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Dynamic constrained multi-objective optimization problems (DCMOPs) involve objectives, constraints, and parameters that change over time. This kind of problem presents a greater challenge for evolutionary algorithms because it requires the population to quickly track the changing pareto-optimal set (PS) under constrained conditions while maintaining the feasibility and good distribution of the population. To address these challenges, this paper proposes a dynamic constrained multi-objective optimization algorithm based on co-evolution and diversity enhancement (CEDE), in which we have made improvements to both the static optimization and dynamic response parts, innovatively utilizing the valuable information latent in the optimization process to help the population evolve more comprehensively. The static optimization involves the co-evolution of three populations, through which their mutual synergy can more comprehensively identify potential true PS and provide more useful historical information for dynamic response. Additionally, to prevent the elimination of potentially valuable infeasible individuals (i.e., individuals that are not dominated by feasible individuals) due to pareto domination, we employ an archive set to store and update these individuals. When the environment changes, to effectively enhance population diversity under complex dynamic constraints and help the population to respond quickly to changes, we propose a diversity enhancement strategy, which includes a diversity maintenance strategy and a center point-based exploration strategy. This strategy effectively enhances population diversity in complex and changing environments, helping the population respond quickly to changes. The effectiveness of the algorithm is validated through two test sets. The experimental results show that CEDE can effectively use valuable information to cope with complex dynamic constraint environments. Compared with several of the most advanced algorithms, it is superior in 94% of the test problems, demonstrating strong competitiveness in handling DCMOPs. [ABSTRACT FROM AUTHOR]

Differential evolution multi-objective algorithms effectively address problems with two or three objectives. However, many-objective problems with more than three objectives are challenging because of inadequate selection pressure in environment selection, excessive variation in mutation, and difficulties in representing the Pareto front. This paper introduces a novel approach that combines differential evolution with a knee-oriented strategy to address the mentioned challenges. The approach allows the algorithm to focus on trade-off solutions for representing the surface instead of searching the entire Pareto front. Specifically, the algorithm consists of two stages: knee exploration stage and knee exploitation stage. Each stage utilizes different dominance relationships and mutation operators to enhance selection pressure in high-dimensional spaces. Moreover, a Manhattan distance-domination range is designed to update the reference vector by identifying multiple localized knee points in high-dimensional space. The experimental results demonstrate superior performance to other state-of-the-art algorithms on 50 knee-oriented benchmark problem test sets, including CKP, DO2DK, DEB2DK, DEB3DK, and PMOPs. [ABSTRACT FROM AUTHOR]

• A comprehensive learning differential evolution (CLDE) is presented. • Three improved components are used to boost CLDE in solving MAED problem. • CLDE is applied to six large-scale MAED cases considering valve point effects. • CLDE outperforms eighteen state-of-the-art algorithms. • The benefit of three components of CLDE is investigated. The role of multi-area economic dispatch (MAED) in power system operation is increasingly significant. It is a non-linear and multi-constraint problem with many local extremes when considering the valve point effects, posing challenges in obtaining a globally optimal solution, especially for large-scale systems. In this study, an improved variant of differential evolution (DE) called CLDE based on comprehensive learning strategy (CLS) is proposed to solve this problem. Three improved strategies are employed to enhance the performance of CLDE. (1) A CLS-based guided mutation strategy is proposed, in which learning exemplars constructed by competent individuals are used to generate mutant vectors to prevent the searching away from global optimum and speed up convergence. (2) A time-varying increasing crossover rate is devised. It can endow CLDE with a larger probability at the later stage to help individuals escape from local extremes. (3) A CLS-based crossover strategy is presented. Trial vectors directly utilize the information from learning exemplars for evolving, which can ensure the search efficiency and population diversity. CLDE is applied to six MAED cases. Compared with DE, it approximately consumes 32 %, 35 %, 10 %, 22 %, 62 %, and 20 % of evaluations to attain comparable results, saves 126.2544$/h, 81.8173$/h, 152.0660$/h, 360.7907$/h, 65.5757$/h, and 1732.8544$/h in fuel costs on average, and exhibits improvements of 34.77 %, 1.80 %, 0.00 %, 76.09 %, 95.15 %, and 16.76 % in robustness, respectively. Moreover, it also outperforms other state-of-the-art algorithms significantly in statistical analysis. Furthermore, the effects of improved strategies on CLDE are thoroughly investigated. [ABSTRACT FROM AUTHOR]

The fixed-charge transportation (FCT) problem, an extension of the classical transportation problem, holds significance in practical logistics scenarios where fixed charges play a crucial role. Fixed charges categorize it as an NP-hard problem, posing challenges for conventional methods due to their inefficiency, high computational costs, and susceptibility to local optima. This paper introduces an enhanced evolutionary algorithm, offline learning-based competitive swarm optimization (OLCSO), tailored to address the FCT problems efficiently. OLCSO draws inspiration from offline learning, where particles benefit from the experiences of high performers. The algorithm incorporates (i) a ranking-based mechanism where losers learn from peer-to-peer winners based on their ranks, (ii) a two-phase cooperative evolutionary mechanism enhancing searchability and convergence of the algorithm. In the first phase, losers learn from personal best experiences and the shifted center of the population, boosting diversity. In the second phase, losers learn from winners and the center of the population, improving exploitation, (iii) a mutation strategy is embedded to update winner locations in each evolutionary procedure, and (iv) to ensure a feasible solution to FCT problems, the paper also introduces negative and fractional repair mechanisms. OLCSO is applied to solve two sets of FCT problems, linear and non-linear. Experimental results are compared with various heuristic and metaheuristic techniques, commonly used for these problems, using diverse metrics. A comparative analysis of OLCSO's design elements is also conducted. The results demonstrate OLCSO's superiority over existing algorithms. [ABSTRACT FROM AUTHOR]

Fast and accurate parameter identification of the photovoltaic (PV) model is crucial for calculating, controlling, and managing PV generation systems. Numerous meta-heuristic algorithms have been applied to identify unknown parameters due to the multimodal and nonlinear characteristics of the parameter identification problems. Although many of them can obtain satisfactory results, problems such as premature convergence and population stagnation still exist, influencing the optimization performance. A novel variant of Differential Evolution, namely, Diversity Improvement-Oriented Differential Evolution (DIODE), is proposed to mitigate these deficiencies and obtain reliable parameters for PV models. In DIODE, an adaptive perturbation strategy is employed to perturb current individuals to mitigate premature convergence by enhancing population diversity. Secondly, a diversity improvement mechanism is proposed, where information on the covariance matrix and fitness improvement of individuals is used as a diversity indicator to detect stagnant individuals, which are then updated by the intervention strategy. Lastly, a novel parameter adaptation strategy is employed to maintain a sound balance between exploration and exploitation. The proposed DIODE algorithm is applied to parameter identification problems of six PV models, including single, double, and triple diode and three PV module models. In addition, a large test bed containing 72 benchmark functions from CEC2014, CEC2017, and CEC2022 test suites is employed to verify DIODE's overall performance in terms of optimization accuracy. Experiment results demonstrate that DIODE can secure accurate parameters of PV models and achieve highly competitive performance on benchmark functions. [ABSTRACT FROM AUTHOR]

Multimodal multiobjective optimization problems (MMOPs) have attracted extensive research interest. These problems are characterized by the presence of multiple equivalent optimal solutions in the decision space, all corresponding to the same optimal values in the objective space. However, effectively finding a high-quality and evenly distributed Pareto sets (PSs) remains a challenge for researchers. This paper introduces a multimodal multiobjective differential evolution algorithm based on enhanced decision space search (MMODE_EDSS). By adopting two types of strategies to enhance the decision space search capability, the algorithm generates multiple high-quality non-dominated solutions. In the early stages of evolution, neighborhood information is used to enhance search capabilities, while in the later stages, data interpolation methods following clustering are employed for searching. Moreover, to improve the overall population distribution, an environmental selection mechanism based on dual-space crowding distance is adopted. The effectiveness of the proposed algorithm, MMODE_EDSS, is evaluated by comparing it with eight state-of-the-art multimodal multiobjective evolutionary algorithms (MMOEAs). Experimental results confirm the significant advantages of MMODE_EDSS. [ABSTRACT FROM AUTHOR]

