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Differential Evolution (DE) is widely recognized as a highly effective evolutionary algorithm for global optimization. It has proven its efficacy in tackling diverse problems across various fields and real-world applications. DE boasts several advantages, such as ease of implementation, reliability, speed, and adaptability. However, DE does have certain limitations, such as suboptimal solution exploitation and challenging parameter tuning. To address these challenges, this research paper introduces a novel algorithm called Enhanced Binary JADE (EBJADE), which combines differential evolution with multi-population and elites regeneration. The primary innovation of this paper lies in the introduction of strategy with enhanced exploitation capabilities. This strategy is based on utilizing the sorting of three vectors from the current generation to perturb the target vector. By introducing directional differences, guiding the search towards improved solutions. Additionally, this study adopts a multi-population method with a rewarding subpopulation to dynamically adjust the allocation of two different mutation strategies. Finally, the paper incorporates the sampling concept of elite individuals from the Estimation of Distribution Algorithm (EDA) to regenerate new solutions through the selection process in DE. Experimental results, using the CEC2014 benchmark tests, demonstrate the strong competitiveness and superior performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes the Love Evolution Algorithm (LEA), a novel evolutionary algorithm inspired by the stimulus–value–role theory. The optimization process of the LEA includes three phases: stimulus, value, and role. Both partners evolve through these phases and benefit from them regardless of the outcome of the relationship. This inspiration is abstracted into mathematical models for global optimization. The efficiency of the LEA is validated through numerical experiments with CEC2017 benchmark functions, outperforming seven metaheuristic algorithms as evidenced by the Wilcoxon signed-rank test and the Friedman test. Further tests using the CEC2022 benchmark functions confirm the competitiveness of the LEA compared to seven state-of-the-art metaheuristics. Lastly, the study extends to real-world problems, demonstrating the performance of the LEA across eight diverse engineering problems. Source codes of the LEA are publicly available at https://ww2.mathworks.cn/matlabcentral/fileexchange/159101-love-evolution-algorithm. [ABSTRACT FROM AUTHOR]

This paper extends our previous algorithm, termed as Particle Swarm Optimization with Distributed Acceleration Constants (PSODAC), which has been introduced for mitigating congestion based on rescheduling in a deregulated environment. The proposed variant adopts a sequential hybridization of the PSODAC principle with Differential Evolution, which is a well-known evolutionary algorithm. The variant in this paper is termed as Sequentially Hybridized Differential Evolution with Particle Swarm Optimization (SH-DEPSO). The experimental investigations are carried out in the IEEE 14 bus system in two scenarios namely, single point congestion and multipoint congestion. Firstly, the performance investigation is carried out on mitigating the congestion using cost analysis, stability analysis, complexity analysis, and strategy analysis. Secondly, the characteristics of the algorithm are observed by performing convergence analysis and investigating the quality of the solution dynamics. The studies demonstrate the competing performance of SH-DEPSO over PSODAC and the traditional PSO. [ABSTRACT FROM AUTHOR]

Multi-objective problems have gained much attention during the last decade. To balance the diversity and the convergence of the multi-objective differential evolution algorithm (MODE), an improved MODE is proposed based on the affinity propagation clustering (APC) and the non-dominated count approach in this paper. The proposed algorithm is referred to as AP-MODE, which improves the search efficiency by utilizing the affinity propagation approach to find out the population distribution structure for guiding search. In addition, mating restriction probability is used to select parent individuals for recombination from the neighborhoods or the whole population. Meanwhile, the mating restriction probability is updated according to the non-dominated count approach at each generation. This proposed algorithm is verified by comparing it with some state-of-the-art multi-objective evolutionary algorithms, and the simulation results on DTLZ test problems indicate that AP-MODE can efficiently achieve two goals of multi-objective optimization, i.e., the convergence to actual Pareto front and uniform spread of individuals along Pareto front. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) is a proficient optimizer and has been broadly implemented in real life applications of various fields. Several mutation based adaptive approaches have been suggested to improve the algorithm efficiency in recent years. In this paper, a novel self-adaptive method called SaMDE has been designed and implemented on the mutation-based modified DE variants such as modified randomized localization-based DE (MRLDE), donor mutation based DE (DNDE), and sequential parabolic interpolation based DE (SPIDE), which were proposed by the authors in previous research. Using the proposed adaptive technique, an appropriate mutation strategy from DNDE and SPIDE can be selected automatically for the MRLDE algorithm. The experimental results on 50 benchmark problems taken of various test suits and a real-world application of minimization of the potential molecular energy problem validate the superiority of SaMDE over other DE variations. [ABSTRACT FROM AUTHOR]

The differential evolution (DE) algorithm is a simple and efficient population-based evolutionary algorithm. In DE, the mutation strategy and the control parameter play important roles in performance enhancement. However, single strategy and fixed parameter are not universally applicable to problems and evolution stages with diverse characteristics; besides, the weakness of the advanced DE optimization framework, called selective-candidate framework with similarity selection rule (SCSS), is found by focusing on its single strategy and fixed parameter greedy degree (GD) setting. To address these problems, we mainly combine the multiple candidates generation with multi-strategy (MCG-MS) and the adaptive similarity selection (ASS) rule. On the one hand, in MCG-MS, two symmetrical mutation strategies, "DE/current-to-pbest-w/1" and designed "DE/current-to-cbest-w/1", are utilized to build the multi-strategy to produce two candidate individuals, which prevents the over-approximation of the candidate in SCSS. On the other hand, the ASS rule provides the individual selection mechanism for multi-strategy to determine the offspring from two candidates, where parameter GD is designed to increase linearly with evolution to maintain diversity at the early evolution stage and accelerate convergence at the later evolution stage. Based on the advanced algorithm jSO, replacing its offspring generation strategy with the combination of MCG-MS and ASS rule, this paper proposes multi-strategy differential evolution algorithm with adaptive similarity selection rule (MSDE-ASS). It combines the advantages of two symmetric strategies and has an efficient individual selection mechanism without parameter adjustment. MSDE-ASS is verified under the Congress on Evolutionary Computation (CEC) 2017 competition test suite on real-parameter single-objective numerical optimization, and the results indicate that, of the 174 cases in total, it wins in 81 cases and loses in 30 cases, and it has the smallest performance ranking value, of 3.05. Therefore, MSDE-ASS stands out compared to the other state-of-the-art DEs. [ABSTRACT FROM AUTHOR]

