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Many real-life problems can be formulated as numerical optimization problems. Such problems pose a challenge for researchers when designing efficient techniques that are capable of finding the desired solution without suffering from premature convergence. This paper proposes a novel evolutionary algorithm that blends the exploitative and explorative merits of two main evolutionary algorithms, namely the Stochastic Fractal Search (SFS) and a Differential Evolution (DE) variant. This amalgam has an effective interaction and cooperation of an ensemble of diverse strategies to derive a single framework called Iterative Cyclic Tri-strategy with adaptive Differential Stochastic Fractal Evolutionary Algorithm (Ic3-aDSF-EA). The component algorithms cooperate and compete to enhance the quality of the generated solutions and complement each other. The iterative cycles in the proposed algorithm consist of three consecutive phases. The main idea behind the cyclic nature of Ic3-aDSF-EA is to gradually emphasize the work of the best-performing algorithm without ignoring the effects of the other inferior algorithm during the search process. The cooperation of component algorithms takes place at the end of each cycle for information sharing and the quality of solutions for the next cycle. The algorithm's performance is evaluated on 43 problems from three different benchmark suites. The paper also investigates the application to a set of real-life problems. The overall results show that the proposed Ic3-aDSF-EA has a propitious performance and a reliable scalability behavior compared to other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

• Using machine learning to recommend appropriate parameters and operators for differential evolution algorithm. • The fitness landscape features are used as a basis for recommending parameters for the optimization problems. • A mutation operator selector based on AdaBoost & decision tree, and a parameter selector based on BP neural network are established for the differential evolution algorithm. Due to the problems of low accuracy and increasing control parameters in the existing parameter adaptive methods of differential evolution (DE) algorithm, in this paper a mutation operator selector and a parameter selector are proposed through Fitness Landscape (FL) analysing. At first, the performance differences of the two categories of mutation operators named DE / b e s t / 1 and DE / c u r r e n t - t o - r a n d / 1 were analyzed on many test problems. Secondly, the relationship between the FL and mutation operator is founded by using ensemble learning and decision tree, and achieved a classifier named mutation operator selector. Thirdly, the relationship between the FL and algorithm parameters is founded by using a neural network, and then a classifier named parameter selector is achieved. Finally, the improved DE algorithm equip with the two selectors is tested on the CEC2017 benchmark set. The results show that the proposed improved DE algorithm is outperforms both the basis DE algorithm and other three state-of-the-arts algorithms. [ABSTRACT FROM AUTHOR]

The performance of differential evolution (DE) significantly depends on the settings of mutation strategies and control parameters. Inappropriate settings may cause an imbalance between exploration and exploitation of the algorithm, thus resulting in two extremes: premature convergence and failure to converge. In this paper, we propose a Differential Evolution using Leader-Adjoint populations (LADE), which simultaneously integrates four mutation strategies to meet the needs of exploration and exploitation at different evolutionary stages. In LADE, the population in each generation is divided into leader population and adjoint population by using a leader-adjoint model. The leader population adopts two mutation strategies with strong exploration ability to maintain the diversity and avoid premature convergence, while the adjoint population uses the other two mutation strategies with strong exploitation ability to promote convergence and avoid stagnation. In addition, the interaction and collaboration between both populations are achieved through the sharing between their individuals, thus achieving a good trade-off between exploration and exploitation. The performance of LADE is evaluated on single-objective benchmark problems of the 2017 Institute of Electrical and Electronics Engineers Congress on Evolutionary Computation (IEEE CEC2017). Experimental results indicate that LADE shows competitive convergence performance, and outperforms various state-of-the-art DE variants and two well-known metaheuristics. [ABSTRACT FROM AUTHOR]

The performance of differential evolution (DE) significantly depends on the settings of mutation strategies and control parameters. Inappropriate settings may cause an imbalance between exploration and exploitation of the algorithm, thus resulting in two extremes: premature convergence and failure to converge. In this paper, we propose a Differential Evolution using Leader-Adjoint populations (LADE), which simultaneously integrates four mutation strategies to meet the needs of exploration and exploitation at different evolutionary stages. In LADE, the population in each generation is divided into leader population and adjoint population by using a leader-adjoint model. The leader population adopts two mutation strategies with strong exploration ability to maintain the diversity and avoid premature convergence, while the adjoint population uses the other two mutation strategies with strong exploitation ability to promote convergence and avoid stagnation. In addition, the interaction and collaboration between both populations are achieved through the sharing between their individuals, thus achieving a good trade-off between exploration and exploitation. The performance of LADE is evaluated on single-objective benchmark problems of the 2017 Institute of Electrical and Electronics Engineers Congress on Evolutionary Computation (IEEE CEC2017). Experimental results indicate that LADE shows competitive convergence performance, and outperforms various state-of-the-art DE variants and two well-known metaheuristics. [ABSTRACT FROM AUTHOR]

The combined heat and power economic dispatch (CHPED) problem is a complicated non-convex optimization problem with several constraints that has been a challenging and important task in the power system. Great efforts have been made to solve the small-scale CHPED problem, and there is considerable scope for research in the large-scale CHPED problem with lots of local optima. This paper presents a neighborhood-based differential evolution algorithm with direction induced strategy (NDIDE) to solve the large-scale CHPED problem. In NDIDE, a novel mutation strategy, named neighborhood nonelite direction induced strategy based on DE/rand/1 (DE/ldrand/1), is proposed to explore some untrodden areas of a search space using the direction information of pointing to inferior solutions within a small neighborhood. Such a strategy helps to strengthen the exploitation of some selected neighborhoods. Consequently, a good balance between exploration and exploitation abilities could be achieved. NDIDE is implemented on the CHPED systems with 7, 84, 96 and 192 units. The dispatch schedules obtained from NDIDE are feasible in three large CHPED systems and show the advantages of NDIDE in terms of cost savings and the robustness over the results obtained by three state-of-the-art differential evolution algorithms as well as recent works in this field. [ABSTRACT FROM AUTHOR]