Using infeasible information to balance objective optimization and constraint satisfaction is a very promising research direction to address constrained multi-objective problems (CMOPs) via evolutionary algorithms (EAs). The existing constrained multi-objective evolutionary algorithms (CMOEAs) still face the issue of striking a good balance when solving CMOPs with diverse characteristics. To alleviate this issue, in this paper we develop a two-stage different evolution with a dynamic population assignment strategy for CMOPs. In this approach, two cooperative populations are used to provide feasible driving forces and infeasible guiding knowledge. To adequately utilize the infeasibility information, a dynamic population assignment model is employed to determine the primary population, which is used as the parents to generate offspring. The entire search process is divided into two stages, in which the two populations work in weak and strong cooperative ways, respectively. Furthermore, multistrategy-based differential evolution operators are adopted to create aggressive offspring. The superior exploration and exploitation ability of the proposed algorithm is validated via some state-of-the-art CMOEAs over artificial benchmarks and real-world problems. The experimental results show that our proposed algorithm gained a better, or more competitive, performance than the other competitors, and it is an effective approach to balancing objective optimization and constraint satisfaction. [ABSTRACT FROM AUTHOR]

Since the inception of Differential Evolution (DE), the vast majority of studies on it indicate that exponential crossover does not solve the real-parameter optimization in continuous spaces very well. However, we find that once the appropriate crossover rate C R and its corresponding parameter control are found, the DE variants with exponential crossover can achieve comparable performance with the ones employing binomial crossover. In this paper, a new DE algorithm, called Global Opposition Learning and Diversity ENhancement based DE with exponential crossover (GOLDEN-DE), is proposed to fill the gap in this field. The GOLDEN-DE algorithm has the following highlights: First, a novel global opposition learning mechanism is proposed in our GOLDEN-DE algorithm; Second, a Novel Parameter Control, namely NPC technique, with fitness-independent characteristic is incorporated in the GOLDEN-DE algorithm. Third, a novel population Diversity ENhancement (DEN) mechanism is proposed, and individuals in the stagnation status can be re-calculated in order to enhance population diversity. Fourth, a time stamp mechanism for handling too old inferior solutions in the external archive is also put forward. We evaluate the GOLDEN-DE algorithm for real-parameter single-objective global optimization on 88 benchmarks from the three universal test sets, including CEC2013, CEC2014, and CEC2017 test suites, and experiment results show that our GOLDEN-DE algorithm is competitive with several state-of-the-art DE variants. [ABSTRACT FROM AUTHOR]

Emerging Unmanned Aerial Vehicle (UAV) application patterns, including the Loyal Wingman and Unmanned Swarms, have significantly challenged the administration and defense against illegal or trespassing UAVs. The weapon-target assignment (WTA) problem, a famous combinatorial optimization problem in military operations research, is decisive for the success of UAV defense programming. Related investigations face two main challenges: 1) Constructing a multi-objective optimization model reflecting the complexities of new UAV application patterns, and 2) solving the time-consuming WTA problem with high-dimension decision variables as it is NP-complete. This paper introduces a modified differential evolution based on a new mapping method called Pareto-Optimal-Matching that solves multi-objective binary optimization problems and constructs a 3 objective Sensor-Weapon-Target Assignment model. The proposed algorithm overcomes the inherent limitation of traditional differential evolution, which only performs well in continuous problems. Promising results were obtained based on different simulation metrics under various problems (proposed model, MOKP, and ZDT5), validating the superior performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Multimodal optimization problems (MMOPs) include multiple optima, which are common in practical fields. However, the success of solving MMOPs requires the algorithm to have both exploration and exploitation performance. How to select a reasonable search strategy is a difficult problem facing MMOPs. In this research, a differential evolution based on strategy adaptation and deep reinforcement learning, termed SA-DQN-DE, is proposed to select mutation strategies reasonably and search the optima effectively, which mainly includes three aspects. First, strategy adaptation, which calculates selection probability based on the feedback of different mutation operators in previous evolution, and assigns mutation operations to each individual to provide guidance for the next stage of evolution is developed. Secondly, a new historical individual preservation method is designed to improve search efficiency. Thirdly, deep reinforcement learning is applied to select multiple local search operators to refine the accuracy of potential optimal solutions. The performance of SA-DQN-DE is tested on publicly acknowledged CEC2013 benchmark MMOP set. The experimental results demonstrate that the proposed SA-DQN-DE has competitive performance compared with some of its peer multimodal optimization algorithms. [ABSTRACT FROM AUTHOR]

Gene selection is a pivotal process in machine-learning-driven medical diagnostics, where the goal is to identify a subset of genes from microarray expression profiles that can enhance the predictive accuracy of classifiers for disease diagnosis. The two key objectives of gene selection are to reduce the dimensionality of the data and to improve the accuracy of disease diagnosis, which is typically a multi-objective optimization problem. In recent years, multi-objective evolutionary algorithms (MOEAs) have gained wide attention in feature selection research, and several related algorithms have been produced. However, most algorithms tend to get stuck in local optimality when searching for solutions from a high-dimensional space. To solve the gene selection problem effectively, this study introduces a recursive multi-objective differential evolution algorithm with elite recursive strategy (RMODE-E) and a recursive multi-objective differential evolution algorithm with Pareto front recursive strategy (RMODE-P). RMODE-E amalgamates the features selected by the top E elite individuals, RMODE-P consolidates the features selected by the Pareto front set, and the combined features then serve as the foundation for subsequent recursive rounds of searching. The proposed feature subspace combination strategy not only reduces the recursive search space but also improves the capacity to find globally optimal feature subsets. Extensive experiments were conducted to compare our proposed algorithms with eight state-of-the-art evolutionary algorithms to validate their effectiveness. Experimental results demonstrate that RMODE-P has better global search capability as it achieves better best classification accuracy, mean classification accuracy , and minimal gene subset size. [ABSTRACT FROM AUTHOR]

Ensemble learning of multiple search strategies has demonstrated effectiveness in improving the performance of differential evolution (DE) for global optimization. In existing ensemble learning methods, offspring for each target solution is generated by one of the strategies from the strategy pool according to the optimization requirement of the considered problem. However, since the genetic material of an offspring generally comes from one single strategy, the advantages of different strategies could not be simultaneously utilized for optimizing decision variables with different properties. To deal with this problem, this paper proposes the collective ensemble learning (CEL) paradigm, which merges the advantages of multiple strategies for generating an offspring. CEL mainly includes the component decomposition (CD) and component integration (CI) mechanisms. The CD mechanism divides the target solutions and the candidates generated by different generation strategies into exploitative and explorative components respectively, in consideration of the evolution status at the dimension level. Then, the CI mechanism is implemented to integrate the appropriate components to form the offspring according to the sub-similarity measurement performed at the component level. The effectiveness and advantages of CEL have been validated and discussed by performance comparisons with the baseline, each single mechanism, existing ensemble learning methods, as well as several state-of-the-art DE variants. [ABSTRACT FROM AUTHOR]