Two goals of multi-objective evolutionary algorithms are effectively improving their convergence and diversity and making the Pareto set evenly distributed and close to the real Pareto front. At present, the challenges to be solved by the multi-objective evolutionary algorithm are to improve the convergence and diversity of the algorithm, and how to better solve functions with complex PF and/or PS shapes. Therefore, this paper proposes a gray wolf optimization-based self-organizing fuzzy multi-objective evolutionary algorithm. Gray wolf optimization algorithm is used to optimize the initial weights of the self-organizing map network. New neighborhood relationships for individuals are built by self-organizing map, which can maintain the invariance of feature distribution and map the structural information of the current population into Pareto sets. Based on this neighborhood relationship, this paper uses the fuzzy differential evolution operator, which constructs a fuzzy inference system to dynamically adjust the weighting parameter in the differential operator, to generate a new initial solution, and the polynomial mutation operator to refine them. Boundary processing is then conducted. Experiments on 15 problems of GLT1-6 and WFG1-9 and the algorithm proposed in this paper achieve the best on 18 values. And the result shows that the convergence and diversity of the proposed algorithm are better than several state-of-the-art multi-objective evolutionary algorithms. [ABSTRACT FROM AUTHOR]

Complex systems provide an opportunity to analyze the essence of phenomena by studying their intricate connections. The networks formed by these connections, known as complex networks, embody the underlying principles governing the system's behavior. While complex networks have been previously applied in the field of evolutionary computation, prior studies have been limited in their ability to reach conclusive conclusions. Based on our investigations, we are against the notion that there is a direct link between the complex network structure of an algorithm and its performance, and we demonstrate this experimentally. In this paper, we address these limitations by analyzing the dynamic complex network structures of five algorithms across three different problems. By incorporating mathematical distributions utilized in prior research, we not only generate novel insights but also refine and challenge previous conclusions. Specifically, we introduce the biased Poisson distribution to describe the algorithm's exploration capability and the biased power-law distribution to represent its exploitation potential during the convergence process. Our aim is to redirect research on the interplay between complex networks and evolutionary computation towards dynamic network structures, elucidating the essence of exploitation and exploration in the black-box optimization process of evolutionary algorithms via dynamic complex networks. [ABSTRACT FROM AUTHOR]

The knapsack problem (KP) is a discrete combinatorial optimization problem that has different utilities in many fields. It is described as a non-polynomial time (NP) problem and has several applications in many fields. The differential evolution (DE) algorithm has been successful in solving continuous optimization problems, but it needs further work to solve discrete and binary optimization problems and avoid local optima. According to the literature, no DE search operator or algorithm is optimal for all optimization tasks. As a result, using more than one search operator in a single algorithm architecture, called multi-operator-based algorithms, is a solution to address this problem. These methods outperformed single-based methods for continuous optimization problems. Thus, in this paper, a binary multi-operator differential evolution (BMODE) approach is presented to tackle the 0–1 KP. The presented methodology utilizes multiple differential evolution (DE) mutation strategies with complementary characteristics, with the best mutation operator being asserted utilizing the produced solutions' quality and the population's diversity. In BMODE, two types of transfer functions (TFs) (S-shaped and V-shaped) are used to transfer the continuous solutions to binary ones to be able to calculate the fitness function value. To handle the capacity constraints, a feasibility rule is utilized and some of the infeasible solutions are repaired. The performance of BMODE is tested by solving 40 instances with multiple dimensions, i.e., low, medium, and high. Experimental results of the proposed BMODE are compared with well-known state-of-the-art 0–1 knapsack algorithms. Based on Wilcoxon's nonparametric statistical test ( α = 0.05 ), the proposed BMODE can obtain the best results against the rival algorithms in most cases, and can work well on stability and computational accuracy. [ABSTRACT FROM AUTHOR]

In recent times, numerous innovative and specialized algorithms have emerged to tackle two and three multi-objective types of problems. However, their effectiveness on many-objective challenges remains uncertain. This paper introduces a new Many-objective Sine–Cosine Algorithm (MaOSCA), which employs a reference point mechanism and information feedback principle to achieve efficient, effective, productive, and robust performance. The MaOSCA algorithm's capabilities are enhanced by incorporating multiple features that balance exploration and exploitation, direct the search towards promising areas, and prevent search stagnation. The MaOSCA's performance is evaluated against popular algorithms such as the Non-dominated sorting genetic algorithm-III (NSGA-III), the Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D) integrated with Differential Evolution (MOEADDE), the Many-objective Particle Swarm Optimizer (MaOPSO), and the Many-objective JAYA Algorithm (MaOJAYA) across various test suites, including DTLZ1-DTLZ7 with 5, 9, and 15 objectives and car cab design, water resources management, car side impact, marine design, and 10-bar truss engineering design problems. The performance evaluation is carried out using various performance metrics. The MaOSCA demonstrates its ability to achieve well-converged and diversified solutions for most problems. The success of the MaOSCA can be attributed to the multiple features of the SCA optimizer integrated into the algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a study on improving the estimation accuracy and convergence rate of hysteresis modeling of MFC actuators using mutation enhanced differential evolution (MEDE) algorithm, a modified version of the differential evolution algorithm. The proposed MEDE algorithm uses three mutation strategies, i.e., best, rand, and pbest. To model the secondary path of a smart flexible beam with MFC actuators, a Hammerstein model that combines an asymmetric Bouc-Wen model with an ARX model connected in series is proposed. The fitness function values of the Hammerstein model are compared with evolutionary algorithms. [ABSTRACT FROM AUTHOR]

