromone evaporation to remove redundant pheromone trails. In addition, it has been shown that if the ant solutions in memory become irreparably infeasible it is possible to replace them with elite immigrants, based on the best-so-far ant, and still obtain a good performance.

The multiobjective evolutionary algorithm based on decomposition (MOEA/D) has been shown to be very efficient in solving multiobjective optimization problems (MOPs). In practice, the Pareto-optimal front (POF) of many MOPs has complex characteristics. For example, the POF may have a long tail and sharp peak and disconnected regions, which significantly degrades the performance of MOEA/D. This paper proposes an improved MOEA/D for handling such kind of complex problems. In the proposed algorithm, a two-phase strategy (TP) is employed to divide the whole optimization procedure into two phases. Based on the crowdedness of solutions found in the first phase, the algorithm decides whether or not to delicate computational resources to handle unsolved subproblems in the second phase. Besides, a new niche scheme is introduced into the improved MOEA/D to guide the selection of mating parents to avoid producing duplicate solutions, which is very helpful for maintaining the population diversity when the POF of the MOP being optimized is discontinuous. The performance of the proposed algorithm is investigated on some existing benchmark and newly designed MOPs with complex POF shapes in comparison with several MOEA/D variants and other approaches. The experimental results show that the proposed algorithm produces promising performance on these complex problems.

Multipopulation methods are effective in solving dynamic optimization problems. However, to efficiently track multiple optima, algorithm designers need to address a key issue: how to adapt the number of populations. In this paper, an adaptive multipopulation framework is proposed to address this issue. A database is designed to collect heuristic information of algorithm behavior changes. The number of populations is adjusted according to statistical information related to the current evolving status in the database and a heuristic value. Several other techniques are also introduced, including a heuristic clustering method, a population exclusion scheme, a population hibernation scheme, two movement schemes, and a peak hiding method. The particle swarm optimization and differential evolution algorithms are implemented into the framework, respectively. A set of multipopulation-based algorithms are chosen to compare with the proposed algorithms on the moving peaks benchmark using four different performance measures. The effect of the components of the framework is also investigated based on a set of multimodal problems in static environments. Experimental results show that the proposed algorithms outperform the other algorithms in most scenarios.

It is known that Pareto dominance has its own weaknesses as the selection criterion in evolutionary multiobjective optimization. Algorithms based on Pareto criterion (PC) can suffer from problems such as slow convergence to the optimal front and inferior performance on problems with many objectives. Non-Pareto criterion (NPC), such as decomposition-based criterion and indicator-based criterion, has already shown promising results in this regard, but its high selection pressure may lead to the algorithm to prefer some specific areas of the problem's Pareto front, especially when the front is highly irregular. In this paper, we propose a bi-criterion evolution (BCE) framework of the PC and NPC, which attempts to make use of their strengths and compensates for each other's weaknesses. The proposed framework consists of two parts: PC evolution and NPC evolution. The two parts work collaboratively, with an abundant exchange of information to facilitate each other's evolution. Specifically, the NPC evolution leads the PC evolution forward and the PC evolution compensates the possible diversity loss of the NPC evolution. The proposed framework keeps the freedom on the implementation of the NPC evolution part, thus making it applicable for any non-Pareto-based algorithm. In the PC evolution, two operations, population maintenance and individual exploration, are presented. The former is to maintain a set of representative nondominated individuals and the latter is to explore some promising areas that are undeveloped (or not well-developed) in the NPC evolution. Experimental results have shown the effectiveness of the proposed framework. The BCE works well on seven groups of 42 test problems with various characteristics, including those in which Pareto-based algorithms or non-Pareto-based algorithms struggle.

This paper proposes a novel adaptive local search algorithm for tackling real-valued (or continuous) dynamic optimization problems. The proposed algorithm is a simple single-solution based metaheuristic that perturbs the variables separately to select the search direction for the following step and adapts its step size to the gradient. The search directions that appear to be the most promising are rewarded by a step size increase while the unsuccessful moves attempt to reverse the search direction with a reduced step size. When the environment is subject to changes, a new solution is sampled and crosses over the best solution in the previous environment. Furthermore, the algorithm makes use of a small archive where the best solutions are saved. Experimental results show that the proposed algorithm, despite its simplicity, is competitive with complex population-based algorithms for tested dynamic optimization problems.

Increasing interest in simultaneously optimizing many objectives (typically more than three objectives) of problems leads to the emergence of various many-objective algorithms in the evolutionary multi-objective optimization field. However, in contrast to the development of algorithm design, how to assess many-objective algorithms has received scant concern. Many performance indicators are designed in principle for any number of objectives, but in practice are invalid or infeasible to be used in many-objective optimization. In this paper, we explain the difficulties that popular performance indicators face and propose a performance comparison indicator (PCI) to assess Pareto front approximations obtained by many-objective algorithms. PCI evaluates the quality of approximation sets with the aid of a reference set constructed by themselves. The points in the reference set are divided into many clusters, and the proposed indicator estimates the minimum moves of solutions in the approximation sets to weakly dominate these clusters. PCI has been verified both by an analytic comparison with several well-known indicators and by an empirical test on four groups of Pareto front approximations with different numbers of objectives and problem characteristics.

Ant colony optimization (ACO) algorithms have proved to be able to adapt for solving dynamic optimization problems (DOPs). The integration of local search algorithms has also proved to significantly improve the output of ACO algorithms. However, almost all previous works consider stationary environments. In this paper, the MAX -MIN Ant System, one of the best ACO variations, is integrated with the unstringing and stringing (US) local search operator for the dynamic travelling salesman problem (DTSP). The best solution constructed by ACO is passed to the US operator for local search improvements. The proposed memetic algorithm aims to combine the adaptation capabilities of ACO for DOPs and the superior performance of the US operator on the static travelling salesman problem in order to tackle the DTSP. The experiments show that the MAX -MIN Ant System is able to provide good initial solutions to US and the proposed algorithm outperforms other peer ACO-based memetic algorithms on different DTSPs.