• The adaptation of parameter and strategy is realized through accompanying evolution. • Accompanying population and generalized opposition-based learning enhance the population diversity. • Radial spatial projection is used for dynamic analysis of evolutionary direction. Differential evolution (DE) is an intelligent optimization algorithm inspired by biological evolution. Setting a mutation strategy and control parameters that meet the optimization requirements are the premise for DE to achieve good performance. This paper proposes a parameter and strategy adaptive differential evolution algorithm based on accompanying evolution (APSDE). Through the accompanying population, in which individuals are composed of suboptimal solutions, the mutation strategy and control parameters are optimized to realize the adaptation of the strategy and parameters of the main population. Population diversity is enhanced in evolution by generating reverse individuals. In addition, radial spatial projection technology is utilized to track the change in evolution direction with optimization. The performance of APSDE is validated under four sets of benchmark problem suites from the Institute of Electrical and Electronics Engineers (IEEE) Congress on Evolutionary Computation (CEC), and compared with state-of-the-art optimization algorithms. The results show that the proposed algorithm has better optimization performance than the competitive algorithms because of its efficient adaptive mechanism and its excellent population diversity. [ABSTRACT FROM AUTHOR]

Solving nonlinear equation systems (NESs) is one of the most important tasks in numerical computing. The NESs usually have multiple roots, and quickly locating their roots in a single algorithm run with a limited number of iterations has always been the algorithm improvement direction. In order to further enhance the efficiency of the existing methods, a density clustering-based differential evolution algorithm (DCDE) for the NESs problem solving is proposed in this paper. Firstly, density-based spatial clustering of applications with noise (DBSCAN) is used to divide the population into clusters and noises, which provides a better direction for population evolution. Secondly, a cluster evaluation factor is proposed, which not only divides the clusters into excellent clusters and non-excellent clusters, but also prevents the migration of excellent clusters and maintain the diversity of populations. Then, a migration strategy and individual generation mechanism are proposed to guide non-excellent clusters to migrate to promising regions. Finally, combined with an archive technique, the individuals which satisfy the solution requirements are archived and randomly initialized to further improve population diversity. To verify the effectiveness of the proposed algorithm, comparative experimental results of the propsoed DCDE with other state-of-the-art algorithms for thirty NESs problems solving show that the proposed DCDE is the most effective algorithm to locate more roots in a single run. [ABSTRACT FROM AUTHOR]

• An improved gaining-sharing knowledge-based algorithm named MSGSK is proposed. • A parameter adjustment strategy is developed to adjust relative parameters of MSGSK. • A backtracking differential mutation strategy is designed to enrich the population diversity. • A strategy selection mechanism is presented to integrate the former two strategies. • MSGSK extracts more accurate parameters for five PV models. The determination of photovoltaic (PV) model parameters has essential theoretical and practical significance for the performance evaluation, power monitoring, and power generation efficiency calculation of PV systems. In this paper, a multi-strategy gaining-sharing knowledge-based algorithm (MSGSK) is developed to determine these parameters. In our previous work, it has been demonstrated that gaining-sharing knowledge-based algorithm (GSK) is well suited for solving the concerned problem. To enhance its performance, a parameter adjustment strategy is developed to adjust the knowledge rate and knowledge ratio of GSK. Besides, a backtracking differential mutation strategy by combining the mutation scheme of differential evolution and the updating scheme of backtracking search optimization algorithm is developed to enrich the population diversity. Furthermore, a strategy selection mechanism is introduced to integrate the former two strategies to balance exploration and exploitation in different stages of the evolutionary process. The suggested MSGSK algorithm is applied to five PV cases (SDM, DDM, Photowatt-PW201, STM6-40/36, and STP6-120/36). From the experimental data, it can be observed that MSGSK extracts the PV model parameters more precisely than the basic GSK. Furthermore, it exhibits faster convergence speed and higher accuracy compared to other advanced algorithms found in the literature. [ABSTRACT FROM AUTHOR]

• Analyze DE algorithm two key issues: parameter sensitivity and search imbalance. • A complementary mutation strategy based on complementary symmetric selection and a Gaussian distribution mutation is proposed. • Data fusion-based parameter adaptation method proposed for parameter rationalization. • A novel variant of DE called DACDE is designed and results shown competitive edge. As an excellent optimization algorithm widely used to solve various practical problems, differential evolution (DE) algorithm has few parameters, yet its performance is significantly affected by these parameters. To address this issue, this paper presents a novel variant of DE called DACDE, which utilizes data fusion-based parameter adaptation and a complementary mutation strategy. Most parameter adaptation methods based on successful history only analyze the mean of parameters and ignore their degree of dispersion. In DACDE, the successful parameter distribution is recorded and described by both the mean and variance. Data fusion is then used to combine records and generate an estimated distribution, which is applied to a Gaussian distribution to generate new parameters. Inspired by opposition-based learning, we introduce a complementary mutation strategy. This strategy employs a symmetric selection mechanism to adapt to the varying search abilities required by the algorithm at different stages. The new variant is verified on 32 single-objective functions from CEC 2011 and 2014 benchmark suites, and the results show that DACDE is competitive compared to other 29 evolutionary algorithms. [ABSTRACT FROM AUTHOR]