Combined heat and power economic emission dispatch (CHPEED) can obtain good economic and environmental benefits, but the dispatch problem presents non-convex, nonlinear, multi-constrained and multi-objective characteristics. Thus, a two-stage cooperative multi-objective differential evolutionary algorithm (TCADEA) is proposed in this paper. The algorithm uses a two-stage framework: the first stage uses a two-population strategy to divide the population into an elite population and an ordinary population, where the elite population is used to obtain better target values and the ordinary population is used to search the target space to ensure the diversity of the population and update the two populations by different adaptive differential operators. In addition, the ε constraint processing technique is used to handle the constraints. The second stage combines two populations into one and generates offspring through the constrained dominance principle (CDP) and adaptive differential evolution to maintain well-distributed population. The actual case results show that the TCADEA algorithm reduces $0.034 × 106, $0.008 × 106, $0.07 × 106 and 113 × 105 lb, 102 × 105 lb, 155 × 105 lb in fuel cost and emissions compared to MODE, NSGA-II, and TOP, respectively. [ABSTRACT FROM AUTHOR]

As one of the evolutionary algorithms, firefly algorithm (FA) has been widely used to solve various complex optimization problems. However, FA has significant drawbacks in slow convergence rate and is easily trapped into local optimum. To tackle these defects, this paper proposes an improved FA combined with extremal optimization (EO), named IFA-EO, where three strategies are incorporated. First, to balance the tradeoff between exploration ability and exploitation ability, we adopt a new attraction model for FA operation, which combines the full attraction model and the single attraction model through the probability choice strategy. In the single attraction model, small probability accepts the worse solution to improve the diversity of the offspring. Second, the adaptive step size is proposed based on the number of iterations to dynamically adjust the attention to the exploration model or exploitation model. Third, we combine an EO algorithm with powerful ability in local-search into FA. Experiments are tested on two group popular benchmarks including complex unimodal and multimodal functions. Our experimental results demonstrate that the proposed IFA-EO algorithm can deal with various complex optimization problems and has similar or better performance than the other eight FA variants, three EO-based algorithms, and one advanced differential evolution variant in terms of accuracy and statistical results. [ABSTRACT FROM AUTHOR]

The decomposition-based algorithm, for example, multiobjective evolutionary algorithm based on decomposition (MOEA/D), has been proved effective and useful in a variety of multiobjective optimization problems (MOPs). On the basis of MOEA/D, the MOEA/D-DE replaces the simulated binary crossover (SBX) operator with differential evolution (DE) operator, which is used to enhance the diversity of the solutions more effectively. However, the amplification factor and the crossover probability are fixed in MOEA/D-DE, which would lead to a low convergence rate and be more likely to fall into local optimum. To overcome such a prematurity problem, this paper proposes three different adaptive operators in DE with crossover probability and amplification factors to adjust the parameter settings adaptively. We incorporate these three adaptive operators in MOEA/D-DE and MOEA/D-PaS to solve MOPs and many-objective optimization problems (MaOPs), respectively. This paper also designs a sensitive experiment for the changeable parameter η in the proposed adaptive operators to explore how η would affect the convergence of the proposed algorithms. These adaptive algorithms are tested on many benchmark problems, including ZDT, DTLZ, WFG, and MaF test suites. The experimental results illustrate that the three proposed adaptive algorithms have better performance on most benchmark problems. [ABSTRACT FROM AUTHOR]

In multi-objective bilevel optimisation problems, the upper-level performance of different lower-level optimal solutions may be very different, even though they belong to the same lower-level problem. It may lead to poor optimisation results. Therefore, the lower-level search should search lower-level non-dominated solutions that are also non-dominated in the upper-level objective space. In this paper, we use two populations in the lower-level search. The first population maintains non-dominance and diversity in the lower-level objective space and provides the second population with convergence pressure from the lower level. The second population selects the upper-level non-dominated solutions that are not dominated by the first population in the lower-level objective space, which make the second population maintain the non-dominance at both upper and lower levels. Besides, to improve the search efficiency, we set up the upper-level mating pool to generate the upper-level vectors of offsprings near the upper-level vectors of the better individuals in the current population. To balance convergence and diversity, the selection operator of a decomposition based multi-objective evolutionary algorithm is adopted. The proposed algorithm has been evaluated on a set of benchmark problems and a real-world optimisation problem. Experimental results demonstrate that the proposed algorithm is efficient and effective. [ABSTRACT FROM AUTHOR]

The design of genetic operators is absolutely one of the core work of evolutionary algorithms research. However, the essence of the evolutionary algorithms is that a lot of algorithm design is based on the manual result analysis, summarize, refine, feedback, and then, the algorithms are designed adaptively and correspondingly. This kind of design scheme needs artificial statistics and analysis of large amounts of data, which greatly increases the burden of the designers. To solve this problem, an evolutionary algorithm framework based on genetic operator automatic design is proposed in this paper. In the first step, Gene Expression Programming and Differential Evolution methods are combined together and used to design the genetic operators automatically and adaptively, this hybrid method can not only explore solutions in problem space for the problem solving as most classical evolutionary algorithms do, but also generate genetic operators automatically in operator space for the proper operators extraction and selection related to the evolutionary algorithms. In the second step, the designed operators are adopted into the typical evolutionary algorithms to verify the performance and the result shows that the new designed genetic operator is superior to or at least equivalent to some existing DE variants in a set of classical benchmark functions. More importantly, this paper is not aimed at designing high performance algorithms, but to provide a new perspective for algorithms designing, and to provide a reference scheme for the machine algorithms designing. [ABSTRACT FROM AUTHOR]

Generally, the performance of evolutionary algorithms (EAs) greatly depends on the setting of their control parameters. Many adaptive setting technologies have been developed to solve the time-consuming task of parameter settings. However, the adaptive technologies for the grey prediction evolution algorithm (GPE), which was proposed by Hu et al. in 2020 with two control parameters, have not been investigated. This paper proposes four adaptive GPE algorithms according to three typical adaptive technologies, i.e. probability distributions, statistics and mathematical models in the field of EAs. Four proposed adaptive GPE are separately based on the uniform distribution (aGPEu), normal distribution (aGPEn), average fitness (aGPEa) and chaotic sequences (aGPEc). The performance of the four proposed adaptive GPE algorithms is evaluated on CEC2014, CEC2017 benchmark functions and a suite of eight engineering constrained design problems. The experimental results show the superiority and competitiveness of all the four proposed algorithms. [ABSTRACT FROM AUTHOR]