Many metaheuristic methods have been proposed and have shown promising performance in solving multi-objective optimization problems (MOPs). As a representative example, the competitive swarm optimizer (CSO) exhibits excellent performance in solving large-scale MOPs. However, CSO performs poorly when used straightforwardly for constrained MOPs with complex constraints or objective spaces. In this paper, we propose a dual-swarm-based CSO framework that co-evolves two swarms with different orientations: (i) CSO is improved using genetic algorithms, namely CSO-GA to form a convergence-directed swarm without considering constraints to accelerate the convergence. (ii) CSO is further improved by differential evolution, namely CSO-DE to form a search-directed swarm by considering constraints to enhance diversity and improving the search for the constrained Pareto front. Moreover, a new constraint relaxation method is proposed that combines the particle swarm feasible rate and current evolutionary generation to dynamically adjust the factor for decreasing or increasing constraint relaxation. Extensive experiments with 37 benchmark instances and nineteen real-world constrained MOPs demonstrate that our proposed algorithm yields significantly better or at least more competitive results than ten state-of-the-art methods. • A dual-swarm-based CSO framework is proposed for CMOPs. • Two swarms co-evolve to form different orientations. • A new constraint relaxation method is presented. • Results demonstrate the superiority of our approach. [ABSTRACT FROM AUTHOR]

• A model was created to examine the reliability of maintenance budget allocation. • The model was applied to network-level pavement maintenance in Canada. • The impacts of algorithm selection and parameter tuning were studied. • The significance of pavement clustering in increasing reliability was highlighted. • The importance of incorporating actual pavement improvement curves was clarified. The purpose of this paper is to increase the reliability of the network-level pavement maintenance budget allocation by reducing uncertainties of algorithm selection and parameter tuning. In this paper, reliability is defined as the ability of a network-level pavement maintenance plan to improve the condition of a pavement network within a certain budget. In order to quantify reliability, the reliability index is defined as the ratio between the post-maintenance network condition and the net maintenance cost. With this purpose in mind, a two-objective optimization model was developed. To test its applicability, the model was applied to a pavement network in Canada. The model was solved using the Non-Dominated Sorting Genetic Algorithm II and the differential evolution algorithms. Finally, the reliability indices of algorithms and termination criteria were computed. The results indicated that the differential evolution algorithm recommended less frequent but more intense interventions that made the solutions expensive and less reliable. This paper contributed to the network-level pavement maintenance body of knowledge by (1) developing a multi-objective optimization model to reduce uncertainties of parameter tuning and algorithm selection; (2) increasing the reliability of budget allocation; (3) showcasing the significance of pavement clustering in increasing reliability; and (4) developing and incorporating actual pavement improvement curves. [Display omitted] [ABSTRACT FROM AUTHOR]

The performance of differential evolution (DE) algorithm heavily depends on the evolutionary scale, which is controlled by the generation operations including mutation, crossover and the control parameters including mutation factor and crossover rate. Adjusting the evolutionary scale to suit different types of problems is a critical yet challenging open question in DE research. To efficiently address this issue, this paper proposes a novel DE based on evolutionary scale adaptation, termed as ESADE. First, a successful scale estimation mechanism is proposed to measure the appropriate evolutionary scale by utilizing the successful evolutionary feedback from the solution space provided by the trial vectors and the target vectors. With the appropriate evolutionary scale, an evolutionary scale adaptation mechanism pre-selects the closest or the farthest trial vector from each target vector, which corresponds to a small or large evolutionary scale respectively to match the search requirements of different evolutionary stages. The effectiveness of the ESA method is demonstrated by performance comparisons with each single baseline strategy, state-of-the-art DEs and state-of-the-art multi-strategy methods on 29 benchmark functions with three dimensionalities. Further applications on several real-world optimization problems also reveal the competitive performance of ESADE. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel adaptive differential evolution algorithm for global optimization problems by introducing an enhanced mutation operator and a new mixed control parameter setting based on dual performance evaluation metrics. To further strengthen the search efficiency of algorithm and availably balance its exploration and exploitation, a dual performance metrics-based mutation operator is first proposed to implement the search of population by organically integrating the fitness value and history update of individual to find the potential promising areas and allocate the suitable search resources for them. Meanwhile, a dual performance metrics-based mixed parameter setting is developed to yield appropriate associated parameters for each individual by comprehensively measuring its search characteristic and requirement based on both its fitness value and history update. In addition, a new restart strategy is further put forward to boost the search performance of algorithm by reasonably replacing the meaningless individuals measured by both their fitness values and history updates with the randomly generated individuals based on Gaussian walk. In contrast to the existing DE versions, the new algorithm organically takes advantage of the fitness value and history update of individual to assign the proper computational resources for each potential promising region, create the suitable parameters for different individuals, and eliminate the valueless individuals from population. Thereby, it is capable of heightening the search efficiency of algorithm and maintaining a good balance between exploration and exploitation effectively. At last, the performance of the proposed algorithm is evaluated by comparing with 19 typical or up-to-date algorithms on 42 benchmark functions from both IEEE CEC2017 and CEC2022 test suites. Compared to these opponents, the proposed algorithm achieves significantly better performance on 60 out of 77 cases based on the multiproblem Wilcoxon signed-rank test at a significant level of 0.05, and thus is a more promising optimizer. [ABSTRACT FROM AUTHOR]

In many-objective optimization problems (MaOPs), balancing convergence and diversity while rapidly converging to the Pareto front is an arduous task for evolutionary algorithms. In addition, with the increase of the number of targets, the number of non-dominant solutions increases exponentially, and the individual selection pressure is insufficient. For this problem, we propose a many-objective evolution algorithm assisted by an ideal hyperplane (MaOEA-IH). To begin, the ideal hyperplane is built from the extremums of each dimension of objective space, guiding the individual to the Pareto front of search. Second, a parallel p -norm mating selection strategy based on the ideal hyperplane is proposed to improve convergence. In addition, two other factors are taken into account: (1) different p-norms are used to measure different spatial scales; and (2) individual selection uncertainty is defined by incorporating a probabilistic perturbation mechanism. Following that, the sum of objectives is applied to shift-based density estimation, which serves as an evaluation criterion in the environmental selection operation. This method increases the chances of solutions with high convergence and diversity entering the next generation, thereby increasing selection pressure. On three benchmark problems of DTLZ, WFG, and MaF, we compare MaOEA-IH with seven excellent algorithms. The results demonstrate that the MaOEA-IH proposed is highly competitive in solving MaOPs. [ABSTRACT FROM AUTHOR]

Opposition-based learning (OBL) is an effective strategy that adjusts the population to accelerate the convergence of the algorithm. However, OBL involves two phases (generation and calculation) that are seldom mentioned simultaneously. Besides, individual information in OBL is not fully used to guide evolution. First, a novel neighborhood generation strategy is proposed to fully use individual information. There are numerous variants of the neighborhood structure. Three prominent neighborhood structures are designed to demonstrate their benefits in various dimensions. Second, a multi-operator calculation method with two distributions is introduced to reach the equilibrium between diversification and intensification. Consequently, this paper proposes three multi-operator neighborhood-based OBL variants (MNOBLs). Compared with the traditional OBL variants, MNOBLs generate the opposite population by using a neighborhood of the individuals. A well-balanced calculation method can lead to good convergence behavior. Subsequently, the proposed MNOBLs are embedded into the basic differential evolution (DE) algorithm to obtain the proposed algorithms. The extensive and rigorous numerical experiments are designed at three levels: strategies, algorithms, and functions. Specifically, the effectiveness and efficiency of the proposed algorithms are verified by comparing them with 13 state-of-the-art DE variants and four metaheuristics on the CEC 2017, and CEC 2022 test suites, and two real-world optimization problems. The comprehensive results show that the proposed OBL variants provide promising results for most problems. [ABSTRACT FROM AUTHOR]

