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[Display omitted] • A framework is proposed for population-based optimization algorithms' convergence. • DIRECT's partition and population evolutions are repeated in this framework. • The global convergence of the framework is proved. • Framework is applied successfully on three population-based optimization algorithms. Population-based optimization algorithms, such as genetic algorithm and particle swarm optimization, have become a class of important algorithms for solving global optimization problems. However, there is an issue that the global convergence is often absent for most of them. This paper proposes a partition-based convergence framework for population-based optimization algorithms to solve this troubling problem. In this framework, regular partitions and evolutions of populations are implemented alternatively. Specifically, the initial population is generated from a regular partition on the search space; after several generations of evolution of the population, the evolution result is returned to join in the regular partition again, and a new population is generated. Repeat such progress until some stop condition is satisfied. Global convergence is guaranteed for the framework. Then this convergence framework is applied to particle swarm optimization, differential evolution, and genetic algorithm. The modified algorithms are globally convergent and perform better than the original version. [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]

Standard evolutionary optimization algorithms assume that the evaluation of the objective and constraint functions is straightforward and computationally cheap. However, in many real-world optimization problems, these evaluations involve computationally expensive numerical simulations or physical experiments. Surrogate-assisted evolutionary algorithms (SAEAs) have recently gained increased attention for their performance in solving these types of problems. The main idea of SAEAs is the integration of an evolutionary algorithm with a selected surrogate model that approximates the computationally expensive function. In this paper, we propose a surrogate model based on a Lipschitz underestimation and use it to develop a differential evolution-based algorithm. The algorithm, called Lipschitz Surrogate-assisted Differential Evolution (LSADE), utilizes the Lipschitz-based surrogate model, along with a standard radial basis function surrogate model and a local search procedure. The experimental results on seven benchmark functions of dimensions 30, 50, 100, and 200 show that the proposed LSADE algorithm is competitive compared with the state-of-the-art algorithms under a limited computational budget, being especially effective for the very complicated benchmark functions in high dimensions. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms are widely used to solve multimodal optimization problems. The two main challenges faced while solving MMOPs are locating multiple optimal solutions and improving the accuracy of these solutions. In this paper, we have proposed an adaptive algorithm based on differential evolution using the distributed framework in mutation strategy and an elite archive mechanism termed Adaptive Differential Evolution with Archive to deal with these challenges. The following techniques have been proposed and integrated to locate multiple diverse optimal solutions with refined accuracy. Firstly, each individual in the population is treated as a possible exemplar and is expected to reach an optimal value by exploring the nearby search space. The search space is controlled by using an adjustable range mechanism. An adaptive mutation strategy is then used to ensure that all the good solutions or individuals of the population move to better positions. Next, an elite archive is constructed for stagnated individuals to avoid getting stuck in local optimas. The experimental results on the 20 multimodal functions from IEEE Congress on Evolutionary Computation 2013 illustrate that the performance of the proposed algorithm is better than the existing multimodal optimization algorithms in terms of finding more number of accurate solutions. [ABSTRACT FROM AUTHOR]

• A novel mean-median velocity updating formula is proposed to guide individuals motion. • A new random differential mutation strategy is devised. • A back-diffusion strategy is proposed to restore the diversity of population. To accelerate the convergence speed and enhance robustness, a back-diffusion median integrated evolutionary algorithm (BMIEA) is proposed combining the advantages of particle swarm optimization (PSO) and differential evolution algorithm (DE) in this paper. The BMIEA includes three mainly optimization strategies. (1) Firstly, a new mean-median velocity updating formula is proposed to control optimal path of individuals. It can accelerate the convergence speed via reducing adverse effects of outliers on the population. (2) Secondly, a random differential mutation (RDM) inspired by the DE is devised to avoid the individuals trapping into local optimum via getting one more chance to explore optimal position while exploiting local region in each evolution. (3) Thirdly, a targeted exploration method i.e., back-diffusion operation, is proposed inspired by the duality principle to further accelerate the convergence rate and enhance robustness of algorithm. A series of simulation experiments have verified that BMIEA algorithm has revealed competitiveness compared with 13 state-of-art GOBL-based optimization algorithms. [ABSTRACT FROM AUTHOR]