Wireless sensor network is large-scale, self-organizing and reliable. It is widely used in the military, disaster management, environmental monitoring, and other fields. Algorithms for localization can be classified as range-based or range-free based on their ability to achieve effective localization. Range-based algorithms require hardware support, which increases deployment costs and complexity. Instead of measuring distance directly, range-free algorithms estimate the position based on hop counts between nodes. While simpler in terms of hardware requirements, this algorithm suffers from large localization errors. To address this problem, this paper proposes an improved 3D DV-Hop localization algorithm (3D DEHDV-Hop) using a differential evolutionary algorithm. First of all, theoretical analysis shows a correlation between the volume of the intersection area containing the communication range between neighbors and the number of shared single-hop nodes. Then, using the number of shared single-hop nodes between nodes, the number of hops is converted from a discrete value to an exact continuous value. Finally, the localization problem is transformed into a minimum optimization problem by incorporating a differential evolutionary algorithm. As compared to the other four algorithms compared, 3D DEHDV-Hop improves localization accuracy by an average of 10.3% under different anchor node densities, 13.7% under different communication radiuses, and 12.1% under different anchor node numbers. [ABSTRACT FROM AUTHOR]

In this paper, a multi-operator differential evolution algorithm (MODE) is proposed to solve the Optimal Power Flow problem, called MODE-OPF. The MODE-OPF utilizes the strengths of more than one differential evolution operator in a single algorithmic framework. Additionally, an adaptive method is proposed to update the number of solutions evolved by each DE operator based on both the diversity of the population and the quality of solutions. This adaptive method has the ability to maintain diversity at the early stages of the optimization process and boost convergence at the later ones. The performance of the proposed MODE-OPF is tested by solving OPF problems for both small and large IEEE bus systems (i.e., IEEE-30 and IEEE-118) while considering intermittent solar and wind power generation. To prove the suitability of this proposed algorithm, its performance has been compared against several state-of-the-art optimization algorithms, where MODE-OPF outperforms other algorithms in all experimental results thereby improving a network's performance with lower cost. MODE-OPF decreases the total generation cost up to 24.08%, the real power loss up to 6.80% and the total generation cost with emission up to 8.56%. • Development of an adaptive method (AM) for optimizing diversity and solution quality. • Innovative constraint handling approach, progressively adding constraints for improved performance. • Incorporation of intermittent renewable energy models for realistic problem solving. • Extensive validation on IEEE 30-bus and IEEE 118-bus networks, outperforming state-of-the-art algorithms in cost, loss, and environmental impact reduction. [ABSTRACT FROM AUTHOR]

The differential evolution (DE) algorithm is widely regarded as one of the most influential evolutionary algorithms for addressing complex optimization problems. However, the fixed mutation strategy limits the adaptive ability of DE, and the lack of utilization of historical information limits the optimization ability of DE. In this paper, an indicator-based self-learning differential evolution algorithm (ISDE) is proposed. A jump out mechanism based on deep reinforcement learning is adopted to control the mutation intensity of the population. The neural network in the jump out mechanism is designed as a decision maker. The mutation intensity of the population is controlled by the neural network, and the neural network are trained by a double deep Q network algorithm based on the continuous data generated during the evolution process. A population range indicator (PRI) is utilized to describe individual differences in the population. A diversity maintenance mechanism is designed to maintain individual differences according to the value of PRI. The experimental results reveal that the comprehensive performance of ISDE is superior to comparison algorithms on CEC 2017 real-parameter numerical optimization. [ABSTRACT FROM AUTHOR]

Assembly sequence planning is one of the key issues in DFA and computer-aided assembly process planning research for concurrent engineering. The purpose of this paper is to solve the problem of insufficient individual intelligence in evolutionary algorithms for assembly sequence planning, and a evolutionary algorithm for assembly sequence planning is designed. In this paper, the particle swarm optimization (PSO) algorithm is used to optimize the hybrid assembly sequence planning and assembly line balance problems. According to the assembly sequence problem, the number of assembly tool changes and the number of assembly orientation changes are transformed into the operation time of the assembly line. At the same time, the transportation of heavy parts in the assembly balance problem is considered. Then, by extracting the connection relationship and information of the parts, the disassembly method is used to inversely obtain the disassembly support matrix, and then, it is used to obtain the priority relationship diagram of the assembly operation tasks that indicate the order constraints of the job tasks on the assembly line. Aiming at the shortcoming that particle swarm optimization algorithm is easy to fall into local optimum, a various population strategy is adopted to shorten the evolution stagnation time, improve the evolution efficiency of particle swarm optimization algorithm, and enhance the optimization ability of the algorithm. Combined with the three evaluation indicators of assembly geometric feasibility, assembly process continuity, and assembly tool change times, a fitness function is constructed to achieve multi-objective optimization. Finally, experiments show that the multi-agent evolutionary algorithm is incorporated into the planning process to obtain an accurate solution through the various population strategy–particle swarm optimization algorithm, which proves the feasibility of the compound algorithm and has better performance in solving assembly sequence planning problems. [ABSTRACT FROM AUTHOR]

Camera calibration is an avoidable process for computationalvision applications, such as 3D reverse engineering, industrial robot calibration, optic-pattern recognition, simultaneous localization and mapping, autonomous visual-driving and photogrammetric vision. The camera calibration problem is too complex, nonlinear and multimodal. Traditional camera calibration methods using gradient-based optimization often trap to one of the many local solutions available. Accurate computation ability of traditional camera calibration methods is limited since they use gradient-based optimization methods. Since evolutionary computing algorithms can avoid local solutions of numerical problems, they have the potential to accurately compute the required camera calibration parameters for high-precision computationalvision applications. In this paper, the camera calibration parameters are computed by using 11 evolutionary computing algorithms, i.e., WDE, ABC, PSO, COBIDE, DE, CS, GWO, TLBO, MVMO, FOA and LSHADE. In order to make unbiased evaluation of the camera calibration results provided by the related evolutionary computing algorithms, two gradient-based traditional camera calibration methods, i.e., Zhang and Bouguet, have been used in the conducted experiments in this paper. The camera calibration results of the related methods were used to model a 3D physical test scene by using Structure from Motion photogrammetry method. The reference data set of the related 3D physical scene has been captured by using a 3D terrestrial laser scanner. Statistical comparison of the camera calibration results exposed that WDE supplies statistically better results than other comparison algorithms. [ABSTRACT FROM AUTHOR]