As optimization problems become more and more complex in real-world scenarios, the effectiveness of many existing differential evolution (DE) methods is critically challenged. To circumvent this predicament, this paper proposes a triple competitive DE (TCDE) to tackle increasingly complicated optimization problems. Specifically, a triple competition mechanism is devised to first randomly arrange individuals into exclusive triples and then let individuals in each triple compete with each other. Subsequently, heterogeneous mutation schemes are designed to update the three individuals in each triple based on the competition results. With the cooperation between these two techniques, on the one hand, better individuals in the triples tend to exploit the areas where they lie to find high-accuracy solutions, while worse individuals in the triples prefer to explore the intricate problem space to locate promising regions. On the other hand, different individuals are mutated by following the guidance of different leading exemplars, which ensures that individuals traverse the sophisticated solution space in diverse directions along with slight intensification to optimal regions. Furthermore, a modified adaptive parameter adjustment scheme is designed for individuals in each triple by considering their differences so as to meet the expectation that better individuals focus on exploitation while worse individuals concentrate on exploration. Finally, experiments are performed to first compare TCDE with totally 10 advanced DE variants and then further compare it with totally 10 CEC winners and their latest variants on the CEC'2014 and the CEC'2017 problem suites with totally 4 different dimensionality settings. Experimental results prove that TCDE achieves highly competitive or even much better performance than the totally 20 compared methods. Particularly, TCDE is demonstrated to be especially capable of solving complicated optimization problems. Furthermore, the efficacy of TCDE in tackling real-world optimization problems is substantiated through experiments conducted on the CEC'2011 real-world optimization problem set. [ABSTRACT FROM AUTHOR]

Differential Evolution (DE), as a promising population-based stochastic optimization algorithm, has drawn attention from researchers of various fields owing to its simple operation, strong robustness and few control parameters. However, classic DE suffers from drawbacks such as premature convergence and stagnation resulted from reduced population diversity when tackling complicated optimization problems with high dimensions. To mitigate these deficiencies, Differential Evolution with Perturbation mechanism and Covariance Matrix based stagnation indicator (PCM-DE) is proposed in this paper. There are three main modifications in the algorithm. First, a two-phase parameter adaptation strategy based on fitness value is proposed to guide the search towards promising direction according to different stages of evolution. Second, a perturbation mechanism for archived population is proposed, where a new weight coefficient is defined by exploiting information of fitness value and position in archived individuals. Third, a stagnation indicator based on covariance matrix is proposed to assess the population diversity and the information of variance is employed to perturb stagnant individuals. To validate the effectiveness of PCM-DE, it is compared with several state-of-the-art DE variants and non-DE based algorithms under a large test suite containing 100 benchmark functions. Besides, three truss optimization problems are also employed to verify the feasibility and scalability of the algorithm. The experiment results confirm its highly competitive performance in terms of solution accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

• The gradient information and dimension perturbation mutation are integrated. • Both the local and global search potentials are explored for each solution. • The dynamic local and global searches are adapted to the current search state. • Effective exploration and exploitation are designed in the reduced search space. • GIDPM performs better than MMA in designing the sandwich panel with truss cores. Surrogate-assisted evolutionary algorithms (SAEAs) have recently shown excellent abilities in solving computationally expensive optimization problems (EOPs), but most of them are not designed for high-dimensional EOPs (HEOPs). A new algorithm where the gradient information is well-incorporated into dimension perturbation mutation called as GIDPM for HEOPs, is proposed and fully investigated in this paper. Specifically, for each solution, a local candidate offspring pool is obtained by combining the gradient descent information and dimension perturbation mutation, and the DE/current-to-rand/2/bin is employed to generate a global candidate offspring pool. Then an offspring selection strategy is used to identify the exact offspring solutions, in which the overall qualities of two pools, the directions of near gradient descent of candidate solutions, and the distributions and RBF predictions of candidate solutions are considered in turn, to achieve appropriate local exploitation or global exploration. In addition, an Autoencoder-embedded search strategy is used to quickly jump out of the local optima caused by some small ripples or oscillations of the landscape after each several iterations to achieve leapfrog search. The GIDPM maintains a good balance between exploration and exploitation. Experimental studies on benchmark problems demonstrate that the GIDPM achieves better convergence performance when the problem dimension is larger than or equal to 30, and the better performance of GIDPM can be achieved with the increase of dimension. The GIDPM is also used for the design of the sandwich panel with truss cores. Compared with gradient-based algorithm, the GIDPM obtains the design with better structural performance. [ABSTRACT FROM AUTHOR]

A Supervised Parallel Optimisation (SPO) is presented. The proposed framework couples different optimisation algorithms to solve single-objective optimisation problems. The supervision balances the exploration and exploitation capabilities of the distinct optimisers included, providing a general framework to solve problems with diverse characteristics. In this work, five optimisation algorithms are included in the ensemble: Particle Swarm Optimisation (PSO), Genetic Algorithm (GA), Covariance Matrix Adaption-Evolution Strategy (CMA-ES), Differential Evolution (DE), and Modified Cuckoo Search (MCS). A geometric path-finding problem with numerous local minima is used to demonstrate the advantage of SPO. The effectiveness of the approach is compared with that of stand-alone incidences of the integrated optimisation strategies and with state-of-the-art algorithms. In addition, a benchmark test suit composed of engineering applications is utilised to validate the general applicability of SPO with respect to a variety of problems. The good solutions generated by SPO are shown to be generally reproducible, while isolated algorithms, at best, render good solutions only occasionally. • A supervised parallel optimisation (SPO) ensembles distinct optimisers. • SPO balances exploration/exploitation to solve diverse problems. • Extensive tests based on SPO ensemble using optimisers PSO, GA, CMAES, DE, MCS. • SPO outperforms isolated algorithms finding reproducible solutions. • The strategy reduces the necessity of exhaustive hyperparameter fine-tuning. [ABSTRACT FROM AUTHOR]

Many surrogate-assisted evolutionary algorithms (SAEA) with outstanding performance have been developed to handle Expensive Constrained Optimization Problems (ECOPs). But most of them are limited to solving ECOPs with continuous variables and inequality constraints. Therefore, a Kriging-assisted Double Population Differential Evolution (KDPDE) is proposed to deal with mixed-integer ECOPs with inequality and equality constraints. In particular, promising regions near the feasible region are created by Integer restriction Relaxation-based Double Population (IRDP) search framework, and then an Expected Improvement-based Classification local Search (EICS) is adopted to guide the infeasible solutions in the promising region into the feasible region. In order to improve the robustness of the algorithm, the widely distributed elite solutions are utilized by Elite solutions Retention-based Multi-directional Exploration (ERME) for diverse exploration, and the repetition rate information of individuals in the population is used by Population Diversity Maintenance Operation (PDMO) to adaptively avoid the population from falling into a local region. Therefore, KDPDE is capable of balancing the performance between convergence and robustness for mixed-integer ECOPS with mixed constraints. Experimental studies on several benchmark problems and a real-world application example demonstrate that KDPDE has excellent performance on solving such kind of problems under a limited computational budget. [ABSTRACT FROM AUTHOR]

Current multimodal multiobjective optimization (MMO) has mostly focused on locating multiple equivalent global Pareto optimal sets (PSs) or local PSs in the decision space, rarely considering finding both simultaneously. To address this issue, this paper explores a crowded individual activation multiobjective differential evolution algorithm based on subpopulation region solution selection, named CAMODE_SR. In CAMODE_SR, a subpopulation region solution selection mechanism is developed to search for more uniformly distributed global and local Pareto optimal solutions. Specifically, two types of specific neighborhood radii are designed depending on the location information of the Pareto optimal solutions discovered during evolution. The two types of radii construct specific neighborhoods for the global and local optimal solutions to maintain the solutions with better diversity. To improve the exploitation capacity of the population, a crowded individual activation mechanism is proposed by developing an activation function associated with iteration. The activation function activates the crowded individuals in local regions to exploit more superior solutions near global optimal solutions. The proposed CAMODE_SR achieves a good tradeoff between the performance of locating both global and local PSs. Extensive experiments on the CEC 2020 MMO benchmark functions demonstrate that the proposed CAMODE_SR is significantly superior to nine state-of-the-art MMEAs in tackling multimodal multiobjective optimization problems with global and local PSs. • Propose a multiobjective differential evolution for global and local Pareto sets. • Design two types of specific neighborhood radii for the Pareto optimal solutions. • Develop a subpopulation region solution selection for the proposed algorithm. • Develop a crowded individual activation mechanism for the proposed algorithm. [ABSTRACT FROM AUTHOR]