In association rules mining from data that have numeric-valued attributes, automatically adjusting the attribute intervals at the time of the mining process without a preprocess is very critical for preventing data loss and attribute interactions. In this paper, differential evolution and sine cosine algorithm based novel hybrid multi-objective evolutionary optimization methods are proposed for rapidly and directly mining the reduced high-quality numerical association rules by simultaneously adjusting the relevant intervals of related attributes without finding the frequent itemsets. These algorithms perform a global search and find the high-quality rules set in only one execution by modeling the rule mining task as a multi-objective problem that simultaneously meets different conflicting metrics. The algorithms proposed in this paper ensure the discovered rules to have high confidence and support and to be comprehensible. The proposed methods automate the rule mining process by directly finding the minimum intervals for the attributes and eliminating the need for minimum confidence and minimum support determined beforehand for each data set. The performances of new algorithms proposed in this study were tested with those of the state-of-the-art algorithms. The results show superiority of the proposed methods on the data sets that contain fewer attributes and higher number of instances. [ABSTRACT FROM AUTHOR]

Surrogate-assisted evolutionary algorithms (SAEAs) are promising methods for addressing computationally expensive problems. This paper proposes a multiple surrogates and offspring-assisted differential evolution (MSODE) algorithm for high-dimensional expensive problems. Ensemble models consisting of multiple base models are built based on bagging. The ensemble models contribute toward reducing the variations of predictions and the uncertainty of base models. The algorithm proposes a multiple-offspring evolution strategy in which it generates multiple offspring for each parent individual to enhance the search ability of the population. The appropriate number of offspring was investigated, considering the tradeoff between optimization results and efficiency. MSODE consists of a global prescreening search, local search, and uncertainty prescreening search. The global prescreening search adopts a global ensemble to prescreen promising offspring. The local search accelerates the convergence by searching for the optimum of a local ensemble. The uncertainty prescreening search requires a number of fitness evaluations that slightly deteriorate the results. A comprehensive analysis was conducted to determine the optimal parameter settings. MSODE was compared with meta -heuristic algorithms and SAEAs on a series of benchmark problems. The results show that MSODE behaves better than most algorithms and is competitive against the best ones. [ABSTRACT FROM AUTHOR]

• In this paper, proposing a novel design of DE for Knapsack problems is reported. • A dual representation of solutions in continuous and binary is introduced. • New efficient fitness evaluation and repairing method is proposed. • Results demonstrated the efficiency of Novel DE in solving Knapsack problems. • Novel DE defined new solutions, better than best-known ones for 5 large instances. The capability of the conventional differential evolution algorithm to solve optimization problems in continuous spaces has been well demonstrated and documented in the literature. However, differential evolution has been commonly considered inapplicable for several binary/permutation-based real-world problems because of its arithmetic reproduction operator. Moreover, many limitations of the standard differential evolution algorithm, such as slow convergence and becoming trapped in local optima, have been defined. In this paper, a novel technique which makes a simple differential evolution algorithm suitable and very effective for solving binary-based problems, such as binary knapsack ones, is proposed. It incorporates new components, such as representations of solutions, a mapping method and a diversity technique. Also, a new efficient fitness evaluation approach for calculating and, at the same time, repairing knapsack candidate solutions, is introduced. To assess the performance of this new algorithm, four datasets with a total of 44 instances of binary knapsack problems are considered. Its performance and those of 22 state-of-the-art algorithms are compared, with the experimental results demonstrating its superiority in terms of both the quality of solutions and computational times. It is also capable of finding new solutions which are better than the current best ones for five large knapsack problems. [ABSTRACT FROM AUTHOR]

In this paper, a new differential evolution (DE) algorithm is presented for solving global optimization problems by guiding the individuals adaptively to explore different decision regions and setting the control parameters properly for individuals. To consolidate algorithm efficiency and preserve population diversity, we first introduce a proration-based mutation strategy. This strategy dynamically selects promising individuals from population as guiders and proportionately allocates the individuals following them based on their fitness values and unsuccessful updates. Besides, we design a multi-segment mixed parameter setting to provide suitable parameters for individuals, considering feedback information from the population, individual requirements, and parameters' interaction. Additionally, we devise an adaptive population maintaining mechanism to refresh the population by replacing individuals with higher unsuccessful updates and removing those with poor fitness values. Unlike previous DE versions, our new algorithm dynamically and appropriately explores promising areas, refines parameter suitability, and accelerates convergence by updating and removing unpromising individuals. This enhances the algorithm search efficiency and achieves a good balance between exploration and exploitation. Finally, we evaluate the proposed algorithm's performance by comparing it with 17 typical or state-of-the-art algorithms on IEEE CEC2014 and CEC2017 test suites. Experimental results indicate that the proposed algorithm is a more promising optimizer. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive memetic differential evolution with multi-niche sampling and neighborhood crossover strategies for global optimization. In the proposed algorithm, a multi-niche sampling strategy is designed to sample a subpopulation for evolution at each generation. In this strategy, the entire population is firstly divided into multiple niches by employing a certain niching strategy at each generation. A subpopulation is then dynamically sampled from the resulting niches such that supporting a diverse search at the early stage of evolution while an intensive search towards the end of evolution. The above strategy will be further coupled with a neighborhood crossover, which is devised to encourage high potential solutions for exploitation while low potential solutions for exploration, thus appropriately searching the solution space. Additionally, an adaptive local search (ALS) scheme along with an adaptive elimination operation (AEO) have been designed. The ALS aims to appropriately fine-tune promising solutions in the sampled subpopulation while the AEO tends to adaptively eliminate unpromising individuals in the population during evolution. The performance of the proposed algorithm has been evaluated on CEC'2015 benchmark functions and compared with related methods. Experimental results show that our algorithm can achieve a superior performance and outperform related methods. The results also confirm the significance of devised strategies in the proposed algorithm. [ABSTRACT FROM AUTHOR]