The main focus of this paper is on the family of evolutionary algorithms and their real-life applications. We present the following algorithms: genetic algorithms, genetic programming, differential evolution, evolution strategies, and evolutionary programming. Each technique is presented in the pseudo-code form, which can be used for its easy implementation in any programming language. We present the main properties of each algorithm described in this paper. We also show many state-of-the-art practical applications and modifications of the early evolutionary methods. The open research issues are indicated for the family of evolutionary algorithms. [ABSTRACT FROM AUTHOR]

In multi-objective bilevel optimisation problems, the upper-level performance of different lower-level optimal solutions may be very different, even though they belong to the same lower-level problem. It may lead to poor optimisation results. Therefore, the lower-level search should search lower-level non-dominated solutions that are also non-dominated in the upper-level objective space. In this paper, we use two populations in the lower-level search. The first population maintains non-dominance and diversity in the lower-level objective space and provides the second population with convergence pressure from the lower level. The second population selects the upper-level non-dominated solutions that are not dominated by the first population in the lower-level objective space, which make the second population maintain the non-dominance at both upper and lower levels. Besides, to improve the search efficiency, we set up the upper-level mating pool to generate the upper-level vectors of offsprings near the upper-level vectors of the better individuals in the current population. To balance convergence and diversity, the selection operator of a decomposition based multi-objective evolutionary algorithm is adopted. The proposed algorithm has been evaluated on a set of benchmark problems and a real-world optimisation problem. Experimental results demonstrate that the proposed algorithm is efficient and effective. [ABSTRACT FROM AUTHOR]

Reducing the number of lower-level function evaluations (LFEs) is crucial to designing a bilevel evolutionary algorithm (BLEA) for bilevel optimization. Direct neighbor solution transfer (DST) is regularly used in BLEA because it can improve the lower-level search efficiency and reduce the number of LFEs. But this method still faces the challenge of misleading searches to make the algorithm converge to the wrong optimum. This paper proposes a bilevel improved multi-operator differential evolution algorithm (BL-IMODE) for bilevel optimization, which uses the knowledge transfer and adaptive coordinate systems approach. Specifically, this paper proposes a lower-level search knowledge transfer (LLS-KT) and a lower-level (LL) optimal solution distribution information transfer (LLO-DIT) mechanism to implement knowledge transfer. In LLS-KT, transferring LL solutions to the LL optimizer is similar to DST, but the LLS-KT transfers multiple solutions and thus has less possibility of misleading searches than DST. Moreover, the LLO-DIT transfers the LL optimal solution distribution information to the LL optimizer for generating promising offspring solutions. Since this method does not directly transfer LL solutions, it avoids misleading searches. Additionally, the adaptive coordinate systems (ACS) approach is used in two-level optimizers to suit different fitness landscapes and further reduce the number of LFEs. In ACS, three differential evolution mutation operators are produced in two coordinate systems. An adaptive strategy is used to select the suitable differential evolution mutation operator to generate promising offspring solutions in the Eigen coordinate or original coordinate system. Experimental studies on three test suites benchmark problems for comparison with seven state-of-the-art algorithms are conducted. The results show BL-IMODE has a significant advantage over the comparative algorithms. Finally, BL-IMODE is applied to tackle the inverse optimal control problem. • We propose a bilevel improved multi-operator differential evolution algorithm. • We propose a knowledge transfer approach to avoid misleading search. • We propose an adaptive coordinate systems approach to improve search efficiency. • We outperform all existing approaches in most test instances. [ABSTRACT FROM AUTHOR]

• We propose an improved differential evolution (DE) algorithm by composite binary crossover and Pareto refining operations to the DE. • DE solves the quantifying fraudulent transactions problem by minimizing the selected feature cost while maximizing the quantification ability. • We show that the proposed DE outperforms four other variants of DE and five state-of-the-art EAs on various credit datasets. • The results are also statically validated through the Friedman test and Wilcoxon post-hoc analysis. [Display omitted] Identification of fraudulent credit card transactions is a complex problem mainly due to the following factors: 1) The relative behavior of customers and fraudsters may alter over time. 2) The ratio of legitimate to fraudulent transactions is highly imbalanced, and 3) Investigators examine a small segment of transactions in a reasonable time frame. Researchers have proposed various algorithms to identify potential fraud in a new incoming transaction. However, these approaches require significant human investigator effort and are sometimes misleading. To address this issue, this paper proposes an improved multiobjective differential evolution (DE) algorithm to estimate the distribution of fraudulent transactions in a set of new incoming transactions, referred to as quantifying fraudulent transactions. Our paper has three major novelties. First, we present the problem formulation of cost-based feature selection with maximum quantification ability. Second, we improve the DE by applying effective trial vector generation algorithms to the random control parameter settings to exploit the advantage of individual DE variants. Third, we develop the maximum-relevancy-minimum-redundancy-based Pareto refining operator to enhance the self-learning ability of individuals in Pareto solutions. We compare our approach against four other modifications of DE and five state-of-the-art evolutionary algorithms on real-time credit datasets in streaming and non-streaming frameworks using hyper-volume, two-set coverage, and spread performance metrics. [ABSTRACT FROM AUTHOR]

This paper aims to improve premature convergence and low precision of the differential evolution algorithm. An adaptive constrained differential evolution algorithm based on a probability interval update mechanism (PIMDE) is proposed. First, the interval probability update mechanism is developed to adaptively generate the mutation probability value, and the hybrid mutation strategy is formulated by effectively selecting complementary mutation strategies based on the mutation probability. Subsequently, the adaptive mechanism is employed to dynamically adjust the mutation strategy and parameters; as a result, the global detection and local search ability of the algorithm can be balanced, and the search efficiency of the algorithm can be enhanced. To verify determine the performance of the proposed algorithm, ten standard constrained optimization problems and five engineering optimization problems are analyzed. As revealed from experimental results, PIMDE can effectively solve COPs with high precision and robustness. [ABSTRACT FROM AUTHOR]