This paper presents a meta-objective optimization approach, called Bi-Goal Evolution (BiGE), to deal with multi-objective optimization problems with many objectives. In multi-objective optimization, it is generally observed that 1) the conflict between the proximity and diversity requirements is aggravated with the increase of the number of objectives and 2) the Pareto dominance loses its effectiveness for a high-dimensional space but works well on a low-dimensional space. Inspired by these two observations, BiGE converts a given multi-objective optimization problem into a bi-goal (objective) optimization problem regarding proximity and diversity, and then handles it using the Pareto dominance relation in this bi-goal domain. Implemented with estimation methods of individuals' performance and the classic Pareto nondominated sorting procedure, BiGE divides individuals into different nondominated layers and attempts to put well-converged and well-distributed individuals into the first few layers. From a series of extensive experiments on four groups of well-defined continuous and combinatorial optimization problems with 5, 10 and 15 objectives, BiGE has been found to be very competitive against five state-of-the-art algorithms in balancing proximity and diversity. The proposed approach is the first step towards a new way of addressing many-objective problems as well as indicating several important issues for future development of this type of algorithms.

Rescheduling in railway networks is a challenging problem in both practice and theory. It requires good quality solutions in reasonable computation time to resolve unexpected situations, involving different problem scales, railway network infrastructures, objectives, and constraints. This paper presents a comprehensive survey on different problem models for rescheduling in railway networks by a clear classification. Some frequently used models are described in detail through reviewing their variables and constraints. This paper also focuses on the solution approaches proposed in the literature. The main ideas of the solution approaches with the objectives are described. Based on our review results, the analysis of the problem models used in various problem types and the solution approaches used in different problem models are presented. Conclusion and suggestions for further research to rescheduling in railway networks are drawn toward the end of the paper.

Quantum-behaved particle swarm optimization (QPSO) has shown to be an effective algorithm for solving global optimization problems that are of high complexity. This paper presents a new QPSO algorithm, denoted LI-QPSO, which employs a model-based linear interpolation method to strengthen the local search ability and improve the precision and convergence performance of the QPSO algorithm. In LI-QPSO, linear interpolation is used to approximate the objective function around a pre-chosen point with high quality in the search space. Then, local search is used to generate a promising trial point around this pre-chosen point, which is then used to update the worst personal best point in the swarm. Experimental results show that the proposed algorithm provides some significant improvements in performance on the tested problems.

An inherent problem in multiobjective optimization is that the visual observation of solution vectors with four or more objectives is infeasible, which brings major difficulties for algorithmic design, examination, and development. This paper presents a test problem, called the Rectangle problem, to aid the visual investigation of high-dimensional multiobjective search. Key features of the Rectangle problem are that the Pareto optimal solutions 1) lie in a rectangle in the two-variable decision space and 2) are similar (in the sense of Euclidean geometry) to their images in the four-dimensional objective space. In this case, it is easy to examine the behavior of objective vectors in terms of both convergence and diversity, by observing their proximity to the optimal rectangle and their distribution in the rectangle, respectively, in the decision space. Fifteen algorithms are investigated. Underperformance of Pareto-based algorithms as well as most state-of-the-art many-objective algorithms indicates that the proposed problem not only is a good tool to help visually understand the behavior of multiobjective search in a high-dimensional objective space but also can be used as a challenging benchmark function to test algorithms' ability in balancing the convergence and diversity of solutions.

Dynamic optimization problems (DOPs) have been a major challenge for ant colony optimization (ACO) algorithms. The integration of ACO algorithms with immigrants schemes showed promising results on different DOPs. Each type of immigrants scheme aims to address a DOP with specific characteristics. For example, random and elitism-based immigrants perform well on severely and slightly changing environments, respectively. In this paper, two hybrid immigrants, i.e., non-interactive and interactive, schemes are proposed to combine the merits of the aforementioned immigrants schemes. The experiments on a series of dynamic travelling salesman problems showed that the hybridization of immigrants further improves the performance of ACO algorithms.

The integration of immigrants schemes with ant colony optimization (ACO) algorithms showed promising results on different dynamic optimization problems (DOPs). The principle of integrating immigrants schemes within ACO is to introduce newly generated ants that will replace other ants in the current population. One of the most advanced immigrants schemes is the elitism-based immigrants scheme, where the best ant from the previous environment is used as the base to generate immigrants. So far, the replacement rate used for elitism-based immigrants in ACO remained fixed during the execution of the algorithm. In this paper the impact of the replacement rate on the performance of ACO algorithms with elitism-based immigrants is examined. In addition, an adaptive replacement rate is proposed and compared with fixed and optimized replacement rates based on a series of DOPs. The experiments show that the adaptive scheme provides an automatic way to set a good value, although not the optimal one, for the replacement rate within ACO with elitism-based immigrants for DOPs.

The multipopulation method has been widely used to solve dynamic optimization problems (DOPs) with the aim of maintaining multiple populations on different peaks to locate and track multiple changing optima simultaneously. However, to make this approach effective for solving DOPs, two challenging issues need to be addressed. They are how to adapt the number of populations to changes and how to adaptively maintain the population diversity in a situation where changes are complicated or hard to detect or predict. Tracking the changing global optimum in dynamic environments is difficult because we cannot know when and where changes occur and what the characteristics of changes would be. Therefore, it is necessary to take these challenging issues into account in designing such adaptive algorithms. To address the issues when multipopulation methods are applied for solving DOPs, this paper proposes an adaptive multi-swarm algorithm, where the populations are enabled to be adaptive in dynamic environments without change detection. An experimental study is conducted based on the moving peaks problem to investigate the behavior of the proposed method. The performance of the proposed algorithm is also compared with a set of algorithms that are based on multipopulation methods from different research areas in the literature of evolutionary computation.

The Euclidean minimum spanning tree (EMST), widely used in a variety of domains, is a minimum spanning tree of a set of points in space where the edge weight between each pair of points is their Euclidean distance. Since the generation of an EMST is entirely determined by the Euclidean distance between solutions (points), the properties of EMSTs have a close relation with the distribution and position information of solutions. This paper explores the properties of EMSTs and proposes an EMST-based evolutionary algorithm (ETEA) to solve multi-objective optimization problems (MOPs). Unlike most EMO algorithms that focus on the Pareto dominance relation, the proposed algorithm mainly considers distance-based measures to evaluate and compare individuals during the evolutionary search. Specifically, in ETEA, four strategies are introduced: (1) An EMST-based crowding distance (ETCD) is presented to estimate the density of individuals in the population; (2) A distance comparison approach incorporating ETCD is used to assign the fitness value for individuals; (3) A fitness adjustment technique is designed to avoid the partial overcrowding in environmental selection; (4) Three diversity indicators-the minimum edge, degree, and ETCD-with regard to EMSTs are applied to determine the survival of individuals in archive truncation. From a series of extensive experiments on 32 test instances with different characteristics, ETEA is found to be competitive against five state-of-the-art algorithms and its predecessor in providing a good balance among convergence, uniformity, and spread.