Differential Evolution (DE) is an effective global optimization algorithm, and many existing adaptive variants of it have been proposed to solve engineering problems. It is well known that population feature information that refers to some mathematical statistic feature information of all individuals in the dimension of decision space, and it can reflect the features of the problem to be solved. However, the population feature information has not been fully utilized by DE's adaptive variants. As a result, those adaptive variants do not obtain promising performance in optimizing nonlinear, non-differentiable and non-separable multi-modal problems. To make adequate extraction and effective use of population feature information, we propose an adaptive differential evolution framework based on population feature information in this paper, named PFI for short. In the PFI framework, the population feature information consists of the standard deviation of fitness value and the sum of standard deviation of each dimension of population. Besides, population feature information archive is designed to store the population feature information and success parameters, and the utilization mechanism of population feature information assigns historical success parameters with high population feature similarity to the current corresponding population. Four widely used mutation strategies of DE are incorporated into the PFI framework to evaluate its performance by optimizing CEC2005, CEC2015, CEC2020 benchmark functions and two real world applications to verify the performance of the PFI framework. Experiment results have demonstrated that PFI framework can significantly improve the performance of 4 popular mutation strategies of DE. [ABSTRACT FROM AUTHOR]

This paper presents a novel Differential Evolution algorithm for protein folding optimization that is applied to a three-dimensional AB off-lattice model. The proposed algorithm includes two new mechanisms. A local search is used to improve convergence speed and to reduce the runtime complexity of the energy calculation. For this purpose, a local movement is introduced within the local search. The designed evolutionary algorithm has fast convergence speed and, therefore, when it is trapped into the local optimum or a relatively good solution is located, it is hard to locate a better similar solution. The similar solution is different from the good solution in only a few components. A component reinitialization method is designed to mitigate this problem. Both the new mechanisms and the proposed algorithm were analyzed on well-known amino acid sequences that are used frequently in the literature. Experimental results show that the employed new mechanisms improve the efficiency of our algorithm and that the proposed algorithm is superior to other state-of-the-art algorithms. It obtained a hit ratio of 100% for sequences up to 18 monomers, within a budget of 10 11 solution evaluations. New best-known solutions were obtained for most of the sequences. The existence of the symmetric best-known solutions is also demonstrated in the paper. [ABSTRACT FROM AUTHOR]

The performance of differential evolution (DE) has been significantly influenced by trial vector generation strategies and control parameters. Various powerful trial vector generation strategies with adaptive parameter adjustment methods such that the population generation is guided by the elites have been proposed. This paper aims to strengthen the performance of DE by compositing these powerful trial vector generation strategies, making it possible to obtain the guidance of each individual from multiple elites concurrently and independently. In this manner, the deleterious behavior in which an individual is misguided by various local optimal solutions into unpromising areas could be restrained to a certain extent. An adaptive multiple-elites-guided composite differential evolution algorithm with a shift mechanism (abbreviated as AMECoDEs) has been proposed in this paper. This algorithm concurrently employs two elites-guided trial vector generation strategies for each individual to generate two candidate solutions accordingly, and the best one is adopted to participate in the selection. Moreover, a novel shift mechanism is established to handle stagnation and premature convergence issues. AMECoDEs has been tested on the CEC2014 benchmark functions. Experimental results show that AMECoDEs outperforms various classic state-of-the-art DE variants and is better than or at least comparable to various recently proposed DE methods. [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]