• Importance of the constraint handling operator even for box-constrained problems. • Use of percentage of solutions generated outside the domain as performance measure. • Re-purposing of stochastic objective function f0 for studying algorithmic effects. • Popular EC algorithms generate significant amounts of infeasible solutions. • Distribution of percentages of solutions generated outside the domain is nontrivial. This paper investigates how often the popular configurations of Differential Evolution generate solutions outside the feasible domain. Following previous publications in the field, we argue that what the algorithm does with such solutions and how often this has to happen is important for the overall performance of the algorithm and interpretation of results. Based on observations therein, we conclude that significantly more solutions than what is usually assumed by practitioners need to undergo some sort of 'correction' to conform with the definition of the problem's search domain. A wide range of popular Differential Evolution configurations is considered in this study. Conclusions are made regarding the effect the Differential Evolution components and parameter settings have on the distribution of proportions of infeasible solutions generated in a series of independent runs. Results shown in this study suggest strong dependencies between proportions of generated infeasible solutions and every aspect mentioned above. Further investigation of the distribution of proportions of generated infeasible solutions is required. [ABSTRACT FROM AUTHOR]

Many domination-based multi-objective evolutionary algorithms (MOEAs) are designed for constrained multi-objective optimization problems (CMOPs). However, they still face the challenge of balancing the feasibility, convergence and distribution. This paper tackles this issue by proposing a multi-objective differential evolution algorithm based on domination and a mechanism of constraint-handling switching (MODE-CHS). In constraint-handling switching, if there are no feasible solutions in the population, the population evolves by constraint-handling; otherwise, the population evolves without handling constraints. This mechanism enhances the rate of population convergence to the maximum while obtaining the feasible solutions. Furthermore, in MODE-CHS, the feasible solutions are saved to an external archive and evolve together with the population to explore the feasible region. Meanwhile, to enhance the distribution, the offspring of the external archive also participates in the individual-update procedure of the population. 27 bench-mark test problems and two real-world problems are used for the performance comparison of the proposed algorithm with other five state-of-the-art algorithms. In the experiment, the proposed algorithm, MODE-CHS, is shown to produce satisfactory solutions for most of the tested functions, where other five MOEAs perform relatively worse. The experiment results demonstrate MODE-CHS is very competitive for solving CMOPs. [ABSTRACT FROM AUTHOR]

In differential evolution algorithm (DE), it is a widely accepted method that selecting individuals with higher fitness to generate a mutant vector. In this case, the population evolution is under a fitness-based driving force. Although the driving force is beneficial for the exploitation, it sacrifices performance on the exploration. In this paper, a n ovelty-hybrid- f itness d riving force is introduced to trade off contradictions between the exploration and the exploitation of DE. In the new proposed DE, named as NFDDE, both fitness and novelty values of individuals are considered when choosing individuals to create mutant vectors. In addition, two adaptive scaling factors are proposed to adjust the weights of the fitness-based driving force and the novelty-based driving force, respectively, and then distinct properties of the two driving forces can be effectively utilized. At last, to save computational resources, some individuals with lower novelty are deleted when the population has converged to a certain extent. The comprehensive performance of NFDDE is extensively evaluated by comparisons between it and other 9 state-of-art DE variants based on CEC2017 test suite. In addition, distinct properties of the newly introduced strategies and involved parameters are further confirmed by a set of experiments. [ABSTRACT FROM AUTHOR]

Differential Evolution (DE) is one of the most effective approaches in Evolutionary Computation to tackling complex black-box optimization, however, the overall performance of a DE variant is heavily dependent on its mutation strategy and the associated parameter control schemes. According to the "No free Lunch theorem", every mutation strategy has its own fatal defect, therefore, DE variant with a single mutation strategy can not tackle all optimization problems. Furthermore, DE variant with ensemble of mutation strategies usually needs more parameter control schemes, which inevitably decreases the practicality of it. Here in this paper, a novel Cooperative Strategy based DE (CS-DE) with population diversity enhancement is proposed, and the CS-DE algorithm has the following contributions: First, a cooperative strategy pool containing two similar mutation strategies is advanced in the algorithm, and the two mutation strategies share the same parameter control. Second, a novel grouping strategy is proposed, then the two mutation strategies can be chosen in an adaptive manner by different individuals in generating trial vectors during the evolution. Third, novel adaptation schemes for the three control parameters F , CR and PS as well as a stagnation based re-initialization mechanism are also proposed in our CS-DE algorithm. 58 benchmarks from the CEC2013 and CEC2014 test suites are employed in algorithm validation, and experiment results show the competitiveness of the CS-DE algorithm with several state-of-the-art DE variants. [ABSTRACT FROM AUTHOR]

• The concept and verification method of affine invariance are presented. • Six algorithms are employed to analyze their affine invariances. • PSO, OFA and DE are affine invariant, GWO, SCA and BOA are not affine invariant. • Multiple experimental comparisons are executed to verify algorithms' affine invariance. An algorithm whose performance depends on the objective function being aligned with a privileged coordinate system is a poor choice in general because it is unlikely that the optimal orientation will be known in advance. In this paper, a property of meta -heuristic algorithms, named affine invariance, is introduced to verify whether the algorithm is depended on the privileged coordinate system or not. The concept of affine invariance is described in detail, and some classical algorithms, efficient in most test and actual problems, are proved to be affine invariant. While some recent algorithms in the literature are proved to be not affine invariant. As a conclusion, particle swarm optimization (PSO), differential evolution (DE) and optimal foraging algorithm (OFA) are affine invariant, while grey wolf optimizer (GWO), sine cosine algorithm (SCA) and butterfly optimization algorithm (BOA) are not affine invariant. Furthermore, comparison tests are designed to support the theoretical analysis results. In these tests, same random numbers and initial population are used to avoid the influence of randomness, thus, the conclusion is reliable. [ABSTRACT FROM AUTHOR]