Multimodal optimization problems (MOPs) need to locate the global optima as many as possible and refine the accuracy of the identified optima as high as possible. How to divide niches reasonably and search solutions effectively are two difficult problems facing MOPs. In this paper, a coarse- and fine-grained niching-based differential evolution (CFNDE) algorithm with micro-search strategy is proposed to divide population reasonably and search the optima effectively, which mainly includes four contributions. Firstly, a framework of coarse- and fine-grained niching (CFN) strategy is proposed, where the coarse-grained clustering method provides the information of clusters to the fine-grained clustering method to accurately divide the population into niches. Secondly, a micro-search-based mutation (MSM) strategy is proposed to accelerate the convergence of population, which searches for the optimal solution in the range between the current individual and the nearest individual. Thirdly, a multi-level local search (MLLS) strategy that incorporates the cluster-level and population-level search mechanisms is proposed to refine the accuracy of solutions. Finally, a stagnation detection and re-search (SDR) strategy is proposed to re-search the local optima in evolution. We compare CFNDE with the-state-of-art multimodal optimization algorithms on the widely used benchmark CEC'2013. The experimental results show that CFNDE performs better than or similar to some recently proposed algorithms in 17 out of 20 tested functions. Besides, the proposed CFNDE is also applied to the multirobot task allocation problems and CFNDE provides multiple completely different optimal scheduling schemes to deal with emergencies. [ABSTRACT FROM AUTHOR]

Real parameter single objective optimization has been studied for decades. In recent, long-term search is emphasized based on the consideration that, in the field, solving difficulty often scales exponentially with the increase of function dimensionality. For long-term search, Differential Evolution (DE) still performs outstanding among types of population-based metaheuristics. In this paper, based on IMODE – a DE algorithm with three mutation strategies, we propose AMCDE – Differential Evolution with Alternation between steady Monopoly and transient Competition of mutation strategies. Our algorithm has two states. In the steady state – monopoly, a selected mutation strategy controls the whole population. Once improvement in fitness becomes difficult, the transient state – competition – arises. In the competition state, similar with IMODE, each of the mutation strategies controls a proportion of positions in the population and competes with the others. For enhancement, we propose that positions controlled by the winner among the three mutation strategies continue to be controlled by the mutation strategy in the next generation. Besides, in the competition state, the original selection strategy of IMODE is revised by us for diversification, while adaptation of the crossover rate is updated. Our experiment is based on three CEC benchmark test suites and the CEC 2011 suite of real world optimization problems. AMCDE is compared with seven peers. Based on experimental results, our algorithm demonstrates superior or at the very least comparable performance for long-term search compared to the peers. Moreover, we do experimental observation on AMCDE. [ABSTRACT FROM AUTHOR]

Satellite range scheduling always plays a crucial role in tracking, telemetry, and control of the spacecraft. With the significant increase in the number and type of satellites in orbit, the demands of users for satellite range scheduling are becoming more and more diverse. However, existing studies for the satellite range scheduling problem (SRSP) rarely consider multiple optimization objectives, which is quite significant in practice. Hence, this paper investigates a multi-objective satellite range scheduling problem (MO-SRSP) that optimizes three objectives simultaneously: the overall profits of tasks, load-balance of antennas, and completion timeliness of tasks. To address MO-SRSP, this paper establishes a mathematical model on the basis of analysis of MO-SRSP and proposes a multi-objective evolutionary algorithm, which is called multi-objective differential evolution algorithm based on space division and adaptive selection strategy (MODE-SDAS). The space division strategy will uniformly divide the objective space into a set of subspaces and preserve a set of non-dominated solutions in each subspace during the environmental selection even if some of these solutions are dominated by other solutions in other subspaces, so as to maintain the diversity of the algorithm. The adaptive selection strategy will adaptively allocate computational resources to different subspaces to improve the convergence of the population. Besides, problem-specific designs such as coding and encoding methods, the discrete differential evolution operator, as well as objective-specific individual variation operators are incorporated into the algorithm to enhance the search capability. Finally, extensive experiments based on simulation test cases are carried out to verify the effectiveness and efficiency of MODE-SDAS. The comparison results show that MODE-SDAS significantly outperforms its competitors in terms of three metrics. Meanwhile, knee point analysis, sensitivity analysis, and application insights are presented. • A tri-objective satellite range scheduling problem. • A multi-objective differential evolution algorithm is proposed. • Space division and adaptive selection strategies are combined. • Problem-specific and objective-specific designs are applied. [ABSTRACT FROM AUTHOR]

Solving constrained optimization problems (COPs) with evolutionary algorithms (EAs) is a popular research direction due to its potential and diverse applications. One of the key issues in solving COPs is the choice of constraint handling techniques (CHTs), as different CHTs can lead to different evolutionary directions. Combining EAs with deep reinforcement learning (DRL) is a promising and emerging approach for solving COPs. Although DRL can help solve the problem of pre-setting operators in EAs, neural networks need to obtain diverse training data within a limited number of evaluations in EAs. Based on the above considerations, this work proposes a DRL assisted co-evolutionary differential evolution, named CEDE-DRL, which can effectively use DRL to help EAs solve COPs. (1) This method incorporates co-evolution into the extraction of training data for the first time, ensuring the diversity of samples and improving the accuracy of the neural network model through information exchange between multiple populations. (2) Multiple CHTs are used for offspring selection to ensure the algorithm's generality and flexibility. (3) DRL is used to evaluate the population state, taking into account feasibility, convergence, and diversity in the state setting and using the overall degree of improvement as a reward. The neural network selects suitable parent populations and corresponding archives for mutation. Finally, (4) to avoid premature convergence and local optima, an adaptive operator selection and individual archive elimination mechanism is added. Comparisons with state-of-the-art algorithms on benchmark functions CEC2010 and CEC2017 show that the proposed method performs competitively and produced robust solutions. The results of the application test set CEC2020 show that the proposed algorithm is also effective in real-world problems. • A DRL-based co-evolutionary differential evolution is proposed for the COPs. • Multiple CHTs are used for offspring selection to ensure the generality and flexibility. • DRL is used to evaluate the population state and selects suitable mating population. • Adaptive operator selection and individual archive elimination mechanism are developed. [ABSTRACT FROM AUTHOR]