Penalty function is well-known for constrained evolutionary optimization. An open question in the penalty function is how to tune the penalty coefficient. This paper proposes an adaptive fuzzy penalty method to address this issue, where the coefficient is adjusted at both the individual level and the population level. At the individual level, each individual chooses a penalty coefficient from a predefined domain according to some fuzzy rules. At the population level, the domain of the crisp output is adjusted adaptively by using population information. To enhance the population diversity, an effective mutation scheme is developed. Due to its numerous merits, differential evolution is used to design a search algorithm. By the above processes, a constrained optimization evolutionary algorithm called AFPDE is proposed. Since the objective function value and the degree of constraint violation are normalized, AFPDE is less problem-dependent than the seminal work of the fuzzy penalty method. AFPDE introduces a lower penalty value in the early stage of AFPDE while a higher one in the later stage. Thus, it can escape local optima in the infeasible region. Experiments on three well-known benchmark test sets and two mechanical design problems validate that AFPDE is competitive. [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]

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]

Novel Evolutionary Algorithms are usually tested on sets of artificially-constructed benchmark problems. Such problems are often created to make the search of one global extremum (usually minimum) tricky. In this paper it is shown that benchmarking heuristics on either minimization or maximization of the same set of artificially-created functions (with equal bounds and number of allowed function calls) may lead to very different ranking of tested algorithms. As Evolutionary Algorithms and other heuristic optimizers are developed in order to be applicable to real-world problems, such result may raise doubts on the practical meaning of benchmarking them on artificial functions, as there is little reason that searching for the minimum of such functions should be more important than searching for their maximum. Thirty optimization heuristics, including a number of variants of Differential Evolution, as well as other kinds of Evolutionary Algorithms, Particle Swarm Optimization, Direct Search methods and – following the idea borrowed from No Free Lunch – pure random search are tested in the paper. Some discussion regarding the choice of the mean or the median performance for comparison is addressed and a short debate on the overall performance of particular methods is given. [ABSTRACT FROM AUTHOR]

The tradeoff between exploration and exploitation is critical to the performance of an evolutionary algorithm. Different levels of exploration-exploitation tradeoff are required at different evolutionary stages for achieving a satisfactory performance of an evolutionary algorithm. In this paper, we propose a novel survival analysis method to intelligently guide the maintenance of the exploration-exploitation tradeoff in multiobjective evolutionary algorithms. The survival analysis stems from a deep understanding of the evolutionary search procedure. Through survival analysis, an indicator is derived, which is used to guide the adoption of appropriate recombination operators, based on the assumption that the roles of these operators in terms of their capabilities on exploration-exploitation can be asserted. In the developed algorithm, a differential evolution recombination operator and a new sampling strategy are hybridized. Empirical comparison with five well-known multiobjective evolutionary algorithms on a number of test instances with complex Pareto sets and Pareto fronts indicates the effectiveness and superiority of the developed algorithm in terms of commonly-used performance metrics on these test instances. [ABSTRACT FROM AUTHOR]

Abstract: Differential Evolution (DE) is one of the most popular optimization methods for real-valued problems and a large number of its variants have been proposed so far. However, bringing together different ideas that already led to successful DE versions is rare in the literature. In the present paper a novel DE algorithm is proposed, in which three among the most efficient concepts already applied separately within DE framework are gathered together, namely: (1) the adaptation of algorithm control parameters and probabilities of using different mutation strategies; (2) the use of Nelder–Mead algorithm as a local search method hybridized with DE; and (3) the splitting mutation into Global and Local models, when Local mutation model is based on the concept of neighborhood of individuals organized on a ring topology. The performance of the novel algorithm, called Adaptive Memetic DE with Global and Local neighborhood-based mutation operators is compared with 13 different DE variants on a set of 25 popular problems which include rotated, shifted and hybrid composition functions. It is found that, although none DE algorithm outperforms all the others for the majority of problems, on average the proposed approach perform better than all 13 DE algorithms selected for comparison. The proposed algorithm is another heuristic approach developed to solve optimization problems. The question may arise, whether proposing novel methods is useful as No Free Lunch theorems for optimization state that the expected performance of all possible heuristics on all possible problems is equal. In the last section of the paper the limitations and implications of No Free Lunch theorems are discussed based on rich, but unfortunately frequently neglected literature. A very simple continuous and differentiable minimization problem is proposed, for which it is empirically verified that each among considered 14 DE algorithms perform poorer than random sampling. It is also empirically shown that when all considered DE algorithms search for the maximum of the proposed problem, they found lower minimum than DE algorithms searching for the minimum. Such result is not unexpected according to No Free Lunch theorems and should be considered as a precaution from generalization of good performance of heuristic optimization methods. [Copyright &y& Elsevier]