In this work, discrete dynamic optimization problems (DOPs) are theoretically \nanalysed according to the modifications produced in the fitness landscape during the optimization process. Using the proposed analysis framework, the following DOPs are analysed: problems generated by the XOR DOP generator, three versions of the dynamic 0-1 knapsack problem, one problem involving evolutionary robots in dynamic environments, and the random dynamics NK-model. The XOR DOP generator creates benchmark DOPs from any binary static optimization problem, which allows to explore the properties of the static problem in a dynamic environment. Three types of transformations occurring in the fitness landscapes are observed in the DOPs analysed here. They are caused by: i) permutation of solutions in the search space; ii) duplication of solutions; and iii) adding deviations to the fitness of a subset of solutions. The XOR DOP generator creates a special type of permutation that is not found in the other investigated DOPs. In this way, a new benchmark problem generator is proposed here based on the analysis performed, allowing to produce DOPs with six types of fitness landscape transformations, including those similar to the problems investigated in this paper. When compared to the XOR DOP generator, new algorithms can be tested and compared in a wider range of dynamic environments using the new generator. It is important to observe that some of the fitness transformations analysed here, like those caused by the duplication of solutions, are not currently explored in the evolutionary dynamic optimization area.

For large electricity users, such as smelting plants, their electric loads cannot exceed a concerted limit in production. Traditional single-furnace optimization methods aim to satisfy the electric demand of a furnace to improve its production, and hence cannot consider the maximum demand constraint in a smelting plant. Maximum demand (MD) control is often utilized to keep the total electric demand within the limit via shedding the electric loads of some furnaces once the demand approaches the limit. However, the control method will enlarge the fluctuation of electric loads, which does harm to the production and causes a decline in energy-efficiency. In this paper, we propose a multifurnace optimization strategy to improve the production targets of a whole plant instead of a single furnace. In the strategy, an offline multiobjective load scheduling is first performed to assign electric loads for furnaces in each sampling period, taking into account of the MD constraint and production constraints. A multiobjective particle swarm optimization algorithm, combined with population initialization and constraint-handing strategies, is proposed to search for the Pareto optimal set of the scheduling problem, from which decision-makers can select one solution as the load scheduling program. A double closed-loop control mechanism is used to change the scheduled load into detailed load setpoints of furnaces and keep the actual loads up with the load setpoints. In the outer loop, the detailed load setpoints of furnaces are dynamically adjusted based on the deviation of actual loads from the scheduled loads. Thereafter, the desired setpoints are sent to the automatic control mechanism of each furnace, which is in the inner loop and responsible to keep the actual load up with the setpoint via a proportional-integral-derivative (PID) controller. The case study on a typical magnesia-smelting plant shows that the proposed multifurnace optimization strategy can achieve an increase of about 12.29% in the production output, an improvement of about 0.46% of the magnesia in the product, and a slight reduction of 2.35% in electricity cost over the results of MD control. Note to Practitioners - For large electricity users, such as smelting plants, they are subjected to the maximum electric demand constraint. The maximum demand control device is widely adopted to solve the problem, but it will cause a decline in production output and energy-efficiency. This paper was motivated by improving the multiple production targets (i.e, the total production output, the product quality, and the total electricity cost) of a plant via load scheduling and control. In contrast to the maximum demand control, the load scheduling and control approach is a beforehand strategy that can optimize the operation. A case study on a magnesia-smelting plant shows that the proposed approach performs better than the maximum demand control technique.

Diversity assessment of Pareto front approximations is an important issue in the stochastic multiobjective optimization community. Most of the diversity indicators in the literature were designed to work for any number of objectives of Pareto front approximations in principle, but in practice many of these indicators are infeasible or not workable when the number of objectives is large. In this paper, we propose a diversity comparison indicator (DCI) to assess the diversity of Pareto front approximations in many-objective optimization. DCI evaluates relative quality of different Pareto front approximations rather than provides an absolute measure of distribution for a single approximation. In DCI, all the concerned approximations are put into a grid environment so that there are some hyperboxes containing one or more solutions. The proposed indicator only considers the contribution of different approximations to nonempty hyperboxes. Therefore, the computational cost does not increase exponentially with the number of objectives. In fact, the implementation of DCI is of quadratic time complexity, which is fully independent of the number of divisions used in grid. Systematic experiments are conducted using three groups of artificial Pareto front approximations and seven groups of real Pareto front approximations with different numbers of objectives to verify the effectiveness of DCI. Moreover, a comparison with two diversity indicators used widely in many-objective optimization is made analytically and empirically. Finally, a parametric investigation reveals interesting insights of the division number in grid and also offers some suggested settings to the users with different preferences.

This paper proposes a variation operator, called segment-based search (SBS), to improve the performance of evolutionary algorithms on continuous multiobjective optimization problems. SBS divides the search space into many small segments according to the evolutionary information feedback from the set of current optimal solutions. Two operations, micro-jumping and macro-jumping, are implemented upon these segments in order to guide an efficient information exchange among "good" individuals. Moreover, the running of SBS is adaptive according to the current evolutionary status. SBS is activated only when the population evolves slowly, depending on general genetic operators (e.g., mutation and crossover). A comprehensive set of 36 test problems is employed for experimental verification. The influence of two algorithm settings (i.e., the dimensionality and boundary relaxation strategy) and two probability parameters in SBS (i.e., the SBS rate and micro-jumping proportion) are investigated in detail. Moreover, an empirical comparative study with three representative variation operators is carried out. Experimental results show that the incorporation of SBS into the optimization process can improve the performance of evolutionary algorithms for multiobjective optimization problems.

