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

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

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

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

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

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

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]

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