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]

In this paper, we develop a quick and effective position control strategy based on the differential evolution (DE) algorithm for a planar three-link passive-active-active (PAA) underactuated system with first-order nonholonomic constraint. Due to the existence of the constraint, when the angular velocities of the two active links are proportional, the planar PAA system is transformed from a first-order nonholonomic system to a holonomic system like an Acrobot. Making full use of the angular constraint of the like-Acrobot, we employ the DE algorithm to calculate the target angles of all links and the target ratio between the angular velocities of the two active links. After that, one continuous controller for one active link is designed to ensure the target ratio in the whole control process; meantime, the other continuous controller for the other active link is designed to make its angle asymptotically converge to the corresponding target value. In this way, the angles of all links can asymptotically converge to the corresponding target values according to the angular constraint, and thus the position control of the system is realized using the continuous control method. Finally, the simulation results demonstrate the quickness and effectiveness of our proposed control method. [ABSTRACT FROM AUTHOR]

Abstract: Motivated by the recent success of diverse approaches based on differential evolution (DE) to solve constrained numerical optimization problems, in this paper, the performance of this novel evolutionary algorithm is evaluated. Three experiments are designed to study the behavior of different DE variants on a set of benchmark problems by using different performance measures proposed in the specialized literature. The first experiment analyzes the behavior of four DE variants in 24 test functions considering dimensionality and the type of constraints of the problem. The second experiment presents a more in-depth analysis on two DE variants by varying two parameters (the scale factor F and the population size NP), which control the convergence of the algorithm. From the results obtained, a simple but competitive combination of two DE variants is proposed and compared against state-of-the-art DE-based algorithms for constrained optimization in the third experiment. The study in this paper shows (1) important information about the behavior of DE in constrained search spaces and (2) the role of this knowledge in the correct combination of variants, based on their capabilities, to generate simple but competitive approaches. [ABSTRACT FROM AUTHOR]

Abstract: How much attention should be paid to the promising infeasible solutions during the evolution process is investigated in this paper. Stochastic ranking has been demonstrated as an effective technique for constrained optimization. In stochastic ranking, the comparison probability will affect the position of feasible solution after ranking, and the quality of the final solutions. In this paper, the dynamic stochastic selection (DSS) is put forward within the framework of multimember differential evolution. Firstly, a simple version named DSS-MDE is given, where the comparison probability decreases linearly. The algorithm DSS-MDE has been compared with two state-of-the-art evolution strategies and three competitive differential evolution algorithms for constrained optimization on 13 common benchmark functions. DSS-MDE is also evaluated on four well-studied engineering design examples, and the experimental results are significantly better than current available results. Secondly, other dynamic settings of the comparison probability for DSS-MDE are also designed and tested. From the experimental results, DSS-MDE is effective for constrained optimization. Finally, DSS-MDE with a square root adjusted comparison probability is evaluated on the 22 benchmark functions in CEC’06, and the experimental results on most functions are competitive. [Copyright &y& Elsevier]