It is commonly accepted that Pareto-based evolutionary multiobjective optimization (EMO) algorithms encounter difficulties in dealing with many-objective problems. In these algorithms, the ineffectiveness of the Pareto dominance relation for a high-dimensional space leads diversity maintenance mechanisms to play the leading role during the evolutionary process, while the preference of diversity maintenance mechanisms for individuals in sparse regions results in the final solutions distributed widely over the objective space but distant from the desired Pareto front. Intuitively, there are two ways to address this problem: 1) modifying the Pareto dominance relation and 2) modifying the diversity maintenance mechanism in the algorithm. In this paper, we focus on the latter and propose a shift-based density estimation (SDE) strategy. The aim of our study is to develop a general modification of density estimation in order to make Pareto-based algorithms suitable for many-objective optimization. In contrast to traditional density estimation that only involves the distribution of individuals in the population, SDE covers both the distribution and convergence information of individuals. The application of SDE in three popular Pareto-based algorithms demonstrates its usefulness in handling many-objective problems. Moreover, an extensive comparison with five state-of-the-art EMO algorithms reveals its competitiveness in balancing convergence and diversity of solutions. These findings not only show that SDE is a good alternative to tackle many-objective problems, but also present a general extension of Pareto-based algorithms in many-objective optimization.

One approach integrated with genetic algorithms (GAs) to address dynamic optimization problems (DOPs) is to maintain diversity of the population via introducing immigrants. Many immigrants schemes have been proposed that differ on the way new individuals are generated, e.g., mutating the best individual of the previous environment to generate elitism-based immigrants. This paper examines the performance of elitism-based immigrants GA (EIGA) with different immigrant mutation probabilities and proposes an adaptive mechanism that tends to improve the performance in DOPs. Our experimental study shows that the proposed adaptive immigrants GA outperforms EIGA in almost all dynamic test cases and avoids the tedious work of fine-tuning the immigrant mutation probability parameter.

Balancing convergence and diversity plays a key role in evolutionary multiobjective optimization (EMO). Most current EMO algorithms perform well on problems with two or three objectives, but encounter difficulties in their scalability to many-objective optimization. This paper proposes a grid-based evolutionary algorithm (GrEA) to solve many-objective optimization problems. Our aim is to exploit the potential of the grid-based approach to strengthen the selection pressure toward the optimal direction while maintaining an extensive and uniform distribution among solutions. To this end, two concepts-grid dominance and grid difference-are introduced to determine the mutual relationship of individuals in a grid environment. Three grid-based criteria, i.e., grid ranking, grid crowding distance, and grid coordinate point distance, are incorporated into the fitness of individuals to distinguish them in both the mating and environmental selection processes. Moreover, a fitness adjustment strategy is developed by adaptively punishing individuals based on the neighborhood and grid dominance relations in order to avoid partial overcrowding as well as guide the search toward different directions in the archive. Six state-of-the-art EMO algorithms are selected as the peer algorithms to validate GrEA. A series of extensive experiments is conducted on 52 instances of nine test problems taken from three test suites. The experimental results show the effectiveness and competitiveness of the proposed GrEA in balancing convergence and diversity. The solution set obtained by GrEA can achieve a better coverage of the Pareto front than that obtained by other algorithms on most of the tested problems. Additionally, a parametric study reveals interesting insights of the division parameter in a grid and also indicates useful values for problems with different characteristics.

Maintaining population diversity is a crucial issue for the performance of evolutionary algorithms (EAs) in dynamic environments. In the literature of EAs for dynamic optimization problems (DOPs), many studies have been done to address this issue based on change detection techniques. However, many changes are hard or impractical to be detected in real-world applications. Although, some research has been done by means of maintaining diversity without change detection. These methods are not effective because the continuous focus on diversity slows down the optimization process. This paper presents a maintaining diversity method without change detection based on a clustering technique. The method was implemented through particle swarm optimization (PSO), which was named CPSOR. The performance of the CPSOR algorithm was evaluated on the GDBG benchmark. A comparison study with another algorithm based on change detection has shown the effectiveness of the CPSOR algorithm for tracking and locating the global optimum in dynamic environments.

A recent integration showed that ant colony optimization (ACO) algorithms with immigrants schemes perform well on different variations of the dynamic travelling salesman problem. In this paper, we address ACO for the dynamic vehicle routing problem (DVRP) with traffic factor where the changes occur in a cyclic pattern. In other words, previous environments will re-appear in the future. Memory-based immigrants are used with ACO in order to collect the best solutions from the environments and use them to generate diversity and transfer knowledge when a dynamic change occurs. The results show that the proposed algorithm, with an appropriate size of memory and immigrant replacement rate, outperforms other peer ACO algorithms on different DVRP test cases.

In this paper, the problem of dynamic multicast routing in mobile ad hoc networks is investigated. Lots of interesting works have been done on multicast routing since it is proved to be a NP-hard problem. However, most of them consider the static network scenarios only and the multicast tree cannot adapt to the topological changes. In a mobile ad hoc network (MANET), the network topology keeps changing due to its inherent characteristics such as node mobility and energy conservation. Therefore, an effective multicast algorithm should adapt the best multicast tree to the changes accordingly. In this paper, we propose to use two types of hyper-mutation genetic algorithms (GAs) to solve the dynamic multicast routing problem in MANETs. The two GAs are named as high low hyper-mutation GA (hlHMGA) and gradual hyper-mutation GA (grHMGA), respectively. The experimental results show that the first type of hyper-mutation GA (i.e., hlHMGA) can quickly adapt to the environmental changes (i.e., the network topology changes) and produce high quality solutions following each change.

To solve dynamic optimization problems, multiple population methods are used to enhance the population diversity for an algorithm with the aim of maintaining multiple populations in different subareas in the fitness landscape. Many experimental studies have shown that locating and tracking multiple relatively good optima rather than a single global optimum is an effective idea in dynamic environments. However, several challenges need to be addressed when multipopulation methods are applied, e.g., how to create multiple populations, how to maintain them in different subareas, and how to deal with the situation where changes cannot be detected or predicted. To address these issues, this paper investigates a hierarchical clustering method to locate and track multiple optima for dynamic optimization problems. To deal with undetectable dynamic environments, this paper applies the random immigrants method without change detection based on a mechanism that can automatically reduce redundant individuals in the search space throughout the run. These methods are implemented into several research areas, including particle swarm optimization, genetic algorithm, and differential evolution. An experimental study is conducted based on the moving peaks benchmark to test the performance with several other algorithms from the literature. The experimental results show the efficiency of the clustering method for locating and tracking multiple optima in comparison with other algorithms based on multipopulation methods on the moving peaks benchmark.

