Ore-flow blending in open pit mining is a complex real-time scheduling decision problem constrained by high dimensional spatiotemporal dynamics and stochastic uncertainties. Traditional methods often struggle to reconcile the need for long term global stability with the requirement for sub second response times to dynamic events. To address this, we propose a heterogeneous ant colony optimization framework with semantic manifold learning. The framework bridges the gap between static offline learning and dynamic online adaptation. In the offline phase, we introduce a semantic manifold learning mechanism combining genetic programming with quality-diversity optimization. By constructing a behaviorally diverse archive of elite heuristics, this method provides the online system with a "warm start" and diverse initial perspectives, significantly enhancing real-time responsiveness. In the online phase, a heterogeneous ant colony system is deployed where different ant sub populations are coupled with distinct elite rules from the offline archive. This architecture enables parallel exploration of the solution space from multiple semantic perspectives, granting the system intrinsic robustness and high adaptability. Extensive experiments on real-world mine demonstrate that this method significantly outperforms state-of-the-art techniques in ore flow stability control and exhibits superior robustness and scalability across varying road network topologies, equipment configurations, and dynamic scenarios.

In industrial IOT environments, intelligent systems must continually learn from dynamic data streams to maintain diagnostic accuracy for emerging fault types. However, mainstream replay-based incremental learning methods typically depend on knowledge distillation with cumbersome teacher models to preserve past knowledge, resulting in excessive memory overheads that preclude their deployment on resource-constrained edge devices. To overcome this challenge, we propose ME-ACR, a memory-efficient framework driven by attributional consistency reinforcement. ME-ACR first employs cosine-normalized classifier to mitigate the inherent recency bias and establish a stable feature space. Then, two synergistic self-supervised paradigms are designed, which anchors old knowledge without a teacher model. Attributional consistency reinforcement paradigm enforces internal cohesion by promoting consistency among the attribution patterns of correctly classified exemplars. Prototype-distance-based attribution disentanglement paradigm ensures external separation by aligning the topological structure of attribution space with the global geometry of feature space. By preserving the structure of both intra-class and inter-class attributional knowledge, ME-ACR effectively prevents catastrophic forgetting. Extensive experimental results on multiple datasets demonstrate the superiority of the proposed ME-ACR in achieving robust and memory-efficient fault diagnosis under incremental learning scenarios.

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.

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.

Template update is essential for improving the adaptability of tracking algorithms to target appearance variations. While previous methods have leveraged the spatio-temporal complementarity of multi-modal templates for RGBT tracking, a comprehensive analysis of the template update mechanism remains underexplored. In this work, we propose a novel prototype-based framework that decomposes the multi-modal template update process from the perspective of prototype learning into four key components: multi-modal prototype, prototype integration, prototype evaluation, and prototype update algorithm. Our findings highlight that the multi-modal prototype is the most critical factor in enhancing tracking adaptability to appearance variations, leading to more robust target representations. While prototype integration is less crucial when the target representation is already robust, it still contributes to learning a more discriminative representation. Additionally, the accuracy of template updates is strongly influenced by prototype evaluation, which controls the accuracy of the update process. Finally, the prototype update algorithm, which determines when and how template updates occur, is key to maintaining tracking robustness. Building on these insights, we introduce the Multi-modal Prototype RGBT Tracker (MPTrack), which adapts dynamically to appearance variations through prototype learning. MPTrack combines a fixed template from the first frame with both modality-shared and modality-specific templates, forming a robust multi-modal prototype representation. It incorporates a prototype evaluation module that guides updates based on template reliability, and an adaptive update algorithm to manage templates effectively. Additionally, a prototype-guided cross-modal integration module enhances the discriminative power of multi-modal relation modeling. Experimental results on five challenging RGBT tracking benchmarks demonstrate that MPTrack consistently outperforms state-of-the-art methods, setting new performance records. The experimental data and source code will be made publicly available at: https://github.com/mmic-lcl/Datasets-and-benchmark-code.

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.

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.

Dynamic constrained multiobjective optimization problems (DCMOPs) require algorithms to quickly track the feasible Pareto optima under dynamic environments. The existing dynamic constrained multiobjective evolutionary algorithms (DCMOEAs) normally focus on the convergence speed, but cannot well guarantee distribution. To address this issue, a subspace sparsity driven knowledge transfer strategy based DCMOEA is developed in this article, called SSDKT. First, reference points are introduced to partition objective space into multiple subspaces. Subsequently, the feasibility of each subspace is determined by the distribution of all historical feasible optimal solutions in it, and defined as the sparsity of subspace. A predictor based on the gated recurrent unit (GRU) network is further constructed to estimate the sparsity under the future environment. Once a new environment appears, a subspace transfer strategy is designed to generate an initial population. In each feasible subspace, the GRU-based prediction method is developed and competed with Kalman filter to generate the initial solution under the new environment. Based on the predicted solution of the nearest feasible neighbor, a potential initial individual in each infeasible subspace is produced by transferring the corresponding knowledge. The experimental results on various benchmarks verify that, compared with several state-of-the-art DCMOEAs, the proposed algorithm achieves the most competitive performance in solving DCMOPs.