Constrained optimization problems (COPs) are common in many fields. To solve such problems effectively, in this paper, we propose a new constrained optimization evolutionary algorithm (COEA) named CACDE that combines an adaptive trial vector generation strategy-based differential evolution (DE) algorithm with a cluster-replacement-based feasibility rule. In CACDE, some potential mutation strategies, scale factors and crossover rates are stored in candidate pools, and each element in the pools is assigned a selection probability. During the trial vector generation stage, the mutation strategy, scale factor and crossover rate for each target vector are competitively determined based on these selection probabilities. Meanwhile, the selection probabilities are dynamically updated based on statistical information learned from previous searches in generating improved solutions. Moreover, to alleviate the greediness of the feasibility rule, the main population is divided into several clusters, and one vector in each cluster is conditionally replaced with an archived infeasible vector with a low objective value. The superior performance of CACDE is validated via comparisons with some state-of-the-art COEAs over 2 sets of artificial problems and 5 widely used mechanical design problems. The results show that CACDE is an effective approach for solving COPs, basically due to the use of adaptive DE and cluster-replacement-based feasibility rule. [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]

In this paper, a visual analysis methodology is proposed to perform comparative analysis of guided random algorithms such as evolutionary optimization algorithms and community detection algorithms. Proposed methodology is designed based on quantile-quantile plot and regression analysis to compare performance of one algorithm over other algorithms. The methodology is extrapolated as one-to-one comparison, one-to-many comparison and many-to-many comparison of solution quality and convergence rate. Most of the existing approaches utilize both solution quality and convergence rate to perform comparative analysis. However, the many-to-many comparison i.e. ranking of algorithms is done only with solution quality. On the contrary, with proposed methodology ranking of algorithms is done in terms of both solution quality and convergence rate. Proposed methodology is studied with four evolutionary optimization algorithms on 25 benchmark functions. A non-parametric statistical analysis called Wilcoxon signed-rank test is also performed to verify the indication of proposed methodology. Moreover, methodology is also applied to analyze four state-of-the-art community detection algorithms on 10 real-world networks. [ABSTRACT FROM AUTHOR]

This paper proposes a novel sampling-based adaptive bounding evolutionary algorithm termed SABEA that is capable of dynamically updating the search space during the evolution process for continuous optimization problems. The proposed SABEA adopts two bounding strategies, namely fitness-based bounding and probabilistic sampling-based bounding, to select a set of individuals over multiple generations and leverage the value information from these individuals to update the search space of a given problem for improving the solution accuracy and search efficiency. To evaluate the performance of this method, SABEA is applied on top of the classic differential evolution (DE) algorithm and a DE variant, and SABEA is compared to a state-of-the-art Distribution-based Adaptive Bounding Genetic Algorithm (DABGA) on a set of 27 selected benchmark functions. The results show that SABEA can be used as a complementary strategy for further enhancing the performance of existing evolutionary algorithms and it also outperforms DABGA. Finally, a practical problem, namely the model calibration for an agent-based simulation, is used to further evaluate SABEA. The results show SABEA’s applicability to diverse problems and its advantages over the traditional genetic algorithm-based calibration method and DABGA. [ABSTRACT FROM AUTHOR]

Cooperative coevolution (CC) provides a powerful divide-and-conquer architecture for large scale global optimization (LSGO). However, its performance relies highly on decomposition. To make near-optimal decomposition, most developed decomposition strategies either cannot obtain the correct interdependency information or require a lot of fitness evaluations (FEs) in the identification. To alleviate the limitations in previous works, in this paper we propose a fast interdependency identification (FII) algorithm for CC in LSGO. The proposed algorithm firstly identifies separable and nonseparable variables efficiently. Then, the interdependency information of nonseparable variables is further investigated. To make near-optimal decomposition for CC, our algorithm avoids the necessity of obtaining the full interdependency information of nonseparable variables. Therefore, a significant number of FEs can be saved. Extensive experiments have been conducted on two suites of LSGO benchmark functions with up to 2000 variables. FII correctly identified the interdependency information on most benchmark functions with much fewer FEs in comparison with three state-of-the-art algorithms. Furthermore, combined with CC and coupled with a differential evolution variant serving as the optimizer, FII has shown its promising performance in LSGO. [ABSTRACT FROM AUTHOR]