The fitness landscape is a theory applied to the evolutionary dynamics of biological evolution to explain the behavior of evolutionary algorithms in the solution of optimization problems. With the continuous advancement of evolutionary algorithm optimization, a fitness landscape can present more abundant feature information, such as the local fitness, fitness distance correlation, and landscape roughness. These landscape features reflect the optimal solution distribution, quantity, and local unimodal topology of the optimization problem from various angles. This paper expresses the adaptability landscape features of typical optimization problems, engages in a quantitative analysis of the fitness distance correlation information, evaluates the difficulty of solving the problem within the search space, and obtains the correlation degree classification result. The search strategy adapts the mixed mutation and the fitness distance correlation for differential evolution. Empirical studies show that, the fitness distance correlation search strategy for the differential evolution algorithm can avoid falling into the local optimum, improve accuracy and convergence, and solve the single-objective optimization problem in a more comprehensive manner. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) is a well-known evolutionary algorithm with simple operation and excellent performance, which has been applied to solve various optimization problems. To alleviate the problem of premature convergence or population stagnation faced by DE algorithm, this paper proposes an adaptive regeneration framework based on search space adjustment (ARSA), which can be easily embedded into various DE variants. When one individual cannot get improved for several generations, the ARSA framework will be triggered to randomly generate a substitute individual from a dynamic search space which is determined by a given adjustment mechanism controlled by two different levels of parameters. The trigger condition for each individual is adaptively controlled by its status in the current population. The space adjustment mechanism contains two strategies, one focuses on global exploration while the other on local exploitation. Moreover, the ARSA framework does not add any parameters that need to be pre-set, and all the included parameters are adaptive. To verify the availability of ARSA framework for solving complex optimization problems, thirty functions with different dimensions from IEEE CEC 2017 test platform and three real-life problems are employed for comparative experiments. The experimental results indicate that our ARSA framework notably improves the performance of two basic DE algorithms and six state-of-the-art DE variants. [ABSTRACT FROM AUTHOR]

This paper deals with the realistic combined environmental economic dispatch (CEED) problem, considering the running fuel cost along with emission as objectives taking power balance and operating limits of the generators as constraints. A new dynamic algorithm for multiobjective optimization, namely the modified multi-objective cat swarm optimization (MOCSO) has been formulated and successfully implemented to address the nonlinear multi-modal CEED problem. A new constraint handling technique is incorporated in the algorithm to satisfy the nonlinear constraints. Further, to select a single solution from the set of Pareto solutions, best tradeoff solution is obtained through fuzzy inference. A thorough investigation has been carried out on two standard test cases namely, the IEEE 14 bus and IEEE 30 bus test systems. The effectiveness of the algorithm is compared with other competitive evolutionary algorithms, such as the non-dominated sorting genetic algorithm (NSGA-II), strength Pareto evolutionary algorithm2 (SPEA2), multi-objective particle swarm optimization (MOPSO) and multi-objective differential evolution (MODE). Performance estimation is done on the basis of computational time, Pareto fronts and non-parametric performance measures. The statistical analysis is also performed, to show the superiority of the proposed modified MOCSO algorithm. Examination of the performance measures shows that the modified MOCSO provides good Pareto solutions while maintaining diversity. It provides a wide scope to trade a balance between running cost and environmental emission of thermal power plants under different types of challenging constraints. [ABSTRACT FROM AUTHOR]

This paper deals with a multiperiod multiobjective fuzzy portfolio selectiossn problem based on credibility theory. A credibilistic multiobjective mean-VaR model is formulated for the multiperiod portfolio selection problem, whereby the return is quantified by the credibilistic mean and the risk is measured by the credibilistic VaR. We also consider liquidity, cardinality, and upper and lower bound constraints to obtain a more realistic model. Furthermore, to solve the proposed model efficiently, an improved multiobjective bat algorithm termed IMBA is designed, in which three new strategies, i.e., the global best solution selection strategy, candidate solution generation strategy, and competitive learning strategy, are proposed to increase the convergence speed and improve the solution quality. Finally, comparative experiments are presented to show the applicability and superiority of the proposed approaches from two aspects. First, the designed IMBA is compared with seven typical algorithms, i.e., multiobjective particle swarm optimization, multiobjective artificial bee colony, multiobjective firefly algorithm, multiobjective differential evolution, multiobjective bat, the non-dominated sorting genetic algorithm (NSGA-II) and strength pareto evolutionary algorithm 2 (SPEA2), on a number of benchmark test problems. Second, the applicability of the proposed model to practical applications of portfolio selection is given under different circumstances. [ABSTRACT FROM AUTHOR]

Multi-objective evolutionary algorithms (MOEAs) have been successfully employed to solve many scientific and engineering problems. However, many algorithms perform ill in maintaining diversity and convergence simultaneously. In this paper, we devised a novel operator selection framework based on two collaborative indicators, generational distance (GD) and maximum spread (MS) to improve the diversity while maintaining a good convergence. By calculating the variation of GDs and MSs over the past 7 iterations, an instruction is conveyed to select a proper operator to execute next 7 iterations. This process is repeated until it reaches the maximum iteration. Two operators are embedded in this algorithm which are differential evolution operator (DE/rand/1) and our proposed crow search operator which is deemed to be efficient in explorating the search space. MOEA/D is utilized as the basis framework of our proposed algorithm. Experiments indicate that our proposed algorithm is valid and outperforms other famous algorithms in terms of diversity and convergence. In the end, a particular aeroengine maintenance scheduling problem is solved by our proposed algorithm. [ABSTRACT FROM AUTHOR]