Particle swarm optimization (PSO) has been shown as an effective tool for solving global optimization problems. So far, most PSO algorithms use a single learning pattern for all particles, which means that all particles in a swarm use the same strategy. This monotonic learning pattern may cause the lack of intelligence for a particular particle, which makes it unable to deal with different complex situations. This paper presents a novel algorithm, called self-learning particle swarm optimizer (SLPSO), for global optimization problems. In SLPSO, each particle has a set of four strategies to cope with different situations in the search space. The cooperation of the four strategies is implemented by an adaptive learning framework at the individual level, which can enable a particle to choose the optimal strategy according to its own local fitness landscape. The experimental study on a set of 45 test functions and two real-world problems show that SLPSO has a superior performance in comparison with several other peer algorithms.

Component selection is a crucial problem in Component Based Software Engineering (CBSE). CBSE is concerned with the assembly of pre-existing software components that leads to a software system that responds to client-specific requirements. This work deals with the component selection problem which we formulate as multiobjective optimization, involving four objectives: the number of used components, the number of new requirements, the number of provided interfaces and the number of the initial requirements that are not in solution. We use the Pareto dominance principle to deal with the multiobjective optimization problem. Needles to say the last two objectives should be zero. Afterwards, we investigate the problem in an dynamic or changing environment for which two practical scenarios are envisaged: the repository containing the components varies over time and the system requirements change over time. The algorithm employed uses a combination of evolutionary algorithms and repair mechanism. The idea behind this was to avoid restarting the algorithm from randomly generated solutions and to make use of the ones found at the previous step.

The university course timetabling problem (UCTP) is a combinatorial optimization problem, in which a set of events has to be scheduled into time slots and located into suitable rooms. The design of course timetables for academic institutions is a very difficult task because it is an NP-hard problem. This paper investigates genetic algorithms (GAs) with a guided search strategy and local search (LS) techniques for the UCTP. The guided search strategy is used to create offspring into the population based on a data structure that stores information extracted from good individuals of previous generations. The LS techniques use their exploitive search ability to improve the search efficiency of the proposed GAs and the quality of individuals. The proposed GAs are tested on two sets of benchmark problems in comparison with a set of state-of-the-art methods from the literature. The experimental results show that the proposed GAs are able to produce promising results for the UCTP.

This paper proposes a two-phase hybrid approach for the travelling salesman problem (TSP). The first phase is based on a sequence based genetic algorithm (SBGA) with an embedded local search scheme. Within the SBGA, a memory is introduced to store good sequences (sub-tours) extracted from previous good solutions and the stored sequences are used to guide the generation of offspring via local search during the evolution of the population. Additionally, we also apply some techniques to adapt the key parameters based on whether the best individual of the population improves or not and maintain the diversity. After SBGA finishes, the hybrid approach enters the second phase, where the inver over (IO) operator, which is a state-of-the-art algorithm for the TSP, is used to further improve the solution quality of the population. Experiments are carried out to investigate the performance of the proposed hybrid approach in comparison with several relevant algorithms on a set of benchmark TSP instances. The experimental results show that the proposed hybrid approach is efficient in finding good quality solutions for the test TSPs.

This paper presents an updated version of the adaptive learning particle swarm optimizer (ALPSO), we call it ALPSO-II. In order to improve the performance of ALPSO on multi-modal problems, we introduce several new major features in ALPSO-II: (i) Adding particle's status monitoring mechanism, (ii) controlling the number of particles that learn from the global best position, and (iii) updating two of the four learning operators used in ALPSO. To test the performance of ALPSO-II, we choose a set of 27 test problems, including un-rotated, shifted, rotated, rotated shifted, and composition functions in comparison of the ALPSO algorithm as well as several state-of-the-art variant PSO algorithms. The experimental results show that ALPSO-II has a great improvement of the ALPSO algorithm, it also outperforms the other peer algorithms on most test problems in terms of both the convergence speed and solution accuracy.

In the real world, many optimization problems are dynamic. This requires an optimization algorithm to not only find the global optimal solution under a specific environment but also to track the trajectory of the changing optima over dynamic environments. To address this requirement, this paper investigates a clustering particle swarm optimizer (PSO) for dynamic optimization problems. This algorithm employs a hierarchical clustering method to locate and track multiple peaks. A fast local search method is also introduced to search optimal solutions in a promising subregion found by the clustering method. Experimental study is conducted based on the moving peaks benchmark to test the performance of the clustering PSO in comparison with several state-of-the-art algorithms from the literature. The experimental results show the efficiency of the clustering PSO for locating and tracking multiple optima in dynamic environments in comparison with other particle swarm optimization models based on the multiswarm method.

In recent years, there has been a growing interest in the study of particle swarm optimization (PSO) in dynamic environments. This paper presents a new PSO model, called PSO with composite particles (PSO-CP), to address dynamic optimization problems. PSO-CP partitions the swarm into a set of composite particles based on their similarity using a "worst first" principle. Inspired by the composite particle phenomenon in physics, the elementary members in each composite particle interact via a velocity-anisotropic reflection scheme to integrate valuable information for effectively and rapidly finding the promising optima in the search space. Each composite particle maintains the diversity by a scattering operator. In addition, an integral movement strategy is introduced to promote the swarm diversity. Experiments on a typical dynamic test benchmark problem provide a guideline for setting the involved parameters and show that PSO-CP is efficient in comparison with several state-of-the-art PSO algorithms for dynamic optimization problems.