Many real-world problems can be formulated as optimization problems. Such problems pose a challenge for researchers in the design of efficient algorithms capable of finding the best solution with the least computational cost. In this paper, a new evolutionary algorithm is proposed that combines the explorative and exploitative capabilities of two evolutionary algorithms, Cultural Algorithm (CA) and Differential Evolution (DE) algorithm. This hybridization follows the HTH (High-level Teamwork Hybrid) nomenclature in which two meta-heuristics are executed in parallel. The new algorithm named as CADE, manages an overall population which is shared between CA and DE simultaneously. Four modified knowledge sources have been used in proposed CA which are: topographical, situational, normative and domain. The role of the used acceptance function in belief space is to select the knowledge of the best individuals to update the current knowledge. A novel quality function is used to determine the participation ratio for both CA and DE, and then a competitive selection takes place in order to select the proportion of function evaluations allocated for each technique. This collaborative synergy emerges between the DE and CA techniques and is shown to improve the quality of solutions, beyond what each of these two algorithms alone. The performance of the algorithm is evaluated on a set of 50 scalable optimization problems taken from two sources. The first set of 35 came from existing benchmark sets available in the literature. The second set came from the 2014 IEEE Single Function optimization competition. The overall results show that CADE has a favorable performance and scalability behaviors when compared to other recent state-of-the-art algorithms. CADE's overall performance ranked at number 1 for each of the two sets of problems. It is suggested that CADE's success across such a broad spectrum of problem types and complexities bodes well for its application to new and novel applications. [ABSTRACT FROM AUTHOR]

For evolutionary algorithms, the search data during evolution has attracted considerable attention and many kinds of data mining methods have been proposed to derive useful information behind these data so as to guide the evolution search. However, these methods mainly centered on the single objective optimization problems. In this paper, an adaptive differential evolution algorithm based on analysis of search data is developed for the multi-objective optimization problems. In this algorithm, the useful information is firstly derived from the search data during the evolution process by clustering and statistical methods, and then the derived information is used to guide the generation of new population and the local search. In addition, the proposed differential evolution algorithm adopts multiple subpopulations, each of which evolves according to the assigned crossover operator borrowed from genetic algorithms to generate perturbed vectors. During the evolution process, the size of each subpopulation is adaptively adjusted based on the information derived from its search results. The local search consists of two phases that focus on exploration and exploitation, respectively. Computational results on benchmark multi-objective problems show that the improvements of the strategies are positive and that the proposed differential evolution algorithm is competitive or superior to some previous multi-objective evolutionary algorithms in the literature. [ABSTRACT FROM AUTHOR]

Differential Evolution is an efficient metaheuristic for continuous optimization that suffers from the curse of dimensionality. A large amount of experimentation has allowed researchers to find several potential weaknesses in Differential Evolution. Some of these weaknesses do not significantly affect its performance when dealing with low-dimensional problems, so the research community has not paid much attention to them. The aim of this paper is to provide a better insight into the reasons of the curse of dimensionality and to propose techniques to alleviate this problem. Two different weaknesses are revisited and schemes for dealing with them are devised. The schemes increase the diversity of trial vectors and improve on the exploration capabilities of Differential Evolution. Some important mathematical properties induced by our proposals are studied and compared against those of related schemes. Experimentation with a set of problems with up to 1000 dimensions and with several variants of Differential Evolution shows that the weaknesses analyzed significantly affect the performance of Differential Evolution when used on high-dimensional optimization problems. The gains of the proposals appear when highly exploitative schemes are used. Our proposals allow for high-quality solutions with small populations, meaning that the most significant advantages emerge when dealing with large-scale optimization problems, where the benefits of using small populations have previously been shown. [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]