In this study, an energy efficiency study has been carried out through the moment values of a quadrotor applied in the position control with the differential evolution algorithm (DE), which is under the evolutionary algorithms among meta-heuristic algorithms particle swarm optimization (PSO) which is among swarm-based algorithms and gravity search algorithm (GSA) among physics-based algorithms and charged system search (CSS) algorithm, which are all well-known in the literature. The efficient use of energy in electrically powered flying mechanisms is important in terms of completing its task. The aim of this study is to obtain proportional–integral–derivative (PID) coefficients that minimize the energy consumption caused by quadrotor moments. First of all, 12 PID coefficients calculated with traditional Ziegler Nicholes, and trying-error methods for the control of the quadrotor have been trained with DE, PSO, GSA and CSS algorithms and their cost values have been found for this problem. In the study, optimum PID coefficients have been found separately with each algorithm and torque data giving energy efficiency have been obtained by applying them to the state equations. Although the cost minimization convergence value obtained from DE does not look good compared to other algorithms, it has been observed that the moment values of the obtained PID coefficients in the control program are lower. In the study, it has been shown that the PID coefficients obtained from DE reach the target with approximately less energy than the maximum-moment value of the PSO, which provides the closest moment value. It can be thought that this value contributes to energy consumption in each orbital movement of the quadrotor. The simulation results show that the coefficients obtained from DE provide better energy efficiency and are superior to other algorithms compared in terms of energy efficiency. • PID coefficients for quadrotor control are optimized with DE,PSO,CSS,GSA algorithms • The torque values to be applied to each motor were adjusted with these coefficients • The total force applied with DEPID in the z direction is smaller than others • DEPID consumes less energy than the other algorithms in the paper [ABSTRACT FROM AUTHOR]

In this study, an energy efficiency study has been carried out through the moment values of a quadrotor applied in the position control with the differential evolution algorithm (DE), which is under the evolutionary algorithms among meta-heuristic algorithms particle swarm optimization (PSO) which is among swarm-based algorithms and gravity search algorithm (GSA) among physics-based algorithms and charged system search (CSS) algorithm, which are all well-known in the literature. The efficient use of energy in electrically powered flying mechanisms is important in terms of completing its task. The aim of this study is to obtain proportional–integral–derivative (PID) coefficients that minimize the energy consumption caused by quadrotor moments. First of all, 12 PID coefficients calculated with traditional Ziegler Nicholes, and trying-error methods for the control of the quadrotor have been trained with DE, PSO, GSA and CSS algorithms and their cost values have been found for this problem. In the study, optimum PID coefficients have been found separately with each algorithm and torque data giving energy efficiency have been obtained by applying them to the state equations. Although the cost minimization convergence value obtained from DE does not look good compared to other algorithms, it has been observed that the moment values of the obtained PID coefficients in the control program are lower. In the study, it has been shown that the PID coefficients obtained from DE reach the target with approximately less energy than the maximum-moment value of the PSO, which provides the closest moment value. It can be thought that this value contributes to energy consumption in each orbital movement of the quadrotor. The simulation results show that the coefficients obtained from DE provide better energy efficiency and are superior to other algorithms compared in terms of energy efficiency. • PID coefficients for quadrotor control are optimized with DE,PSO,CSS,GSA algorithms • The torque values to be applied to each motor were adjusted with these coefficients • The total force applied with DEPID in the z direction is smaller than others • DEPID consumes less energy than the other algorithms in the paper [ABSTRACT FROM AUTHOR]

Differential evolution with a multi-population based ensemble of mutation strategies (MPEDE) has been considered among the most efficient Evolutionary Algorithms for global optimization. Our research results reveal that the performance of MPEDE may be improved by adding an information sharing mechanism and modifying the grouping mechanism. In MPEDE, the entire population is divided into four subpopulations, and most computing resources are allocated to the best strategy, but a better strategy has the same computing resources as the worst strategy. In order to rationally distribute computational resources, a differential evolution variant with multi-population cooperation and multi-strategy integration (MPMSDE) is proposed in this paper. MPMSDE develops a new grouping method instead of the grouping method in MPEDE, and the new grouping method utilizes the ranking of strategies to assign computational resources to different strategies. Also, an information sharing mechanism is introduced in the largest sub-population to avoid falling into local optimum. In MPMSDE, a new mutation strategy, "DE/pbad-to-pbest-to-gbest/1" , is used to replace the mutation strategy "DE/rand/1" in MPEDE. The new strategy not only uses personal history optimal solution and the worst solution but also uses the global best solution to update individuals. The new strategy can not only balance exploration and exploitation but also can accelerate the convergence of the algorithm. The performance of MPMSDE is compared with MPEDE and other state-of-the-art evolutionary algorithms on CEC2005 and CEC2014 benchmark functions. The experimental results show that the performance of the MPMSDE algorithm is very competitive in calculation accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

Multi-objective differential evolution (MODE) algorithm has been widely used in solving multi-objective optimization problems. In this paper, a hybridization technique is proposed to improve the performance of MODE algorithm in terms of speed and convergence. The proposed hybrid MODE-dynamic-random local search (HMODE-DLS) algorithm combines MODE and dynamic-random local search (DLS) algorithm. To evaluate the proposed algorithm and validate its performance, benchmark test problems (both constrained and non-constrained) are considered to be solved using MODE and the proposed HMODE-DLS algorithms. To compare between the two algorithms, five performance metrices are calculated, which are convergence, spread, generational distance, spacing and hypervolume ratio. Mean and standard deviation values for the performance metrics are reported, and the best in each category is highlighted. The Conv metric results of the new hybrid MODE are compared with other reported ones. Additionally, the effect of local search probability is studied for selected problems. In general, HMODE-DLS performance outshines, in terms of convergence and robustness, compared with other tested algorithms. HMODE-DLS is, generally, faster, and its results are of improved quality compared to MODE algorithm. [ABSTRACT FROM AUTHOR]

The efficiency and effectiveness of differential evolution (DE) greatly depend on the mutation operator due to the principle that different mutation operators are beneficial to different evolutionary states. However, it is not easy to automatically and effectively identify the evolutionary state. In this paper, we propose an evolutionary state estimation method (ESE) based on the correlation coefficient between the population's distributions in objective space (Δf) and solution space (Δx). To be specific, Δf consists of the distances between each individual and the current best individual based on their objective function values, while Δx includes the Euclidean distances between each individual and the current best individual based on their positions in the search space. Based on the correlation coefficient between Δx and Δf, the entire evolutionary process is classified into three kinds of state. At each generation, the evolutionary state is firstly determined according to the correlation coefficient, subsequently adaptively choosing a mutation operator from the corresponding candidate operator pool for each individual to generate its mutation vector. Moreover, a two-level selection mechanism (TLSM) is presented to get away from stagnation. The algorithm combines DE with ESE and TLSM (DEET for short) is proposed. Experimental results on twenty frequently used benchmark functions and the CEC2017 test problems show that DEET exhibits very competitive performance compared with other state-of-the-art DE variants. [ABSTRACT FROM AUTHOR]