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.

Learning with little data is challenging but often inevitable in various application scenarios where the labeled data are limited and costly. Recently, few-shot learning (FSL) gained increasing attention because of its generalizability of prior knowledge to new tasks that contain only a few samples. However, for data-intensive models such as vision transformer (ViT), current fine-tuning-based FSL approaches are inefficient in knowledge generalization and, thus, degenerate the downstream task performances. In this article, we propose a novel mask-guided ViT (MG-ViT) to achieve an effective and efficient FSL on the ViT model. The key idea is to apply a mask on image patches to screen out the task-irrelevant ones and to guide the ViT focusing on task-relevant and discriminative patches during FSL. Particularly, MG-ViT only introduces an additional mask operation and a residual connection, enabling the inheritance of parameters from pretrained ViT without any other cost. To optimally select representative few-shot samples, we also include an active learning-based sample selection method to further improve the generalizability of MG-ViT-based FSL. We evaluate the proposed MG-ViT on classification, object detection, and segmentation tasks using gradient-weighted class activation mapping (Grad-CAM) to generate masks. The experimental results show that the MG-ViT model significantly improves the performance and efficiency compared with general fine-tuning-based ViT and ResNet models, providing novel insights and a concrete approach toward generalizing data-intensive and large-scale deep learning models for FSL.

This work studies the problem of block validation in a blockchain network where a block manager acting as a task publisher sends a task (block validation) to all the workers (miners) within the network. The latter carries out the block validation and finally returns the final results to the former. The goal of this work is to maximize the block manager’s profit by jointly optimizing the latency of the block verification process and the reward offered by the manager to miners. Note that the latency and reward are closely coupled. Therefore, in this case, if it is solved directly, they are offered separately, and their dependency is not well considered, leading to overall poor performance. This work formalizes it as an optimization problem considering both delay and reward, and proposes an evolutionary approach, namely, the reborn dandelion algorithm (RDA), to solve it. Specifically, in the proposed algorithm, each individual contains both delays and rewards for different types of miners. A reborn strategy is designed to reborn an individual to replace the worst one in the current population, with the aim of enhancing its exploration ability. A greedy selection strategy is proposed to enhance its exploitation ability. The experimental results on CEC2013 functions and blockchain network instances indicate that our proposed approach is significantly superior to other evolutionary-based ones.

Due to unaffordable computational costs, the regularized disparity in iterative stereo matching is typically maintained at a lower resolution than the input. To regress the full resolution disparity, most stereo methods resort to convolutions to decode a fixed-scale output. However, they are inadequate for recovering vital high-frequency information lost during downsampling, limiting their performance on full-resolution prediction. In this paper, we introduce AnyStereo, an accurate and efficient disparity upsampling module with implicit neural representation for the iterative stereo pipeline. By modeling the disparity as a continuous representation over 2D spatial coordinates, subtle details can emerge from the latent space at arbitrary resolution. To further complement the missing information and details in the latent code, we propose two strategies: intra-scale similarity unfolding and cross-scale feature alignment. The former unfolds the neighbor relationships, while the latter introduces the context in high-resolution feature maps. The proposed AnyStereo can seamlessly replace the upsampling module in most iterative stereo models, improving their ability to capture fine details and generate arbitrary-scale disparities even with fewer parameters. With our method, the iterative stereo pipeline establishes a new state-of-the-art performance. The code is available at https://github.com/Zhaohuai-L/Any-Stereo.

In dynamic optimization problems where optimal solutions change over time, traditional ant colony optimization (ACO) algorithms face limitations. This study explores the adaptation of multi-colony ACO algorithms, known for their enhanced search capabilities in stationary problems, to tackle optimization problems in dynamic environments. Various strategies for exchanging information between colonies, which is a critical factor influencing algorithm performance, are investigated. Using the dynamic traveling salesman problem as a foundation, we generate test cases to reflect real-world complexities. Our results on a set of problem instances reveal that the choice of communication strategy between colonies significantly impacts the adaptability and efficiency of multi-colony ACO algorithms in tracking moving optimum.