Abstract: Artificial bee colony (ABC) algorithm is a relatively new optimization technique which has been shown to be competitive to other population-based algorithms. However, there is still an insufficiency in ABC regarding its solution search equation, which is good at exploration but poor at exploitation. To address this concerning issue, in this paper, we propose a novel ABC method called as EABC to improve the performance of ABC. In our method, in order to balance the exploration and the exploitation, two new search equations are presented to generate candidate solutions in the employed bee phase and the onlookers phase, respectively. Additionally, we use a more robust calculation to determine and compare the quality of alternative solutions. Experiments are conducted on a set of 48 benchmark functions and also two engineering optimization problems. The results show that EABC significantly improves the performance of ABC, offering faster global convergence, higher solution quality, and stronger robustness when compared with the other algorithms. [Copyright &y& Elsevier]

Abstract: This paper proposes a hybrid evolutionary algorithm for multiobjective optimisation of trusses using real-code population-based incremental learning (RPBIL) to solve multiobjective design problems. Differential evolution (DE) operators are integrated into the main procedure of RPBIL leading to a hybrid algorithm. The newly developed optimiser, along with some established multiobjective evolutionary algorithms (MOEAs) is implemented to solve a number of multiobjective design problems of trusses. Comparative performance based upon a hypervolume indicator shows that the new hybrid multiobjective evolutionary algorithm is superior to the other MOEAs particularly in cases involving large-scale truss design problems. [Copyright &y& Elsevier]

Abstract: In manufacturing industry, turning operations are used to remove unwanted sections of a part to obtain the final product. In this paper a comparison of state-of-the-art optimization techniques to solve multi-pass turning optimization problems is presented.Furthermore, a hybrid technique based on differential evolution algorithm is introduced for solving manufacturing optimization problems. The results have demonstrated the superiority of the hybrid approach over the other techniques like artificial bee colony algorithm, differential evolution algorithm, hybrid particle swarm optimization algorithm, hybrid artificial immune-hill climbing algorithm, hybrid taguchi-harmony search algorithm, hybrid robust genetic algorithm, scatter search algorithm, genetic algorithm and an improved simulated annealing algorithm in terms of convergence speed and efficiency by measuring the number of function evaluations required. [Copyright &y& Elsevier]

Abstract: Differential evolution (DE) is a class of simple yet powerful evolutionary algorithms for global numerical optimization. Binomial crossover and exponential crossover are two commonly used crossover operators in current popular DE. It is noteworthy that these two operators can only generate a vertex of a hyper-rectangle defined by the mutant and target vectors. Therefore, the search ability of DE may be limited. Orthogonal crossover (OX) operators, which are based on orthogonal design, can make a systematic and rational search in a region defined by the parent solutions. In this paper, we have suggested a framework for using an OX in DE variants and proposed OXDE, a combination of DE/rand/1/bin and OX. Extensive experiments have been carried out to study OXDE and to demonstrate that our framework can also be used for improving the performance of other DE variants. [Copyright &y& Elsevier]

Abstract: Differential evolution (DE) is a versatile and efficient evolutionary algorithm for global numerical optimization, which has been widely used in different application fields. However, different strategies have been proposed for the generation of new solutions, and the selection of which of them should be applied is critical for the DE performance, besides being problem-dependent. In this paper, we present two DE variants with adaptive strategy selection: two different techniques, namely Probability Matching and Adaptive Pursuit, are employed in DE to autonomously select the most suitable strategy while solving the problem, according to their recent impact on the optimization process. For the measurement of this impact, four credit assignment methods are assessed, which update the known performance of each strategy in different ways, based on the relative fitness improvement achieved by its recent applications. The performance of the analyzed approaches is evaluated on 22 benchmark functions. Experimental results confirm that they are able to adaptively choose the most suitable strategy for a specific problem in an efficient way. Compared with other state-of-the-art DE variants, better results are obtained on most of the functions in terms of quality of the final solutions and convergence speed. [Copyright &y& Elsevier]