A significant number of search and optimisation techniques whose principles seek inspiration from nature and biology phenomena have been proposed in the last decades. These methods have been successfully applied to solve a wide range of engineering problems. This is also the case of greenhouse environment control, which has been incorporating this type of techniques into its design. This paper addresses evolutionary and bio-inspired methods in the context of greenhouse environment control. Algorithm principles for reference techniques are reviewed, namely: simulated annealing, genetic algorithm, differential evolution and particle swarm optimisation. The last three techniques are considered using single and multiple objective formulations. A review of these algorithms within greenhouse environment control applications is presented, considering single and multiple objective problems, as well as their current trends. [ABSTRACT FROM AUTHOR]

Optimization demands exist everywhere in the real world especially in science studies and engineering practices, and it is important that the method to deal with intricacy optimization problems should itself be relative simple. Particle Swarm Optimization (PSO) and Differential Evolution (DE) both are simple evolutionary algorithms (EAs) which are proposed for single-objective optimization and both of them have been proved to be efficient methods for optimizing applications, however, there are still some weakness existing within them. A innovative evolutionary method named QUasi-Affine TRansformation Evolutionary (QUATRE) algorithm which is derived from, also tackles some weaknesses of PSO and DE algorithm, and obtains better performance on commonly used test suites. The key characteristic of QUATRE is that an automatically generated matrix named evolution matrix M is implemented in evolutionary process, which is taken as an alternative of employing the crossover rate CR. Here in this paper, we present a novel QUATRE variant, named IS-QUATRE, which can explore the search area in a better way comparison with the previous method, and relatively good optimization ability can be obtained by our proposed IS-QUATRE algorithm under CEC2013 test suit. And the conducted experimental results validate that our proposed IS-QUATRE is competitive with some other famous PSO and DE variants. [ABSTRACT FROM AUTHOR]

• The integer-valued vector representing a candidate solution encodes all dataset features. • The feature subset size is determined by using an additional element in the vector. • Feature relevance is represented through its relative position in the vector. • A permutation-matrix-based mutation operator can be used to create new solutions. • A simple repair-based recombination operator is used to ensure feasible solution creation. This paper describes a permutational-based Differential Evolution algorithm implemented in a wrapper scheme to find a feature subset to be applied in the construction of a near-optimal classifier. In this approach, the relevance of a feature chosen to build a better classifier is represented through its relative position in an integer-valued vector, and by using a permutational-based mutation operator, it is possible to create new feasible candidate solutions only. Furthermore, to provide a controlled diversity rate in the population, a straightforward repair-based recombination operator is utilized to evolve a population of candidate solutions. Unlike the other approaches in the existing literature using integer-valued vectors and requiring a predefined subset size, in this approach, this size is determined by an additional element included in the encoding scheme, allowing to find an adequate feature subset size to each specific dataset. Experimental results show that this approach is an effective way to create more accurate classifiers as they are compared with those obtained by other similar approaches. [ABSTRACT FROM AUTHOR]

This paper proposes a subsystem-based structure evolution algorithm for stable IIR digital filter design. The method designs the IIR digital filter through optimizing the filter structure. A filter structure is defined as the connection of the subsystems. A subsystem is a 2-order IIR digital structure with uncertain parameters. Subsystems are randomly connected with the constraints of no feedback branches between subsystems. The subsystem's parameters and the connections between subsystems are optimized by evolutionary algorithms. An adaptive multiple-elites-guided composite differential evolution algorithm (AMECoDEs) is used to optimize this problem. Four classic types of filters, lowpass, highpass, bandpass and bandstop filters are designed. Five state-of-the-art evolutionary algorithms are compared. The simulation results show that AMECoDEs holds the first place on comprehensive performance and convergence rate. At the same time, the poles of filters all reside within the unit circle, which validates the stability of the IIR digital filters. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) is an efficient population-based search algorithm for solving numerical optimization problems. However, the performance of DE is very sensitive to the choice of mutation strategies and their associated control parameters. In this paper, we propose a self-adaptive multi-population differential evolution algorithm, called SAMDE. The population is randomly divided into three equally sized sub-populations, each with different mutation strategies. At the end of each generation, all sub-populations are updated independently and recombined. Each sub-population uses an adaptive mechanism for selecting how current generation control parameters are generated. An improved mutation strategy, "rand assemble/1", is proposed, its base vector is composed proportionally of three randomly selected individuals. The performance of SAMDE is evaluated on the suite of CEC 2005 benchmark functions. A comparative study is carried out with other state-of-the-art optimization techniques. The results show that SAMDE has a competitive performance compared to several other efficient DE variants. [ABSTRACT FROM AUTHOR]

The ubiquitous presence of smart phones and other hand-held computing devices has resulted in a growing feasibility to utilize them as computing resources. However, these mobile devices are constrained in battery and may not possess adequate capability for computationally intensive tasks. Cloud computing allows mobile devices to address their inherent challenges by making it possible to offload computation, completely or partially, to powerful cloud servers. This enables mobile devices to act as compute resources; though, it also results in cost of using cloud servers as well as communication cost involved in offloading. The paper models the computation offloading problem as an optimization problem and makes use of nature-inspired algorithms for deciding whether a task should be executed locally on a mobile device or offloaded to the cloud. The study was performed over four algorithms, namely Genetic Algorithm (GA), Differential Evolution (DE), Particle Swarm Optimization (PSO) and Shuffled Frog Leaping Algorithm (SFLA). Experimental analysis revealed that these algorithms outperform exhaustive search technique by providing a near optimal solution in a reasonable time even for large workflows. Results also establish that GA outperforms DE, PSO and SFLA by around 45%, 65% and 42%, respectively by reducing an application's overall execution cost. [ABSTRACT FROM AUTHOR]