• Two new mutation strategies to enhance the DE performance are proposed. • A new adaptive approach to key control parameters are defined. • The proposed approach has superior classiffication accuracy. • The proposed algorithm's performance is acceptable in feature subset selection. In classification problems, normally there exists a large number of features, but not all of them contributing to the improvement of classification performance. These redundant features make the classification problem time consuming and often result in poor performance. Feature selection methods have been proposed to reduce the number of features, minimize computational cost, and maximize classification accuracy. As a wrapper-based approach, evolutionary algorithms have been widely applied in feature subset selection tasks. However, some of them trap into local minima, especially when the number of features increases, while others are not efficient in computational time. This paper proposes a Modified Differential Evolution (DE) approach to Feature Selection (MDEFS) by utilizing two new mutation strategies to create a feasible balance between exploration and exploitation and maintain the classification performance in an acceptable range concerning both the number of features and accuracy. Some modifications are made to the standard DE crossover and its key control parameters to enhance the proposed algorithm's capabilities further. The proposed method has been compared to several state-of-the-art methods utilizing standard datasets from the UCI repository and results of the experiments demonstrate the superiority of the proposed approach. [ABSTRACT FROM AUTHOR]

In the last decade, the decomposition-based multiobjective optimization evolutionary algorithm (MOEA/D) has displayed promising performance when dealing with multiobjective optimization problems (MOPs). However, for some complex MOPs, the conventional MOEA/D often leads to the loss of population diversity in the iterative process, and the convergence performance of the population is weakened in the mean time. In this paper, a novel MOEA/D, based on improved multiple adaptive dynamic selection strategies and elite archive strategy (MOEA/D-IMA), is proposed to improve the population diversity and convergence. First, a novel differential evolution (DE) operator is constructed, which constitutes an operator pool with other DE operators. According to the search information of the current population, an adaptive dynamic selection strategy is proposed, which is used by MOEA/D-IMA to select a suitable DE operator to replace the simulated binary crossover (SBX) operator. Second, a parameter adaptive dynamic selection strategy is proposed to enhance the robustness of MOEA/D-IMA by using the information of population evolution state. Third, an elite archive strategy is introduced to improve the convergence and diversity of the population where mutual dominance of individuals and their aggregation distance is employed. Finally, the proposed MOEA/D-IMA is compared with several state-of-the-art algorithms on three suits of 18 test problems. Experimental results indicate that the proposed MOEA/D-IMA can significantly improve the optimization performance when coping with MOPs. [ABSTRACT FROM AUTHOR]

For real parameter single objective optimization, Differential Evolution (DE) performs better than other types of population-based metaheuristic. Nevertheless, in the field of DE, it is impossible for a given combination of operators to perform well in all fitness landscapes. Practice has proved that assembling more than one combinations of operators may lead to improvement in solution. However, some DE algorithms with good performance, e.g., one of the best performers in competitions of real parameter single objective optimization among population-based metaheuristics held by the series of IEEE Congress on Evolutionary Computation - L-SHADE-EpSin, are still not involved in ensemble. Furthermore, ensemble based on similar DE algorithms is rarely reported. Based on such a background, we propose L-SHADE-E, ensemble of L-SHADE-EpSin and L-SHADE-RSP in this paper. The two constituent algorithms are both variants of L-SHADE and belong to similar DE algorithms. In our algorithm, L-SHADE-EpSin or L-SHADE-RSP is selected randomly to run at the beginning. If progress on fitness is low for generations, the other constituent algorithm takes over population immediately. Our experiments are based on the CEC 2014 and CEC 2017 benchmark test suites. Altogether, our algorithm is compared with nine DE algorithms and three population-based metaheuristics other than DE. Experimental results show that our algorithm is very competitive. [ABSTRACT FROM AUTHOR]

The performance of differential evolution (DE) mainly depends on its breeding offspring strategy (i.e., trial vector generation strategies and associated control parameters). To take full advantage of several effective breeding offspring strategies proposed in recent years, a fitness-based adaptive differential evolution algorithm (FADE) is proposed in this paper. In FADE, the entire population is split into multiple small-sized swarms, and three popular breeding strategies are saved in an archive which can be utilized by the multiple swarms. In each generation, different individuals in a same swarm adaptively select their own breeding strategy from the archive based on their fitness. With the adaptive breeding strategy, the individuals in a same swarm can exhibit distinct search behaviors. Moreover, the population size can be adaptively adjusted during the evolutionary process according to the performance of the best individual. Based on the adaptive population size, computational resources can be rationally assigned in different evolutionary stages, and then to satisfy diverse requirements of different fitness landscapes. The comprehensive performance of FADE is extensively evaluated by comparisons between it and other eight state-of-art DE variants based on CEC2013 and CEC2017 test suites as well as seven real applications. In addition, the effectiveness and efficiency of the newly introduced adaptive strategies are further confirmed by a set of experiments. [ABSTRACT FROM AUTHOR]

Feature combination selection is used in object classification to select complementary features that can produce a powerful combination. One active area of selecting feature combinations is genome-wide association studies (GWAS). However, selecting feature combinations from high-dimensional GWAS data faces a serious issue of high computational complexity. In this paper, a fast evolutionary optimization method named search-history-guided differential evolution (HGDE) is proposed to deal with the problem. This method applies the search history memorized in a binary space partitioning tree to enhance its power for selecting feature combinations. We perform a comparative study on the proposed HGDE algorithm and other state-of-the-art algorithms using synthetic datasets, and later employ the HGDE algorithm in experiments on a real age-related macular degeneration dataset. The experimental results show that this proposed algorithm has superior performance in the selection of feature combinations. Moreover, the results provide a reference for studying the functional mechanisms of age-related macular degeneration. [ABSTRACT FROM AUTHOR]