Abstract: This paper proposes the employment of multiple scale factor values within distributed differential evolution structures. Four different scale factor schemes are proposed, tested, compared and analyzed. Two schemes simply employ multiple scale factor values and two also include an update logic during the evolution. The four schemes have been integrated for comparison within three recently proposed distributed differential evolution structures and tested on several various test problems. Numerical results show that, on average, the employment of multiple scale factors is beneficial since in most cases it leads to significant improvements in performance with respect to standard distributed algorithms. Although proper choice of a scale factor scheme appears to be dependent on the distributed structure, any of the proposed simple schemes has proven to significantly improve upon the single scale factor distributed differential evolution algorithms. [Copyright &y& Elsevier]

Abstract: This paper proposes a novel and unconventional Memetic Computing approach for solving continuous optimization problems characterized by memory limitations. The proposed algorithm, unlike employing an explorative evolutionary framework and a set of local search algorithms, employs multiple exploitative search within the main framework and performs a multiple step global search by means of a randomized perturbation of the virtual population corresponding to a periodical randomization of the search for the exploitative operators. The proposed Memetic Computing approach is based on a populationless (compact) evolutionary framework which, instead of processing a population of solutions, handles its statistical model. This evolutionary framework is based on a Differential Evolution which cooperatively employs two exploitative search operators: the first is based on a standard Differential Evolution mutation and exponential crossover, and the second is the trigonometric mutation. These two search operators have an exploitative action on the algorithmic framework and thus contribute to the rapid convergence of the virtual population towards promising candidate solutions. The action of these search operators is counterbalanced by a periodical stochastic perturbation of the virtual population, which has the role of “disturbing” the excessively exploitative action of the framework and thus inhibits its premature convergence. The proposed algorithm, namely Disturbed Exploitation compact Differential Evolution, is a simple and memory-wise cheap structure that makes use of the Memetic Computing paradigm in order to solve complex optimization problems. The proposed approach has been tested on a set of various test problems and compared with state-of-the-art compact algorithms and with some modern population based meta-heuristics. Numerical results show that Disturbed Exploitation compact Differential Evolution significantly outperforms all the other compact algorithms present in literature and reaches a competitive performance with respect to modern population algorithms, including some memetic approaches and complex modern Differential Evolution based algorithms. In order to show the potential of the proposed approach in real-world applications, Disturbed Exploitation compact Differential Evolution has been implemented for performing the control of a space robot by simulating the implementation within the robot micro-controller. Numerical results show the superiority of the proposed algorithm with respect to other modern compact algorithms present in literature. [Copyright &y& Elsevier]

Abstract: Despite the popularity of PID (Proportional-Integral-Derivative) controllers, their tuning aspect continues to present challenges for researches and plant operators. Various control design methodologies have been proposed in the literature, such as auto-tuning, self-tuning, and pattern recognition. The main drawback of these methodologies in the industrial environment is the number of tuning parameters to be selected. In this paper, the design of a PID controller, based on the universal model of the plant, is derived, in which there is only one parameter to be tuned. This is an attractive feature from the viewpoint of plant operators. Fuzzy and neural approaches – bio-inspired methods in the field of computational intelligence – are used to design and assess the efficiency of the PID controller design based on differential evolution optimization in nonlinear plants. The numerical results presented herein indicate that the proposed bio-inspired design is effective for the nonlinear control of nonlinear plants. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) was very successful in solving the global continuous optimization problem. It mainly uses the distance and direction information from the current population to guide its further search. Estimation of distribution algorithm (EDA) samples new solutions from a probability model which characterizes the distribution of promising solutions. This paper proposes a combination of DE and EDA (DE/EDA) for the global continuous optimization problem. DE/EDA combines global information extracted by EDA with differential information obtained by DE to create promising solutions. DE/EDA has been compared with the best version of the DE algorithm and an EDA on several commonly utilized test problems. Experimental results demonstrate that DE/EDA outperforms the DE algorithm and the EDA. The effect of the parameters of DE/EDA to its performance is investigated experimentally. [ABSTRACT FROM AUTHOR]