In recent years, the static shortest path (SP) problem has been well addressed using intelligent optimization techniques, e.g., artificial neural networks, genetic algorithms (GAs), particle swarm optimization, etc. However, with the advancement in wireless communications, more and more mobile wireless networks appear, e.g., mobile networks [mobilead hocnetworks (MANETs)], wireless sensor networks, etc. One of the most important characteristics in mobile wireless networks is the topology dynamics, i.e., the network topology changes over time due to energy conservation or node mobility. Therefore, the SP routing problem in MANETs turns out to be a dynamic optimization problem. In this paper, we propose to use GAs with immigrants and memory schemes to solve the dynamic SP routing problem in MANETs. We consider MANETs as target systems because they represent new-generation wireless networks. The experimental results show that these immigrants and memory-based GAs can quickly adapt to environmental changes (i.e., the network topology changes) and produce high-quality solutions after each change.

In recent years, the static shortest path (SP) problem has been well addressed using intelligent optimization techniques, e.g., artificial neural networks (ANNs), genetic algorithms (GAs), particle swarm optimization (PSO), etc. However, with the advancement in wireless communications, more and more mobile wireless networks appear, e.g., mobile ad hoc network (MANET), wireless sensor network (WSN), etc. One of the most important characteristics in mobile wireless networks is the topology dynamics, that is, the network topology changes over time due to energy conservation or node mobility. Therefore, the SP problem turns out to be a dynamic optimization problem (DOP) in MANETs. In this paper, we propose to use elitism-based immigrants GA (EIGA) to solve the dynamic SP problem in MANETs. We consider MANETs as target systems because they represent new generation wireless networks. The experimental results show that the EIGA can quickly adapt to the environmental changes (i.e., the network topology change) and produce good solutions after each change.

Traditional particle swarm optimization (PSO) suffers from the premature convergence problem, which usually results in PSO being trapped in local optima. This paper presents an adaptive learning PSO (ALPSO) based on a variant PSO learning strategy. In ALPSO, the learning mechanism of each particle is separated into three parts: its own historical best position, the closest neighbor and the global best one. By using this individual level adaptive technique, a particle can well guide its behavior of exploration and exploitation. A set of 21 test functions were used including un-rotated, rotated and composition functions to test the performance of ALPSO. From the comparison results over several variant PSO algorithms, ALPSO shows an outstanding performance on most test functions, especially the fast convergence characteristic.

In the real world, many applications are nonstationary optimization problems. This requires that optimization algorithms need to not only find the global optimal solution but also track the trajectory of the changing global best solution in a dynamic environment. To achieve this, this paper proposes a clustering particle swarm optimizer (CPSO) for dynamic optimization problems. The algorithm employs hierarchical clustering method to track multiple peaks based on a nearest neighbor search strategy. A fast local search method is also proposed to find the near optimal solutions in a local promising region in the search space. Six test problems generated from a generalized dynamic benchmark generator (GDBG) are used to test the performance of the proposed algorithm. The numerical experimental results show the efficiency of the proposed algorithm for locating and tracking multiple optima in dynamic environments.

The population-based incremental learning (PBIL) algorithm is a combination of evolutionary optimization and competitive learning. Recently, the PBIL algorithm has been applied for dynamic optimization problems. This paper investigates the effect of the learning rate, which is a key parameter of PBIL, on the performance of PBIL in dynamic environments. A hyper-learning scheme is proposed for PBIL, where the learning rate is temporarily raised whenever the environment changes. The hyper-learning scheme can be combined with other approaches, e.g., the restart and hypermutation schemes, for PBIL in dynamic environments. Based on a series of dynamic test problems, experiments are carried out to investigate the effect of different learning rates and the proposed hyper-learning scheme in combination with restart and hypermutation schemes on the performance of PBIL. The experimental results show that the learning rate has a significant impact on the performance of the PBIL algorithm in dynamic environments and that the effect of the proposed hyper-learning scheme depends on the environmental dynamics and other schemes combined in the PBIL algorithm.

Recently, there has been an increasing interest in applying genetic algorithms (GAs) in dynamic environments. Inspired by the complementary and dominance mechanisms in nature, a primal-dual GA (PDGA) has been proposed for dynamic optimization problems (DOPs). In this paper, an important operator in PDGA, i.e., the primal-dual mapping (PDM) scheme, is further investigated to improve the robustness and adaptability of PDGA in dynamic environments. In the improved scheme, two different probability-based PDM operators, where the mapping probability of each allele in the chromosome string is calculated through the statistical information of the distribution of alleles in the corresponding gene locus over the population, are effectively combined according to an adaptive Lamarckian learning mechanism. In addition, an adaptive dominant replacement scheme, which can probabilistically accept inferior chromosomes, is also introduced into the proposed algorithm to enhance the diversity level of the population. Experimental results on a series of dynamic problems generated from several stationary benchmark problems show that the proposed algorithm is a good optimizer for DOPs.

Abstract Clustering can help aggregate the topology information and reduce the size of routing tables in a mobile ad hoc network (MANET). The maintenance of the cluster structure should be as stable as possible to reduce overhead and make the network topology less dynamic. Hence, stability measures the goodness of clustering. However, for a complex system like MANET, one clustering metric is far from reflecting the network dynamics. Some prior works have considered multiple metrics by combining them into one weighted sum, which suffers from intrinsic drawbacks as a scalar objective function to provide solution for multi‐objective optimization. In this paper, we propose a stability‐aware multi‐metric clustering algorithm, which can (1) achieve stable cluster structure by exploiting group mobility and (2) optimize multiple metrics with the help of a multi‐objective evolutionary algorithm (MOEA). Performance evaluation shows that our algorithm can generate a stable clustered topology and also achieve optimal solutions in small‐scale networks. For large‐scale networks, it outperforms the well‐known weighted clustering algorithm (WCA) that uses a weighted sum of multiple metrics. Copyright © 2008 John Wiley & Sons, Ltd.

The use of evolutionary programming algorithms with self-adaptation of the mutation distribution for dynamic optimization problems is investigated in this paper. In the proposed method, the q-Gaussian distribution is employed to generate new candidate solutions by mutation. A real parameter q, which defines the shape of the distribution, is encoded in the chromosome of individuals and is allowed to evolve. Algorithms with self-adapted mutation generated from isotropic and anisotropic distributions are presented. In the experimental study, the q-Gaussian mutation is compared to Gaussian and Cauchy mutation on three dynamic optimization problems.