Differential Evolution is a well-known stochastic algorithm in Evolutionary Computation (EC) for single-objective numerical optimization, and its powerful variants secured excellent ranks in recent competitions. These winner DE variants all employed binomial crossover which tackles the positional bias in crossover operation by treating the D parameters separately and independently, however, the binomial crossover in these winner DE variants still have bias from the spatial search perspective, and this was the reason why the QU asi- A ffine TR ansformation E volution (QUATRE) algorithm in the literature was proposed. In this paper, a novel QUATRE algorithm with novel adaptation of E volution M atrix and S election operation (QUATRE-EMS) was proposed to further improve the overall performance of the QUATRE variants for numerical optimization and the main highlights can be summarized as follows. First, the number of control parameters is reduced from three in DE to two in QUATRE-EMS by proposing an auto-generated evolution matrix. Second, a novel adaptation scheme of the evolution matrix M is proposed for a better adaptation of the landscape of the objective during evolution; Third, a new selection operation is proposed instead of employing the canonical selection operation in DE. Finally, a large test suite containing 100 benchmarks from CEC2013, CEC2014, CEC2017 and CEC2022 test suites for single-objective numerical optimization is used for algorithm validation, and total 11 state-of-the-art algorithms including our QUATRE-EMS are taken into comparison. The experimental results show the superiority of our algorithm in comparison with former QUATRE variants and several state-of-the-art DE variants. [ABSTRACT FROM AUTHOR]

• A novel CHT is proposed based on Pareto dominance-based ranking and CDP-based ranking. • A search algorithm based on four mutation operators is proposed. • A new constrained multiobjective differential evolution algorithm is proposed. The tradeoff between objective functions and constraints is a key issue that needs to be addressed by constrained multiobjective optimization algorithms, and constraint handling techniques (CHTs) are an important technique for balancing objective functions and constraints. In this paper, a novel CHT that fuses two rankings is proposed. Specifically, each individual is assigned two rankings: one ranking calculated based on Pareto dominance (regardless of constraints) and another calculated based on the constrained dominance principle (CDP). The fitness value of an individual is the weighted sum of these two rankings, and the weight is related to the generation number and the proportion of feasible solutions in the current generation. Based on the proposed CHT, a constrained multiobjective differential evolution algorithm is proposed. To generate high-quality offspring, the proposed constrained multiobjective differential evolution algorithm combines four mutation operations as core components of the search algorithm. The proposed algorithm is compared with eight state-of-the-art algorithms in experiments with five test suites, and the experimental results show that the proposed algorithm performs significantly better than the eight state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Surrogate-assisted evolutionary algorithms have gained increasingly attention due to the promising search capabilities for solving computationally expensive optimization problems. However, when dealing with high-dimensional expensive optimization problems, the effectiveness of surrogate-assisted algorithms deteriorates drastically. In this paper, a novel and efficient hierarchical surrogate-assisted differential evolution (EHSDE) algorithm is proposed towards high-dimensional expensive optimization problems. To balance the exploration and exploitation during the optimization process, EHSDE utilizes a hierarchical framework. In the first phase, the best and the most uncertain offspring are identified respectively. The best offspring is prescreened by a global surrogate model which is built by using a radial basis function network with all the sample points, while the most uncertain offspring is built by the Euclidean distance between offspring and existing sample points. Subsequently, two local surrogate models, which are built by using the most promising sample points and the sample points surrounding the current best solution respectively, are utilized to accelerate the convergence speed. Moreover, experimental studies are conducted on the benchmark functions from 20D to 100D and on an oil reservoir production optimization problem. The results show that the proposed method is effective and efficient for most benchmark functions and for the production optimization problem compared with other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

The challenge of solving nonlinear equation systems is how to locate multiple optimal solutions simultaneously in a single run. To address this issue, this paper proposes a novel algorithm by combining a diversity indicator, multi-objective optimization technique, and clustering technique. Firstly, a diversity indicator is designed to maintain the diversity of the population. Then, a K-means clustering-based selection strategy is introduced to locate the promising solutions. Finally, the local search is used to accelerate the convergence of population. The experimental results on 30 nonlinear equation systems show that the proposed algorithm is better than six state-of-the-art algorithms in terms of convergence rate and success rate. [ABSTRACT FROM AUTHOR]

This paper presents a general control strategy based on the trajectory planning and tracking control for the planar 3-DoF underactuated manipulators with one passive joint at different position. According to the target position of the system, a set of target angles of all links are quickly obtained by using differential evolution algorithm. In order to achieve the control objective of the system from the initial position to the target position, we design the trajectory for each active link of the system, which is composed of two parts. The first part of the trajectory is designed according to the initial and target angle of the active link. The second part of the trajectory is designed based on the constraints between the passive joint and the active joints. Meanwhile, the parameters of the trajectories are optimized by the differential evolution algorithm to ensure that all links reach to their target angles eventually by tracking the designed trajectories. Then, the sliding mode variable structure controllers are designed to make all active links track their trajectories. The effectiveness of the proposed strategy is demonstrated through simulation results. [ABSTRACT FROM AUTHOR]