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.

Model management is an essential component in data-driven surrogate-assisted evolutionary optimization. In model management, the solutions with a large degree of uncertainty in approximation play an important role. They can strengthen the exploration ability of algorithms and improve the accuracy of surrogates. However, there is no theoretical method to measure the uncertainty of prediction of Non-Gaussian process surrogates. To address this issue, this article proposes a method to measure the uncertainty. In this method, a stationary random field with a known zero mean is used to measure the uncertainty of prediction of Non-Gaussian process surrogates. Based on experimental analyses, this method is able to measure the uncertainty of prediction of Non-Gaussian process surrogates. The method's effectiveness is demonstrated on a set of benchmark problems in single surrogate and ensemble surrogates cases.

In data-driven evolutionary optimization, most existing Gaussian processes (GPs)-assisted evolutionary algorithms (EAs) adopt stationary GPs (SGPs) as surrogate models, which might be insufficient for solving most optimization problems. This article finds that GPs in the optimization problems are nonstationary with great probability. We propose to employ a nonstationary GP (NSGP) surrogate model for data-driven evolutionary optimization, where the mean of the NSGP is allowed to vary with the decision variables, while its residue variance follows an SGP. In this article, the nonstationarity of GPs in the tested functions is theoretically analyzed. In addition, this article constructs an NSGP where the SGP is a degenerate case. Performance comparisons of the NSGP with the SGP and the NSGP-assisted EA (NSGP-MAEA) with the SGP-assisted EA (SGP-MAEA) are carried out on a set of benchmark problems and an antenna design problem. These comparison results demonstrate the competitiveness of the NSGP model.

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.

Gaussian processes (GPs) are a kind of non-parametric Bayesian approach. They are widely used as surrogate models in data-driven optimization to approximate the exact functions. However, the cubic computation complexity is involved in building GPs. This paper proposes hyperparameters adaptive sharing based on transfer learning for scalable GPs to address the limitation. In this method, the hyperparameters across source tasks are adaptively shared to the target task by the linear predictor. This method can reduce the computation cost of building GPs without losing capability based on experimental analyses. The method's effectiveness is demonstrated on a set of benchmark problems.

Electric vehicle routing problems are challenging variations of the traditional vehicle routing problem which incorporate the possibility of electric vehicle (EV) recharging at any station, while satisfying the delivery demands of customers. This work addresses the recently formulated capacitated vehicle routing problem (E-CVRP) with variable energy consumption rate. In particular, the cargo weight, which is one of the main factors affecting the energy consumption rate of EVs, is considered (i.e., the heavier the EV the higher the rate). As a solution method, an ant colony optimization algorithm with a local search heuristic is developed. Experiments are conducted on a recently generated benchmark set of E-CVRP instances demonstrating that the performance of the proposed technique improves on the best known so far solutions.

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.

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.

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.

Cooperative co-evolution (CC) is an efficient and practical evolutionary framework for solving large-scale optimization problems. The performance of CC is affected by the variable decomposition. An accurate variable decomposition can help to improve the performance of CC on solving an optimization problem. The variable grouping methods usually spend many computational resources obtaining an accurate variable decomposition. To reduce the computational cost on the decomposition, we propose an efficient recursive differential grouping (ERDG) method in this article. By exploiting the historical information on examining the interrelationship between the variables of an optimization problem, ERDG is able to avoid examining some interrelationship and spend much less computation than other recursive differential grouping methods. Our experimental results and analysis suggest that ERDG is a competitive method for decomposing large-scale continuous problems and improves the performance of CC for solving the large-scale optimization problems.

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 following topics are dealt with: evolutionary computation; genetic algorithms; search problems; optimisation; learning (artificial intelligence); particle swarm optimisation; Pareto optimisation; pattern classification; pattern clustering; computational complexity.

Many artificial benchmark problems have been proposed for different kinds of continuous optimization, e.g., global optimization, multimodal optimization, multiobjective optimization, dynamic optimization, and constrained optimization. However, there is no unified framework for constructing these types of problems and possible properties of many problems are not fully tunable. This will cause difficulties for researchers to analyze strengths and weaknesses of an algorithm. To address these issues, this paper proposes a simple and intuitive framework, which is able to construct different kinds of problems for continuous optimization. The framework utilizes the k -d tree to partition the search space and sets a certain number of simple functions in each subspace. The framework is implemented into global/multimodal optimization, dynamic single objective optimization, multiobjective optimization, and dynamic multiobjective optimization, respectively. Properties of the proposed framework are discussed and verified with traditional evolutionary algorithms.