In this paper, a multi-agent based evolutionary algorithm (MAEA) is introduced to solve dynamic optimization problems. The agents simulate living organism features and co-evolve to find optimum. All agents live in a lattice like environment, where each agent is fixed on a lattice point. In order to increase the energy, agents can compete with their neighbors and can also acquire knowledge based on statistic information. In order to maintain the diversity of the population, the random immigrants and adaptive primal dual mapping schemes are used. Simulation experiments on a set of dynamic benchmark problems show that MAEA can obtain a better performance in non-stationary environments in comparison with several peer genetic algorithms.

In recent years, several approaches have been developed for genetic algorithms to enhance their performance in dynamic environments. Among these approaches, one kind of methods is to adapt genetic operators in order for genetic algorithms to adapt to a new environment. This paper investigates the effect of the selection pressure on the performance of genetic algorithms in dynamic environments. A hyper-selection scheme is proposed for genetic algorithms, where the selection pressure is temporarily raised whenever the environment changes. The hyper-selection scheme can be combined with other approaches for genetic algorithms in dynamic environments. Experiments are carried out to investigate the effect of different selection pressures on the performance of genetic algorithms in dynamic environments and to investigate the effect of the hyper-selection scheme on the performance of genetic algorithms in combination with several other schemes in dynamic environments. The experimental results indicate that the effect of the hyper-selection scheme depends on the problem under consideration and other schemes combined in genetic algorithms.

The design of course timetables for academic institutions is a very hectic job due to the exponential number of possible feasible timetables with respect to the problem size. This process involves lots of constraints that must be respected and a huge search space to be explored, even if the size of the problem input is not significantly large. On the other hand, the problem itself does not have a widely approved definition, since different institutions face different variations of the problem. This paper presents a memetic algorithm that integrates two local search methods into the genetic algorithm for solving the university course timetabling problem (UCTP). These two local search methods use their exploitive search ability to improve the explorative search ability of genetic algorithms. The experimental results indicate that the proposed memetic algorithm is efficient for solving the UCTP.

In recent years the genetic algorithm community has shown a growing interest in studying dynamic optimization problems. Several approaches have been devised. The random immigrants and memory schemes are two major ones. The random immigrants scheme addresses dynamic environments by maintaining the population diversity while the memory scheme aims to adapt genetic algorithms quickly to new environments by reusing historical information. This paper investigates a hybrid memory and random immigrants scheme, called memory-based immigrants, and a hybrid elitism and random immigrants scheme, called elitism-based immigrants, for genetic algorithms in dynamic environments. In these schemes, the best individual from memory or the elite from the previous generation is retrieved as the base to create immigrants into the population by mutation. This way, not only can diversity be maintained but it is done more efficiently to adapt genetic algorithms to the current environment. Based on a series of systematically constructed dynamic problems, experiments are carried out to compare genetic algorithms with the memory-based and elitism-based immigrants schemes against genetic algorithms with traditional memory and random immigrants schemes and a hybrid memory and multi-population scheme. The sensitivity analysis regarding some key parameters is also carried out. Experimental results show that the memory-based and elitism-based immigrants schemes efficiently improve the performance of genetic algorithms in dynamic environments.

In recent years, interest in studying evolutionary algorithms (EAs) for dynamic optimization problems (DOPs) has grown due to its importance in real-world applications. Several approaches, such as the memory and multiple population schemes, have been developed for EAs to address dynamic problems. This paper investigates the application of the memory scheme for population-based incremental learning (PBIL) algorithms, a class of EAs, for DOPs. A PBIL-specific associative memory scheme, which stores best solutions as well as corresponding environmental information in the memory, is investigated to improve its adaptability in dynamic environments. In this paper, the interactions between the memory scheme and random immigrants, multipopulation, and restart schemes for PBILs in dynamic environments are investigated. In order to better test the performance of memory schemes for PBILs and other EAs in dynamic environments, this paper also proposes a dynamic environment generator that can systematically generate dynamic environments of different difficulty with respect to memory schemes. Using this generator, a series of dynamic environments are generated and experiments are carried out to compare the performance of investigated algorithms. The experimental results show that the proposed memory scheme is efficient for PBILs in dynamic environments and also indicate that different interactions exist between the memory scheme and random immigrants, multipopulation schemes for PBILs in different dynamic environments.

This paper proposes a self-adaptation method to control not only the mutation strength parameter, but also the mutation distribution for evolutionary algorithms. For this purpose, the isotropic q-Gaussian distribution is employed in the mutation operator. The q-Gaussian distribution allows to control the shape of the distribution by setting a real parameter q and can reproduce either finite second moment distributions or infinite second moment distributions. In the proposed method, the real parameter q of the q-Gaussian distribution is encoded in the chromosome of an individual and is allowed to evolve. An evolutionary programming algorithm with the proposed idea is presented. Experiments were carried out to study the performance of the proposed algorithm.

Addressing dynamic optimization problems has attracted a growing interest from the evolutionary algorithm community in recent years due to its importance in the applications of evolutionary algorithms in real world problems. In order to study evolutionary algorithms in dynamic environments, one important work is to develop benchmark dynamic environments. This paper proposes two continuous dynamic problem generators. Both generators use linear transformation to move individuals, which preserves the distance among individuals. In the first generator, the linear transformation of individuals is equivalent to change the direction of some axes of the search space while in the second one it is obtained by successive rotations in different planes. Preliminary experiments were carried out to study the performance of some standard genetic algorithms in continuous dynamic environments created by the proposed generators.

Using diploidy and dominance is one method to enhance the performance of genetic algorithms in dynamic environments. For diploidy genetic algorithms, there are two key design factors: the cardinality of genotypic alleles and the uncertainty in the dominance scheme. This paper investigates the effect of these two factors on the performance of diploidy genetic algorithms in dynamic environments. A generalized diploidy and dominance scheme is proposed for diploidy genetic algorithms, where the cardinality of genotypic alleles and/or the uncertainty in the dominance scheme can be easily tuned and studied. The experimental results show the efficiency of increasing genotypic cardinality rather than introducing uncertainty in the dominance scheme.