• Proposing a binary differential evolution algorithm with self-learning strategy, called MOFS-BDE, to solve multi-objective feature selection problems. • Proposing a new binary mutation operator based on probability difference to guide the individuals to locate potentially optimal areas fast. • Proposing a new one-bit purifying search operator (OPS) for improving the self-learning capability of elite individuals. • Proposing an efficient non-dominated sorting operator with crowding distance to reduce the time consumption of the selection operator in differential evolution. Feature selection is an important data preprocessing method. This paper studies a new multi-objective feature selection approach, called the Binary Differential Evolution with self-learning (MOFS-BDE). Three new operators are proposed and embedded into the MOFS-BDE to improve its performance. The novel binary mutation operator based on probability difference can guide individuals to rapidly locate potentially optimal areas, the developed One-bit Purifying Search operator (OPS) can improve the self-learning capability of the elite individuals located in the optimal areas, and the efficient non-dominated sorting operator with crowding distance can reduce the computational complexity of the selection operator in the differential evolution. Experimental results on a series of public datasets show that the effective combination of the binary mutation and OPS makes our MOFS-BDE achieve a trade-off between local exploitation and global exploration. The proposed method is competitive in comparison with some representative genetic algorithm-, particle swarm-, differential evolution-, and artificial bee colony-based feature selection algorithms. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Multimodal optimization problems (MMOPs) aim to locate multiple global optima simultaneously, which requires a high diversity of solutions. As a diversity preservation strategy customized for evolutionary algorithms (EAs), niching has been extensively incorporated into many algorithms to deal with MMOPs. However, many existing niching techniques require pre-defined parameters to control the size or number of niches, making the algorithm sensitive to parameters. Taking individuals as nodes, the inverse distance of two individuals as edges, and the historical information of recent generations as node attributes, we can construct a population as a network, whose purpose is to divide niches through community detection without relying on sensitive parameters. Inspired by this idea, this paper proposes a network community-based differential evolution for multimodal optimization problems (NetCDE MMOPs). In NetCDE MMOPs , three strategies are proposed and work together. Firstly, the community detection-based niching (CDN) strategy constructs the population as an attribute network and automatically divides it into multiple niches without sensitive parameters. Secondly, the community elites-based updating (CEU) strategy allocates more evolutionary resources to elite individuals of communities, then predicts and updates these elites based on historical information. Finally, the poor individual remolding (PIR) strategy remolds the last-ranking individuals and guides them toward promising positions. After extensive experimentation with the widely adopted CEC'2013 test suit, the experimental results reveal the superiority of NetCDE MMOPs over many successful or recent algorithms for MMOPs. [ABSTRACT FROM AUTHOR]

Abstract Differential evolution (DE) is a simple yet powerful evolutionary algorithm that has been used to solve various complex optimization problems in numerous engineering fields. However, DE has some problems, such as premature convergence and sensitivity to parameter settings. To improve the performance of DE and extend its application, an adaptive differential evolution with the Lagrange interpolation argument algorithm (ADELI) is proposed in this paper. To accelerate the convergence speed of DE, a local search with Lagrange interpolation (LSLI) is introduced into DE. LSLI performs a local search in the neighborhood of the best individual in the current generation to enhance the exploitation capability of DE. Meanwhile, an adaptive argument strategy is presented to adaptively determine whether to use LSLI in terms of its performance in the previous generation, which can balance the global exploration capability and the local exploitation capability of ADELI. To verify the feasibility and effectiveness of ADELI, 30 test functions in the CEC 2014 benchmark sets with different dimensions were simulated. Moreover, a path synthesis problem was also optimized. The results demonstrated that ADELI considerably outperforms other EAs in most functions and obtains the most accurate solution among the compared algorithms in the application of path generation. [ABSTRACT FROM AUTHOR]

Abstract This paper develops a novel algorithm to solve real-world constrained optimization problems, which hybridizes multiobjective optimization techniques with an ϵ-constrained method. First, a constrained optimization problem at hand is transformed into a bi-objective optimization problem. By the transformation, the advantage of multiobjective optimization techniques can be utilized in the constrained optimization area to balance population diversity and convergence. Meanwhile, the ϵ-constrained method is applied, which keeps the population evolving toward feasible region of the constrained optimization problem. In our proposed algorithm, the differential evolution is employed as a search engine to create offspring at each generation. Further, different combinations of mutation operators have been developed to improve the search ability and the population convergence at different stages. The performance of our approach is evaluated on 64 benchmark test functions from three popular test suits. Experimental results demonstrate that our proposed approach is capable of obtaining high-quality solutions on the majority of benchmark test functions, when compared with some other state-of-the-art constrained optimization algorithms. [ABSTRACT FROM AUTHOR]

Mixed-variable optimization problems (MVOPs) that involve continuous and discrete decision variables widely exist in industrial and scientific domains. However, how to solve MVOPs efficiently remains an open issue because the fact that continuous and discrete variables present different spatial distribution features posts a great challenge to algorithmic design. In this paper, a hybrid differential evolution (DE) framework is proposed for MVOPs. The proposed framework, namely DE MV , hybridizes the original DE and the set-based DE for evolving continuous and discrete variables, respectively. The two DEs are selected for hybridization because algorithmic analysis and experimental studies show that they share the same search mechanism. The compatibility and consistency of the two DEs is the key for enabling DE MV to coevolve different types of decision variables efficiently. Experiments are conducted on a set of artificial MVOPs converted from continuous benchmark functions and real-world engineering problems with mixed variables. Experimental results and comparisons with other representative algorithms show that DE MV is effective and efficient. [ABSTRACT FROM AUTHOR]

Over the last two decades, many different differential evolution algorithms for solving optimization problems have been introduced. Although most of these algorithms used a single mutation strategy, several with multiple mutation strategies have recently been proposed. Multiple-operator-based algorithms have been proven to be more effective and efficient than single-operator-based algorithms for solving a wide range of benchmark and practical problems. In these algorithms, adaptive operator selection mechanisms are generally applied to place greater emphasis on the best-performing evolutionary operators based on their performance histories for generating new offspring. In this paper, we investigate using problem landscape information in an adaptive operator selection mechanism. For this purpose, a new algorithm, which considers both this problem landscape information and the performance histories of the operators, for dynamically selecting the most suitable differential evolution operator during the evolutionary process, is proposed. The contributions of each component of the selection mechanism are analyzed and the performance of the proposed algorithm is evaluated by solving 45 unconstrained optimization problems. The results demonstrate the effectiveness and superiority of the proposed algorithm to state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