For computationally expensive constrained optimization problems, one crucial issue is that the existing expected improvement (EI) criteria are no longer applicable when a feasible point is not initially provided. To address this challenge, this paper uses the expected improvement of constraint violation to reach feasible region. A new constrained expected improvement criterion is proposed to select sample solutions for the update of Gaussian process (GP) surrogate models. The validity of the proposed constrained expected improvement criterion is proved theoretically. It is also verified by experimental studies and results show that it performs better than or competitive to compared criteria.

Hyperspectral remote sensing images present rich information on the characteristics of different physical materials. Utilizing the rich information, classifiers can distinguish these different materials. The minimum distance technique, which is commonly used in classification, is sensitive to the distance metric, especially in high-dimensional space. In this letter, we study the effect of the $p$ -norm distance metric on the minimum distance technique and propose a supervised-learning $p$ -norm distance metric to optimize the value of $p$ . In the experimental study, we take the minimum distance and the $k$ -nearest neighbor classifiers as examples to test the proposed supervised-learning $p$ -norm distance metric. The results suggest that the supervised-learning $p$ -norm distance metric can improve the performance of a classifier for hyperspectral remote sensing image classification.

A novel multiobjective technique is proposed for solving constrained optimization problems (COPs) in this paper. The method highlights three different perspectives: 1) a COP is converted into an equivalent dynamic constrained multiobjective optimization problem (DCMOP) with three objectives: a) the original objective; b) a constraint-violation objective; and c) a niche-count objective; 2) a method of gradually reducing the constraint boundary aims to handle the constraint difficulty; and 3) a method of gradually reducing the niche size aims to handle the multimodal difficulty. A general framework of the design of dynamic constrained multiobjective evolutionary algorithms is proposed for solving DCMOPs. Three popular types of multiobjective evolutionary algorithms, i.e., Pareto ranking-based, decomposition-based, and hype-volume indicator-based, are employed to instantiate the framework. The three instantiations are tested on two benchmark suites. Experimental results show that they perform better than or competitive to a set of state-of-the-art constraint optimizers, especially on problems with a large number of dimensions.

Cooperative co-evolution (CC) is an explicit means of problem decomposition in multipopulation evolutionary algorithms for solving large-scale optimization problems. For CC, subpopulations representing subcomponents of a large-scale optimization problem co-evolve, and are likely to have different contributions to the improvement of the best overall solution to the problem. Hence, it makes sense that more computational resources should be allocated to the subpopulations with greater contributions. In this paper, we study how to allocate computational resources in this context and subsequently propose a new CC framework named CCFR to efficiently allocate computational resources among the subpopulations according to their dynamic contributions to the improvement of the objective value of the best overall solution. Our experimental results suggest that CCFR can make efficient use of computational resources and is a highly competitive CCFR for solving large-scale optimization problems.

The travelling salesman problem is a well known combinatorial optimization problem and evolutionary computation methods are one of the important methods to solve it. A difficult issue for evolutionary computation methods is to identify good edges that belong to the global optimum during the search progress. To address this issue, this paper proposes a tour construction algorithm, which is based on a memory-based statistical learning mechanism. A probability matrix is created according to the edge distribution in a memory population, which stores the best solution found by every individual. For each individual, a tour is constructed according to its local personal best solution found so far and the global probability matrix. Two variants of ant colony optimization are chosen to test the effectiveness of the proposed algorithm. The result show that the proposed algorithm is an efficient learning algorithm for the travelling salesman problem.

For the differential evolution (DE) algorithms, there are many parameter adaptation methods, which aim at tuning the mutation factor F and the crossover probability CR. When the population diversity is very small and has been converged in a local optimum, even if the evolution goes on, the population will no longer improve. This is also true for the DE algorithms with adaptive F and CR. The enhancement of population diversity is necessary to DE algorithms. In this paper, we test the JADE algorithm with auto-enhanced population diversity (AEPD) on the newest benchmark functions.

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.

This paper presents a Modified Cuckoo Search (MCS) algorithm for solving flow shop scheduling problem with blocking to minimize the makespan. To handle the discrete variables of the job scheduling problem, the smallest position value (SPV) rule is used to convert continuous solutions into discrete job permutations. The Nawaz-Enscore-Ham (NEH) heuristic method is utilized for generating high quality initial solutions. Moreover, two frequently used swap and insert operators are employed for enhancing the local search. To verify the performance of the proposed MCS algorithm, experiments are conducted on Taillard's benchmark set. Results show that MCS performs better than the standard CS and some previous algorithms proposed in the literature.