Convergence, diversity, and feasibility are crucial factors in solving constrained multi-objective optimization problems (CMOPs). Their imbalance can result in the algorithm failing to converge well to the Pareto front, especially when dealing with complex CMOPs. To address this issue, we propose an adaptive tradeoff evolutionary algorithm (ATEA), which can adjust the environment selection strategy based on the characteristics of problem, aiming to achieve a balance between convergence and diversity while ensuring feasibility of the population. The ATEA divides the search process into three phases: In the extended exploration phase, a global search is conducted using a guided constraint relaxation technique to enable the population to quickly traverse the infeasible region and approach the feasible region. In the tradeoff exploration phase, constraints are further detected and estimated to retain more feasible individuals and competing infeasible individuals, allowing the population to accurately identify all possible feasible regions and gradually expand towards the feasible boundary. The exploitation phase explores under-explored regions in the earlier phases with the aim of accelerating the convergence of the population and escaping from the local optima. Extensive experiments conducted on four benchmark test suites demonstrate that ATEA exhibits superior performance in three benchmark test suites compared with six other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Various benchmark sets have already been proposed to facilitate comparison between metaheuristics, or Evolutionary Algorithms. During the competition, typically algorithms are allowed either to run until the allowed number of function calls is exhausted (and one compares the quality of solutions found), or until a required objective function value is obtained (one compares the speed in reaching the required solution). During the last 20 years several problem sets were defined using the first approach. In this study, we test 73 optimization algorithms proposed between the 1960′s and 2022 on nine competitions based on four sets of problems (CEC 2011, CEC 2014, CEC 2017, and CEC 2020) with different dimensionalities. We intend to test the original versions of 73 algorithms "as they are", with control parameters proposed by the authors of the particular method. The recent benchmark set, CEC 2020, includes fewer problems and allows much more function calls than the former sets. As a result, one group of algorithms perform best on older, a different one on the more recent (CEC 2020) benchmark sets. Almost all algorithms that perform best on CEC 2020 set achieve moderate-to-poor performance on older sets, including real-world problems from CEC 2011. Algorithms that perform best on older sets are more flexible than those that perform best on CEC 2020 benchmark. The choice of the benchmark may have a crucial impact on the final ranking of algorithms. The lack of tuning may affect the results that were obtained in this study, hence it is highly recommended to repeat a similar large-scale comparison with control parameters of each algorithm tuned, best by different methods, separately for each benchmark set. [ABSTRACT FROM AUTHOR]

Parameter setting is a significant and demanding process in metaheuristics. It requires deep understanding of the considered algorithm as well as of the considered optimization problem. Thus, it has attracted ongoing scientific interest counting a considerable number of relevant approaches, which are mostly focused in offline and ad hoc procedures. Interestingly, the parameter tuners contain also their own parameters. It is a basic requirement that these parameters shall be easily tunable and mildly affecting the tuner's performance. The present work proposes an enhanced version of the recently proposed gradient-based parameter adaptation method, which offers an online general-purpose parameter tuning procedure that is applicable to any metaheuristic. The proposed method dynamically tunes the tuner's parameters by using the REINFORCE reinforcement learning paradigm. The method is demonstrated on the differential evolution algorithm for established test suites of variable dimensions as well as for the real-world application of detecting atomic clusters through the minimization of Lennard-Jones potentials. The obtained results are statistically analyzed and compared with state-of-the-art auto-tuning algorithms. The analysis reveals the promising performance of the proposed approach as well as its robustness under the considered experimental setting. [ABSTRACT FROM AUTHOR]

Differential Evolution (DE) -type algorithms perform efficiently on optimization problems, but for some problems, single DE-type algorithms still cannot achieve good results. Integrating multiple algorithms or strategies is an effective way to improve the performance of a single algorithm. This paper proposes a cascaded DE-type algorithm optimization framework with population adaptive allocation and reduction (cDE-APAR), which improves the performance of a single algorithm by cascading two DE-type algorithms and combining related strategies. The first stage of the algorithm runs a single algorithm. The second stage implements the other algorithm in parallel with a local search strategy and a global search strategy, and allocates resources reasonably among the single algorithm and related strategies through adaptive population allocation. Finally, individuals with the worst performance are eliminated through the population reduction strategy to improve the population's quality. In order to verify the performance of the algorithm, extensive simulations were performed using four test suites of CEC2005, CEC2013, CEC2014, and CEC2017. The results show that cDE-APAR significantly improves the performance of a single algorithm. Compared with nine state-of-the-art algorithms, cDE-APAR is significantly better than the comparison algorithms according to the Wilcoxon rank sum test and has significantly improved the accuracy and stability of the solution. [ABSTRACT FROM AUTHOR]

In multimodal multiobjective optimization problems (MMOOPs), there is more than one Pareto-optimal Set (PS) in the decision space corresponding to the same Pareto Front(PF). How to dynamically adjust the evolution direction of the population adaptively is a key problem, to ensure approaching the PF in the global sense with good convergence while finding out more PSs. In this paper, a novel Differential Evolution algorithm based on Reinforcement Learning with Fitness Ranking (DE-RLFR) is proposed. The DE-RLFR is based on the Q-learning framework, and each individual in the population is considered an agent. The fitness ranking values of each agent are used to encode hierarchical state variables. Three typical DE mutation operations are employed as optional actions for the agent. Based on the analysis of the distribution characteristics of the population in objective space, decision space and fitness-ranking space, we design a reward function of the 〉 state , action 〈 pairs to guide the population to move to the PF asymptotically. According to its reinforcement learning experience represented by the corresponding Q table value, each agent could adaptively select a mutation strategy to generate offspring individuals. The evaluation results on eleven MMOOP test functions show that DE-RLFR could quickly and effectively find multiple PSs in the decision space, and approach PF in the global sense. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) is a widely used heuristic algorithm for numerical optimization over continuous space. As the core operator, the mutation operator has a great effect on DE's performance. In this paper, we propose a cooperative ranking-based mutation strategy (CRM) for DE when solving constrained optimization problems (COPs). In CRM, two different ranking criteria are adopted in a cooperative way to move the population towards a feasible global optimum with a faster convergence speed. The first criterion is objective function value-based criterion which is applied for feasible solutions to converge towards the global optimum. The second criterion is overall constraint violation-based criterion which is applied for infeasible solutions to search for feasible regions. The proposed CRM is integrated into the basic DE and two advanced DE variants. The comparison results showed that the DE variants with CRM have a faster convergence speed than the non-CRM-based variants in the majority of test problems. This approach is a promising strategy to improve the search ability of DE variants when solving COPs. [ABSTRACT FROM AUTHOR]

Bilevel optimization problems involve a hierarchical model where an upper level optimization problem is solved with a constraint on the optimality of a nested lower level problem. The use of evolutionary algorithms (EAs) and other metaheuristics has been gaining attention to solve bilevel problems, especially when they contain non-linear/black-box objective(s) and/or constraint(s). However, EAs typically operate in a nested mode wherein a lower level optimization is executed for each upper level solution. Evidently, this process requires excessive number of function evaluations, which might become untenable if the underlying functions are computationally expensive. In order to reduce this expense, the use of approximations (also referred to as surrogates or meta-models) has been suggested previously. However, the previous works have focused only on the use of surrogates for the lower level problem, whereas the computational expense of the upper level problem has not been considered. In this paper, we aim to make two contributions to address this research gap. The first is to introduce an improved nested EA which uses surrogate-assisted search at both levels in order to solve bilevel problems using limited number of function evaluations. The second is the revelation and a systematic investigation of a previously overlooked aspect of bilevel search – that the objective/constraints at the upper and lower levels may involve different computational expense. Consideration of this aspect can help in deciding a suitable strategy, i.e., in which level is the use of surrogates most appropriate for the given problem. Towards this end, four different nested strategies – with surrogate at either level, none or at both levels, are compared under various experimental settings. Numerical experiments are presented on a wide range of problems to demonstrate the efficacy and utility of the proposed contributions. [ABSTRACT FROM AUTHOR]

This paper investigates a hypothesis that in case of hard optimization problems, selection of the proper search space is more relevant than the choice of the solving algorithm. Dynamic Vehicle Routing Problem is used as a test problem and the hypothesis is verified experimentally on the well-known set of benchmark instances. The paper compares Particle Swarm Optimization (PSO) and Differential Evolution (DE) operating in two continuous search spaces (giving in total four distinctive approaches) and a state-of-the art discrete encoding utilizing Genetic Algorithm (GA). The advantage of selected continuous search space over a discrete one is verified on the basis of quality of the final solution and stability of intermediate partial solutions. During stability analysis it has been observed that practical level of uncertainty, resulting from the dynamic nature of the problem, is lower than could be expected from a popular degree of dynamism measure. In order to challenge that issue, benchmark problems have been solved also with a higher level of dynamism and an empirical degree of dynamism has been proposed as an additional measure of the amount of uncertainty of the problem. The results obtained by both continuous algorithms outperform those of state-of-the-art algorithms utilizing discrete problem representation, while the performance differences between them (PSO and DE) are minute. Apart from higher numerical efficiency in solving DVRP, the use of continuous problem encoding proved its advantage over discrete encoding also in terms of intermediate solutions stability. Requests-to-vehicles assignment sequences generated by the proposed approach were approximately 40% more accurate with respect to the final solution than their counterparts generated with a discrete encoding. Analysis of these sequences of intermediate solutions for several benchmark sets resulted in designing a penalty term taking into account a specific dynamic nature of the optimized problem. An addition of this penalty term improved the above-mentioned stability of partial solutions by another 10%. [ABSTRACT FROM AUTHOR]