The study of parameter estimation of a specified model has a long history. In statistics, Bayesian analysis via Markov chain Monte Carlo (MCMC) sampling is an efficient way for parameter estimation. However, the existing MCMC sampling is only performed in the real parameter space. In some situation, complex-valued parametric modeling is more preferable as complex representation brings economies and insights that would not be achieved by real-valued representation. Therefore, to estimate complex-valued parameters, it is more convenient and elegant to perform the MCMC sampling in the complex parameter space. In this paper, firstly, based on the assumption that the observation signal is proper, two complex MCMC algorithms using the Metropolis-Hastings sampling and the differential evolution are proposed, in which the probability density functions (pdfs) in Bayesian estimation are characterized by the usual Hermitian covariance matrices. Secondly, to improve the performance for the case that the observation signal is improper, two augmented complex MCMC algorithms are developed, where the pdfs are computed by the augmented complex statistics. Both theoretical studies and numerical simulations are presented to show the effectiveness of the proposed algorithms in complex-valued parameter estimation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, several variation operators based on Pareto efficiency, extracted from Differential Evolution, Estimation of Distribution Algorithms, Evolution Strategies and Evolutionary Programming, are compared in order to determine whether or not they increase the performance of the non-Pareto based versions. Firstly, we compare the selected variation operators in pairs, each operator with a modification of itself, in which we remove those elements related to the Pareto efficiency. Then, in a second experiment we compare among the selected operators, the variation operators used in the NSGA-II algorithm and the ones presented by the authors, PBCO and RBMO. In all the experiments the variation operators are incorporated in a well-known algorithm usually considered as a reference for making the comparisons, the NSGA-II algorithm. The experiments show that the Pareto based variation operators selected from the literature do not usually present a better behavior than their non-Pareto based versions; and none of them presents a better performance than the one reached by the variation operators defined by the authors, which were entirely built around the Pareto information of the individuals. These facts suggest that more effort should be placed in the design of variation operators devoted to multi-objective algorithms in order to achieve superior results to those obtained by means of general variation operators. [Copyright &y& Elsevier]

• A model of the acceptance probability of poor trial vectors is constructed. • An evolutionary-state-based selection (ESS) strategy is proposed. • A new variant of the differential evolution algorithm (ESDE) is proposed. The survivor selection operation is one of the factors affecting the performance of differential evolution (DE) algorithms. However, in single-objective DE algorithms, researchers seldom address the improvement of survivor selection operations. Most DE algorithms use greedy selection operations. In this research, we propose an evolutionary-state-based selection (ESS) strategy for single-objective DE, which constructs a probability model based on evolutionary states to solve real-parameter optimization problems. In the survivor selection process, it is no longer true that only the winner can survive to the next generation; the loser also has a certain probability of surviving to the next generation, and this probability is related to the evolutionary states. Based on ESS, a new DE variant called evolutionary-state-based differential evolution (ESDE) is proposed. To verify the ESDE and ESS performance, ESDE was compared with eight state-of-the-art DE variants, and ablation experiments were performed on ESDE to analyze the impact of ESS on the ESDE performance. The experimental results show that ESDE is significantly better than the other eight DE variants, and ESS could significantly improve the DE performance. [ABSTRACT FROM AUTHOR]

• Discarded trial vectors were used to improve differential evolution performance. • A best discarded vector selection strategy was proposed. • The best discarded vector selection strategy can be applied to various differential evolution algorithms. In this study, a selection strategy based on discarded trial vectors was constructed to improve the performance of the differential evolution (DE) algorithm. The proposed strategy is called the best discarded vector selection (BDVS) strategy. The uniqueness of BDVS is that the best discarded trial vector for an individual and the best vector for the individual are used to improve the individual. First, an external archive is constructed to record the best discarded trial vectors for each individual. During the survivor selection operation, if a trial vector is worse than the target vector and the target vector is in a stagnant state, then the target vector is replaced with the best vector of the target vector or a vector chosen at random from the external archive. BDVS is a general framework that can easily be integrated into various DE algorithms. In our experiments, BDVS was applied to eight DE algorithms, which were then compared to their original algorithms. BDVS was verified using the 2013 IEEE Congress on Evolutionary Computation (CEC 2013), CEC 2014, and CEC 2017 benchmark test sets and 88 test functions were considered. The experimental results demonstrate that BDVS can significantly improve DE performance. [ABSTRACT FROM AUTHOR]

• A sawtooth-linear population size adaptive method was proposed. • The update formulas of scaling factor and crossover rate were improved. • A new differential evolution variant was proposed. The main parameters that affect the performance of a differential evolution algorithm are the scaling factor, crossover rate, and population size. To adaptively adjust the population diversity and balance the exploration and exploitation abilities of a differential evolution algorithm during the evolution process, this study proposes a sawtooth-linear population size adaptive (SLPSA) method and an improved scaling factor and crossover rate control method. Subsequently, an improved differential evolution algorithm called SLDE is proposed. The SLPSA method constructs an external archive for storing the abandoned trial vectors and periodically adds vectors from external archive to the population during the iterative process, thereby periodically increasing the diversity of the population, which enhances the algorithm's ability to jump out of locally optimal values. Based on a distance-based parameter adaptation method, the update formulas for the scaling factor weight and crossover rate weight are improved. By using 84 benchmark functions from CEC 2011, CEC 2014, CEC 2015, and CEC 2017, the SLDE performance was verified experimentally by analyzing and comparing the proposed SLDE to six state-of-the-art differential evolution algorithms. The experimental results demonstrated that the SLDE performance was significantly better than that of the six state-of-the-art differential evolution algorithms. [ABSTRACT FROM AUTHOR]