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Differential evolution algorithm with multiple mutation strategies based on roulette wheel selection

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Abstract

In this paper, we propose a differential evolution (DE) algorithm variant with a combination of multiple mutation strategies based on roulette wheel selection, which we call MMRDE. We first propose a new, reflection-based mutation operation inspired by the reflection operations in the Nelder–Mead method. We design an experiment to compare its performance with seven mutation strategies, and we prove its effectiveness at balancing exploration and exploitation of DE. Although our reflection-based mutation strategy can balance exploration and exploitation of DE, it is still prone to premature convergence or evolutionary stagnation when solving complex multimodal optimization problems. Therefore, we add two basic strategies to help maintain population diversity and increase the robustness. We use roulette wheel selection to arrange mutation strategies based on their success rates for each individual. MMRDE is tested with some improved DE variants based on 28 benchmark functions for real-parameter optimization that have been recommended by the Institute of Electrical and Electronics Engineers CEC2013 special session. Experimental results indicate that the proposed algorithm shows its effectiveness at cooperative work with multiple strategies. It can obtain a good balance between exploration and exploitation. The proposed algorithm can guide the search for a global optimal solution with quick convergence compared with other improved DE variants.

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Notes

  1. http://www.ntu.edu.sg/home/EPNSugan/index_files/CEC2013/CEC2013.htm

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Acknowledgments

We thank Miguel Leon (from the School of Innovation, Design and Engineering, Malardalen University) for his great help with this study. We greatly appreciate the reviewers for their thoughtful and encouraging comments on our manuscript, which we all think is helpful for improving the quality of our paper. This study was supported by program 2013KCT-15 of the Shanxi Provincial Key Innovative Research Team and the National Natural Science Foundation of China (51409206). We thank LetPub (www.letpub.com) for its linguistic assistance during the preparation of this manuscript.

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Authors and Affiliations

  1. State Key Laboratory of Eco-hydraulics in Northwest Arid Region of China (Xi’an University of Technology), Xi’an, 710048, China

    Wuwen Qian, Junrui Chai, Zengguang Xu & Ziying Zhang

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  1. Wuwen Qian
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  2. Junrui Chai
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  3. Zengguang Xu
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Correspondence to Wuwen Qian.

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Qian, W., Chai, J., Xu, Z. et al. Differential evolution algorithm with multiple mutation strategies based on roulette wheel selection. Appl Intell 48, 3612–3629 (2018). https://doi.org/10.1007/s10489-018-1153-y

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