Engineering optimization problems usually involve computationally expensive simulations and massive design variables. Solving these problems in an efficient manner is still a big challenge. Recently, surrogate-assisted metaheuristic algorithms have been widely studied and are considered to have potential to solve such engineering optimization problems. In this paper, a surrogate-guided differential evolution algorithm is proposed to further improve the optimization efficiency for these problems. Unlike other surrogate-assisted metaheuristic algorithms, it makes a fusion between the differential evolution algorithm and surrogates, which are not just taken as an additional tool to accelerate the convergence of metaheuristic algorithms. Specifically, the proposed algorithm combines the optima predicted by the global and local surrogates with the mutation operator and makes them guide the mutation direction of the differential evolution algorithm, which thus makes the differential evolution algorithm converge fast. A simple surrogate prescreening strategy is also proposed to further improve its optimizing efficiency. In order to validate the proposed algorithm, it is tested by a lot of high dimensional numerical benchmark problems whose dimensions vary from 20 to 200 and is applied to an optimal design of a stepped cantilever beam and an optimal design of bearings in an all-direction propeller. An overall comparison between the proposed algorithm and other optimization algorithms has been made. The results show that the proposed algorithm is promising for optimizing the high dimensional expensive problems especially for the problems whose dimensions are more than 30. [ABSTRACT FROM AUTHOR]

In this paper, we propose a multi-agent based art production framework. In existing artwork creation systems, images were generated using artificial life and evolutionary computation approaches. In artificial life, swarm intelligence or Boids model, and in evolutionary computation, genetic algorithm or genetic programming are commonly used to create images. These automated artwork creation systems make it easy to create artistic images even if the users are not professional artists. Despite the high possibility of these creation systems, however, much research has not been done so far. In this paper, we propose an art production framework that generates images using multi-agents with chaotic dynamics features. Agents act on the canvas following the three rules of Boids model. In addition, each agent possesses a chaotic neural network which trained by differential evolution algorithm, so that colors can be evolved to represent a better style. As a result, we propose an art production framework for generating processing artworks that contain highly complex dynamics. Finally, we created the glitch artworks using the proposed framework, which shows a new glitch style. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a novel saturated control method for a quadrotor to realize three–dimensional spatial trajectory tracking with heterogeneous comprehensive learning particle swarm optimization (HCLPSO). First, the model of the quadrotor is decomposed into cascaded control structure (CCS) with inner attitude control loop and outer position control loop. Second, the saturated control is deployed to confine the thrust force of the quadrotor in the outer position control loop. Then, the inner attitude reference signals can be generated with the outer position control loop through the cascaded control mode. Third, to alleviate the difficulty of the parameter adjustment, HCLPSO algorithm is applied in the control parameter optimization for the quadrotor. The optimization results of the HCLPSO are compared with that of particle swarm optimization (PSO), comprehensive learning particle swarm optimization (CLPSO), genetic algorithm (GA), and differential evolution (DE). At last, simulation results certify that the spatial trajectory tracking control of the quadrotor can be successfully achieved with the proposed method. [ABSTRACT FROM AUTHOR]

Abstract Artificial bee colony algorithm (ABC) has attracted wide attention in the recent decade. Although ABC algorithms can achieve good performance on separable problems by optimizing each variable independently, their performances on complex non-separable problems are still unsatisfactory. In this paper, through incorporating multiple differential search strategies and a self-adaptive mechanism into the framework of ABC, we propose a new ABC algorithm, called self-adaptive differential artificial bee colony (sdABC) algorithm. By means of differential search strategies, more variables will be updated each time based on the combination of mutation and crossover. Thus, sdABC has much enhanced ability for solving complex non-separable problems. Our proposed sdABC algorithm is evaluated on 28 benchmarks functions, including both common separable problems and complex non-separable CEC2015 functions. The experimental results show that sdABC can achieve much more desirable performances than the previous ABC algorithms on both separable and non-separable functions, and is also very competitive compared with well-established differential evolution and other meta-heuristic algorithms. [ABSTRACT FROM AUTHOR]

Abstract In traditional particle swarm optimization (PSO) algorithm, each particle updates its velocity and position with a learning mechanism based on its personal best experience and the population best experience. The learning mechanism in traditional PSO is simple and easy to implement, but it suffers some potential problems, such as the phenomena of "oscillation" and "two steps forward, one step back". Therefore, designing an effective learning strategy to avoid these two phenomena and to improve the search efficiency is an urgent issue for PSO research. This paper proposes a dimensional learning strategy (DLS) for discovering and integrating the promising information of the population best solution according to the personal best experience of each particle. Thereafter, a two-swarm learning PSO (TSLPSO) algorithm based on different learning strategies is proposed. One of the subpopulations constructs the learning exemplars by DLS to guide the local search of the particles, and the other subpopulation constructs the learning exemplars by the comprehensive learning strategy to guide the global search. 16 classic benchmark functions, 30 CEC2014 test functions, and 1 real-world optimization problem are used to test the proposed algorithm against with 5 typical PSO algorithms and 1 state-of-the-art differential evolution (DE) algorithm. The experimental results show that TSLPSO is statistically and significantly better than the compared algorithms for most of the test problems. Moreover, the convergence speed and convergence accuracy of TSLPSO are also significantly improved. [ABSTRACT FROM AUTHOR]

Abstract Differential evolution (DE) has attracted more and more attention. However, the neighborhood and direction information has not been fully utilized in exploration and exploitation stages. A failure remember-driven self-adaptive differential evolution algorithm, ATBDE, is proposed in this paper, which uses "Top-Bottom" strategy with optional archive and a parameter self-adapting strategy driven by "Failure Remember" operation. "Top-Bottom" strategy utilizes historical heuristic information obtained from the successful and failed individuals, respectively, to guide individuals toward the potential more promising regions in an optional archive manner. This strategy is also theoretically analyzed for the best implementation. The failure remember-driven parameter adaption strategy shares the positive search experience from the successful individuals and abandons the negative search experience for those successive failing individuals. Comprehensive experiments show that ATBDE is better than, or at least comparable to, other DE algorithms in terms of convergence performance and accuracy. [ABSTRACT FROM AUTHOR]

Abstract Community detection is one of the key problem areas in social network analysis. It is classified as an NP-hard problem. Although a lot of good approximate algorithms are available for finding clusters in social networks, all those algorithms have serious drawbacks. They have high time complexities and are inefficient in finding shared communities, a phenomenon common in real-world social networks. In this work a novel community detection algorithm is proposed, that is inspired by the fire propagation model, and is named as Fire Spread community detection algorithm (FSA). When a place catches fire, its nearby places are also at risk of getting burned by it. Getting burned by fire depends on several factors, such as distance from the source of fire, the combustive threshold of the material, number of neighbors already in burning state and heat transmission property of the gap between source and current place. Finding a community near a seed node resembles the phenomena of fire propagation originating from a source. Finally, the proposed algorithm is validated by comparing the modularity and conductance scores with some of the state-of-the-art community detection algorithms for which synthetic and real-world networks are used. [ABSTRACT FROM AUTHOR]

