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A new differential evolution algorithm for solving multimodal optimization problems with high dimensionality

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Abstract

Differential evolution (DE) is an efficient intelligent optimization algorithm which has been widely applied to real-world problems, however poor in solution quality and convergence performance for complex multimodal optimization problems. To tackle this problem, a new improving strategy for DE algorithm is presented, in which crossover operator, mutation operator and a new local variables adjustment strategy are integrated together to make the DE more efficient and effective. An improved dynamic crossover rate is adopted to manage the three operators, so to decrease the computational cost of DE. To investigate the performance of the proposed DE algorithm, some frequently referred mutation operators, i.e., DE/rand/1, DE/Best/1, DE/current-to-best/1, DE/Best/2, DE/rand/2, are employed, respectively, in proposed method for comparing with standard DE algorithm which also uses the same mutation operators as our method. Three state-of-the-art evolutionary algorithms (SaDE, CoDE and CMAES) and seven large-scale optimization algorithms on seven high-dimensional optimization problems of CEC2008 are compared with the proposed algorithm. We employ Wilcoxon Signed-Rank Test to further test the difference significance of performance between our algorithm and other compared algorithms. Experimental results demonstrate that the proposed algorithm is more effective in solution quality but with less CPU time (e.g., when dimensionality equals 1000, its mean optimal fitness is less than \(1\hbox {e}{-}9\) and the CPU time reduces by about 19.3% for function Schwefel 2.26), even with a very small population size, no matter which mutation operator is adopted.

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Acknowledgements

This work was supported by the Natural Science Foundation of China under Grants 61571341, 61201312, 91530113 and 11401357, Research Fund for the Doctoral Program of Higher Education of China (No. 2013 0203110017), the Fundamental Research Funds for the Central Universities of China (Nos. BDY171416 and JB140306), the Natural Science Foundation of Shaanxi Province in China (2015JM6275), the project of Youth Star in Science and Technology of Shaanxi Province (2016KJXX-95), the Scientific Research Program funded by Shaanxi Provincial Education Department (No. 16JK1157) and the Scientific Research Program funded by the Projects Program of Academician Workstation of Shaanxi University of Technology (No. fckt201509).

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Correspondence to Junying Zhang.

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The authors declare that they have no conflict of interests regarding the publication of this paper. Shouheng Tuo proposed the improved DE algorithm firstly, did all experiments and written the article; Junying Zhang puts forward many constructive ideas and revised the manuscript in detail; Xiguo Yuan and Longquan Yong give some good ideas for this work.

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Communicated by V. Loia.

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Tuo, S., Zhang, J., Yuan, X. et al. A new differential evolution algorithm for solving multimodal optimization problems with high dimensionality. Soft Comput 22, 4361–4388 (2018). https://doi.org/10.1007/s00500-017-2632-5

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