This paper proposes an adaptive dominance mechanism for diploidy genetic algorithms in dynamic environments. In this scheme, the genotype to phenotype mapping in each gene locus is controlled by a dominance probability, which is learned adaptively during the searching progress and hence is adapted to the dynamic environment. Using a series of dynamic test problems, the proposed dominance scheme is compared to two other dominance schemes for diploidy genetic algorithms. The experimental results validate the efficiency of the proposed dominance learning scheme.

Copyright @ 2006 ACM

Job-shop scheduling is one of the most difficult production scheduling problems in industry. This paper proposes an adaptive neural network and local search hybrid approach for the job-shop scheduling problem. The adaptive neural network is constructed based on constraint satisfactions of job-shop scheduling and can adapt its structure and neuron connections during the solving process. The neural network is used to solve feasible schedules for the job-shop scheduling problem while the local search scheme aims to improve the performance by searching the neighbourhood of a given feasible schedule. The experimental study validates the proposed hybrid approach for job-shop scheduling regarding the quality of solutions and the computing speed.

This paper proposes a genetic algorithm (GA) with random immigrants for dynamic optimization problems where the worst individual and its neighbours are replaced every generation. In this GA, the individuals interact with each other and, when their fitness is close, as in the case where the diversity level is low, one single replacement can affect a large number of individuals. This simple approach can take the system to a kind of self-organization behavior, known as self-organized criticality (SOC), which is useful to maintain the diversity of the population in dynamic environments and hence allows the GA to escape from local optima when the problem changes. The experimental results show that the proposed GA presents the phenomenon of SOC.

Several approaches have been developed into evolutionary algorithms to deal with dynamic optimization problems, of which memory and random immigrants are two major schemes. This paper investigates the application of a direct memory scheme for univariate marginal distribution algorithms (UMDAs), a class of evolutionary algorithms, for dynamic optimization problems. The interaction between memory and random immigrants for UMDAs in dynamic environments is also investigated. Experimental study shows that the memory scheme is efficient for UMDAs in dynamic environments and that the interactive effect between memory and random immigrants for UMDAs in dynamic environments depends on the dynamic environments.

In recent years there has been a growing interest in studying evolutionary algorithms for dynamic optimization problems due to its importance in real world applications. Several approaches have been developed, such as the memory scheme. This paper investigates the application of the memory scheme for population-based incremental learning (PBIL) algorithms, a class of evolutionary algorithms, for dynamic optimization problems. A PBIL-specific memory scheme is proposed to improve its adaptability in dynamic environments. In this memory scheme the working probability vector is stored together with the best sample it creates in the memory and is used to reactivate old environments when change occurs. Experimental study based on a series of dynamic environments shows the efficiency of the memory scheme for PBILs in dynamic environments. In this paper, the relationship between the memory scheme and the multi-population scheme for PBILs in dynamic environments is also investigated. The experimental results indicate a negative interaction of the multi-population scheme on the memory scheme for PBILs in the dynamic test environments.

Investigating and enhancing the performance of genetic algorithms in dynamic environments have attracted a growing interest from the community of genetic algorithms in recent years. This trend reflects the fact that many real world problems are actually dynamic, which poses serious challenge to traditional genetic algorithms. Several approaches have been developed into genetic algorithms for dynamic optimization problems. Among these approches, random immigrants and memory schemes have shown to be beneficial in many dynamic problems. This paper proposes a hybrid memory and random immigrants scheme for genetic algorithms in dynamic environments. In the hybrid scheme, the best solution in memory is retrieved and acts as the base to create random immigrants to replace the worst individuals in the population. In this way, not only can diversity be maintained but it is done more efficiently to adapt the genetic algorithm to the changing environment. The experimental results based on a series of systematically constructed dynamic problems show that the proposed memory-based immigrants scheme efficiently improves the performance of genetic algorithms in dynamic environments.

Job-shop scheduling is one of the most difficult production scheduling problems in industry. This paper presents an improved adaptive neural network together with heuristic methods for job-shop scheduling problems. The neural network is based on constraints satisfaction of job-shop scheduling and can adapt its structure and neuron connections during the solving. Several heuristics are also proposed to be combined with the neural network to guarantee its convergence, accelerate its solving process, and improve the quality of solutions. Experimental study shows that the proposed hybrid approach outperforms two classical heuristic algorithms regarding the quality of solutions.

In recent years the study of dynamic optimization problems has attracted an increasing interest from the community of genetic algorithms and researchers have developed a variety of approaches into genetic algorithms to solve these problems. In order to compare their performance, an important issue is the construction of standardized dynamic test environments. Based on the concept of problem difficulty, This work proposes a new dynamic environment generator using a decomposable trap function. With this generator, it is possible to systematically construct dynamic environments with changing and bounding difficulty and hence, we can test different genetic algorithms under dynamic environments with changing but controllable difficulty levels.

Genetic algorithms (GAs) have been widely used for stationary optimization problems where the fitness landscape does not change during the computation. However, the environments of real world problems may change over time, which puts forward serious challenge to traditional GAs. In this paper, we introduce the application of a new variation of GA called the primal-dual genetic algorithm (PDGA) for problem optimization in nonstationary environments. Inspired by the complementarity and dominance mechanisms in nature, PDGA operates on a pair of chromosomes that are primal-dual to each other in the sense of maximum distance in genotype in a given distance space. This paper investigates an important aspect of PDGA, its adaptability to dynamic environments. A set of dynamic problems are generated from a set of stationary benchmark problems using a dynamic problem generating technique proposed in this paper. Experimental study over these dynamic problems suggests that PDGA can solve complex dynamic problems more efficiently than traditional GA and a peer GA, the dual genetic algorithm. The experimental results show that PDGA has strong viability and robustness in dynamic environments.

This paper presents a constraint satisfaction adaptive neural network, together with several heuristics, to solve the generalized job-shop scheduling problem, one of NP-complete constraint satisfaction problems. The proposed neural network can be easily constructed and can adaptively adjust its weights of connections and biases of units based on the sequence and resource constraints of the job-shop scheduling problem during its processing. Several heuristics that can be combined with the neural network are also presented. In the combined approaches, the neural network is used to obtain feasible solutions, the heuristic algorithms are used to improve the performance of the neural network and the quality of the obtained solutions. Simulations have shown that the proposed neural network and its combined approaches are efficient with respect to the quality of solutions and the solving speed.