Abstract Various powerful differential evolution (DE) algorithms have been developed in the past years, although none of them can consistently perform well on all types of problems. However, it is not straightforward to choose an appropriate algorithm for solving a real-world problem, as the properties of the problem are usually not well understood beforehand. Therefore, how to automatically select an appropriate DE variant for solving a particular problem at hand is an important and challenging task. In the present work, a performance-driven multi-algorithm selection strategy (PMSS) is proposed to alleviate the above mentioned problems for single objective optimization. In PMSS, a learning-forgetting mechanism is introduced to update the selection probability of each algorithm from a pool of DE variants to make sure that the best performing one is chosen during the search process. The effectiveness of PMSS is carefully examined on two suites of widely used test problems and the results indicate that the PMSS is highly effective and computationally efficient. Finally, the proposed algorithm is employed to optimize the energy consumption of sea-rail intermodal transportation. Our simulation results demonstrate that the proposed algorithm is successful achieving satisfactory solution that are able to provide insights into the problem and the algorithm is promising to be applied for solving real sea-rail intermodal and other multimodal transportation planning problems. Highlights • The proposed strategy can automatically select a suitable algorithm to solve a particular problem. • The performance of PMSS is demonstrated on two suites of benchmark functions. • PMSS is utilized to optimize the energy consumption of sea-rail intermodal transportation. [ABSTRACT FROM AUTHOR]

Abstract Proper investments for expansion of generation, transmission and distribution systems in an electric grid is a very important issue that rely on optimal expansion planning of the grid resources. Investments on transmission network influence those in generation and distribution side which motivates a co-optimization of all these different resources of a grid. The co-optimization based Generation - Transmission Expansion planning is a large scale, constrained, hard bound optimization problem. This research article proposes an Information exchange based Clustered Differential Evolution algorithm (IE-CDE) for solving the problem of expansion planning of generation and transmission resources in an electric grid. The proposed algorithm is first tested extensively on the CEC 2017 constrained optimization benchmark problems and the results are compared with those obtained by state-of-the art algorithms to investigate the efficiency of the proposed algorithm in solving challenging constrained optimization problems. Then the proposed algorithm IE-CDE is used to solve the challenging Generation-Transmission expansion planning problem (GT) on a test system called Garver system. The implementation is also extended to incorporate the expansion planning of demand management resources along with generation and transmission resources (GTD) on the same test system mentioned before as well as an additional one called IEEE 24 bus system. The results obtained by proposed IE-CDE on the GT and GTD expansion planning problems are compared with state of the art algorithms in the literature and the comparison reveal that the proposed method is able to find better solutions than the other algorithms yielding lower cost of expansion for the electric grid. The claim for superiority of the proposed method over others is also substantiated by statistical significance tests on the obtained results. [ABSTRACT FROM AUTHOR]

Abstract The theoretical study of Genetic Algorithms and the dynamics induced by their genetic operators is a research field with a long history and many different approaches. In this paper we complete a recently presented approach to model one-point crossover using pretopologies (or Čechtopologies) in two ways. First, we extend it to the case of n -points crossover. We extend the definition of crossover distance between populations to work for n -points crossover, proving that computing it can be performed in polynomial time for any fixed number of crossover points. Secondly, we experimentally study how the distance distribution changes when the number of crossover points increases. In particular, the average distance between a population and the optimum decreases with the increase in the number of crossover points, showing that increasing the latter can reduce the number of crossover operations needed to evolve an optimal solution. [ABSTRACT FROM AUTHOR]

Abstract In general, evolutionary algorithms are very prevalent in solving multi-objective optimization problems. Pareto-based multi-objective evolutionary algorithms are popularly used in solving different multi-objective optimization problems. These algorithms work using several steps, non-dominated sorting being the most salient one. However, this non-dominated sorting step is associated with a high computational complexity. In the past, different approaches have been proposed for non-dominated sorting. In this paper, to address the problem of non-dominated sorting, a framework called DCNS (Divide-and-conquer based non-dominated sorting) is developed. Based on this DCNS framework, four different approaches are proposed. The best case time complexity of our proposed DCNS framework is proved to be O (N log N + M N) for M ≥ 2 where N is the number of solutions and M is the number of objectives. This best case time complexity is better than the best case time complexities of various other approaches. The number of dominance comparisons performed by the proposed framework is lower than those from other state-of-the-art approaches in different scenarios. The proposed framework has the parallelism property and the scope of parallelism is also discussed. [ABSTRACT FROM AUTHOR]

Abstract Seaports play a vital role in our everyday life: they handle 90% of our world trade goods. Improving seaports' efficiency means improving the efficiency of sending and receiving our goods. In seaports, one of the most important and most expensive operations is how to allocate vessels to berths. In this paper, we solve this problem by proposing a new meta-heuristic, which combines the nature-inspired Levy Flight random walk with local search, while taking into account tidal windows. With our algorithm, we meet the following goals: (i) to minimise the cost of all vessels while staying in the port, and (ii) to schedule available berths for the arriving vessels taking into account a multi-tidal planning horizon. In comparison with the state-of-the-art exact method using commercial solver and a competitive heuristic, the computational results prove our approach guarantees feasibility of solutions for all the problem instances and is able to find good solutions in a short amount of time, especially for large-scale instances. We also compare our results to an existing state-of-the-art Particle Swarm Optimisation and our work produces significantly better performances on all the test instances. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a multimodal multiobjective Differential Evolution optimization algorithm (MMODE). The technique is conceived for deployment on problems with a Pareto multimodality, where the Pareto set comprises multiple disjoint subsets, all of which map to the same Pareto front. A new contribution is the formulation of a decision-variable preselection scheme that promotes diversity of solutions in both the decision and objective space. A new mutation-bound process is also introduced as a supplement to a classical mutation scheme in Differential Evolution methods, where offspring that lie outside the search bounds are given a second opportunity to mutate, hence reducing the density of individuals on the boundaries of the search space. New multimodal multiobjective test functions are designed, along with analytical expressions for their Pareto sets and fronts. Some test functions introduce more complicated Pareto-front shapes and allow for decision-space dimensions greater than two. The performance of the MMODE algorithm is compared with five other state-of-the-art methods. The results show that MMODE realizes superior performance by finding more and better distributed Pareto solutions. Highlights • A multimodal multi-objective optimization with differential evolution method is proposed to solve multimodal multi-objective optimization problems. • A preselection scheme and a mutation bound processing method are designed to obtain multiple subsets in the Pareto set and improve their distribution. • Novel test functions with different Pareto set shapes are designed to verify the validity of the proposed algorithm. • Compared with some existing multi-objective optimization algorithms, the proposed algorithm shows statistical superiority. [ABSTRACT FROM AUTHOR]

Abstract The work presented here involves development and detailed investigations of niching methods for multimodal optimization of constrained functions. There is a lack of investigations in the literature on constrained multimodal optimization, hence a number of constrained niching algorithms have been developed here that leverage existing differential evolution-based niching methods with a feasibility rules-domination selection procedure. Furthermore, a suite of 18 benchmark functions has been developed and are presented in this paper; nine newly developed functions are incorporated with nine existing functions from the literature. Optimization results on these analytical functions using the constrained niching algorithms are presented, with analysis provided on the ability to locate multiple global optima, the convergence speed and constraint handling nature of the methods. The differential evolution strategy is also investigated, with SHADE and L-SHADE strategies considered. Finally, a dimensionality study also compares against the only other known constrained niching algorithm. Results indicate that all of the algorithms developed and tested generally perform well for low dimensional, low modality problems, but that local neighbourhood-based methods show the best results across the suite of functions tested. When high-dimensional problems are considered, using the L-SHADE strategy yields excellent results. An accompanying supplementary data file is provided with the manuscript. [ABSTRACT FROM AUTHOR]