In differential evolution (DE) studies, there are many parameter adaptation methods, aiming at tuning the mutation factor F and the crossover probability CR . However, these methods still cannot resolve the issues of population premature convergence and population stagnation. To address these issues, in this paper, we investigate the population adaptation regarding population diversity at the dimensional level and propose a mechanism named auto-enhanced population diversity (AEPD) to automatically enhance population diversity. AEPD is able to identify the moments when a population becomes converging or stagnating by measuring the distribution of the population in each dimension. When convergence or stagnation is identified at a dimension, the population is diversified at that dimension to an appropriate level or to eliminate the stagnation issue. The AEPD mechanism was incorporated into a popular DE algorithm and it was tested on a set of 25 CEC2005 benchmark functions. The results showed that AEPD significantly improved the performance of the original algorithms. In addition, AEPD helped the algorithms become less sensitive to population size, a parameter widely considered problem dependent for many DE algorithms. The DE algorithm with AEPD also has a superior performance in comparison with several other peer algorithms.

In differential evolution (DE), the optimal value of the control parameters is problem-dependent. Many improved DE algorithms have been proposed with the aim of improving the effectiveness for solving general problems. As a very known adaptive DE algorithm, JADE adjusts the crossover probability CR of each individual by a norm distribution, in which the value of standard deviation is fixed, based on its historical record of success. The fixed and small standard deviation results in that the generated CR may not suitable for solving a problem. This paper proposed an improvement for the adaptation of CR, in which the standard deviation is adaptive. The diversity of values of CR was improved. This improvement was incorporated into the JADE algorithm and tested on a set of 25 scalable benchmark functions. The results showed that the adaptation of CR improved the performance of the JADE algorithm, particularly in comparisons with several other peer algorithms on high-dimensional functions.

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.

In differential evolution (DE), there are many adaptive algorithms proposed for parameters adaptation. However, they mainly aim at tuning the amplification factor F and crossover probability CR. When the population diversity is at a low level or the population becomes stagnant, the population is not able to improve any more. To enhance the performance of DE algorithms, in this paper, we propose a method of population adaptation. The proposed method can identify the moment when the population diversity is poor or the population stagnates by measuring the Euclidean distances between individuals of a population. When the moment is identified, the population will be regenerated to increase diversity or to eliminate the stagnation issue. The population adaptation is incorporated into the jDE algorithm and is tested on a set of 25 scalable CEC05 benchmark functions. The results show that the population adaptation can significantly improve the performance of the jDE algorithm. Even if the population size of jDE is small, the jDE algorithm with population adaptation also has a superior performance in comparisons with several other peer algorithms for high-dimension function optimization.

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.

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.

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.

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.

In the paper, for many-objective optimization problems, the authors pointed out that the Pareto Optimality is unfair, unreasonable and imperfect for Many-objective Optimization Problems (MOPs) underlying the hypothesis that all objectives have equal importance and propose a new evolutionary decision theory. The key contribution is the discovery of the new definition of optimality called E-optimality for MOP that is based on a new conception, so called E-dominance, which not only considers the difference of the number of superior and inferior objectives between two feasible solutions, but also considers the values of improved objective functions underlying the hypothesis that all objectives in the problem have equal importance. Two new evolutionary algorithms for E-optimal solutions are proposed. Because the new relation-≺Eof E-dominance is not transitive, so a new way must be found for consideration of convergence properties of algorithms. A Boolean function better used as a select strategy is defined The convergence theorems of the new evolutionary algorithms are proved. Some numerical experiments show that the new evolutionary decision theory is better than Pareto decision theory for many-objective function optimization problems.

Particle swarm optimization (PSO) has shown its fast search speed in many complicated optimization and search problems. However, PSO could often easily fall into local optima. This paper presents an Opposition-based PSO (OPSO) to accelerate the convergence of PSO and avoid premature convergence. The proposed method employs opposition-based learning for each particle and applies a dynamic Cauchy mutation on the best particle. Experimental results on many well- known benchmark optimization problems have shown that OPSO could successfully deal with those difficult multimodal functions while maintaining fast search speed on those simple unimodal functions in the function optimization.

Particle swarm optimization (PSO) has shown its fast search speed in many complicated optimization and search problems. However, PSO could often easily fall into local optima because the particles could quickly get closer to the best particle. At such situations, the best particle could hardly be improved. This paper proposes a new hybrid PSO (HPSO) to solve this problem by adding a Cauchy mutation on the best particle so that the mutated best particle could lead all the rest of particles to the better positions. Experimental results on many well-known benchmark optimization problems have shown that HPSO could successfully deal with those difficult multimodal functions while maintaining fast search speed on those simple unimodal functions in the function optimization