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On the selection of solutions for mutation in differential evolution

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Abstract

Differential evolution (DE) is a kind of evolutionary algorithms, which is suitable for solving complex optimization problems. Mutation is a crucial step in DE that generates new solutions from old ones. It was argued and has been commonly adopted in DE that the solutions selected for mutation should have mutually different indices. This restrained condition, however, has not been verified either theoretically or empirically yet. In this paper, we empirically investigate the selection of solutions for mutation in DE. From the observation of the extensive experiments, we suggest that the restrained condition could be relaxed for some classical DE versions as well as some advanced DE variants. Moreover, relaxing the restrained condition may also be useful in designing better future DE algorithms.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their very constructive and helpful suggestions. This work was supported in part by the National Basic Research Program (973 Program) of China (2011CB013104), in part by the Innovation-driven Plan in Central South University (2015CXS012 and 2015CX007), in part by the National Natural Science Foundation of China (Grant Nos. 61273314 and 61673397), in part by the EU Horizon 2020 Marie Skłodowska-Curie Individual Fellowships (Project ID: 661327), in part by the Hunan Provincial Natural Science Fund for Distinguished Young Scholars (2016JJ1018), in part by the Program for New Century Excellent Talents in University (NCET-13-0596), and in part by State Key Laboratory of Intelligent Control and Decision of Complex Systems, Beijing Institute of Technology.

Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, Changsha, 410083, China

    Yong Wang & Zhi-Zhong Liu

  2. School of Computer Science and Informatics, De Montfort University, Leicester, LE1 9BH, UK

    Yong Wang

  3. Institute of Information Security and Big Data, Central South University, Changsha, 410083, China

    Jianbin Li

  4. Department of Systems Engineering and Engineering Management, City University of Hong Kong, Hong Kong, China

    Han-Xiong Li

  5. State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha, 410083, China

    Han-Xiong Li

  6. School of Data and Computer Science, Sun Yat-sen University, Guangzhou, 510006, China

    Jiahai Wang

Authors
  1. Yong Wang
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  2. Zhi-Zhong Liu
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  3. Jianbin Li
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  4. Han-Xiong Li
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  5. Jiahai Wang
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Corresponding author

Correspondence to Yong Wang.

Additional information

Yong Wang received the BS degree in automation from theWuhan Institute of Technology, China in 2003, and the MS degree in pattern recognition and intelligent systems and the PhD degree in control science and engineering both from the Central South University (CSU), China in 2006 and 2011, respectively. He is currently an associate professor with the School of Information Science and Engineering, CSU. His current research interests include the theory, algorithm design, and application of computational intelligence. Dr. Wang was a recipient of the Hong Kong Scholar by the Mainland - Hong Kong Joint Postdoctoral Fellows Program, China in 2013, the Excellent Doctoral Dissertation by Hunan Province, China in 2013, the New Century Excellent Talents in University by the Ministry of Education, China in 2013, the 2015 IEEE Computational Intelligence Society Outstanding PhD Dissertation Award, the HunanProvincial Natural Science Fund for Distinguished Young Scholars, China in 2016, and EU Horizon 2020 Marie Sklodowska-Curie Fellowship, European Union in 2016. He is currently serving as an associate editor for the Swarm and Evolutionary Computation.

Zhi-Zhong Liu received the BS degree in automation from Central South University, China in 2013, where he is currently pursuing the PhD degree in control science and engineering. His current research interests include evolutionary computation, swarm intelligence, nonlinear equation systems, and multimodal optimization.

Jianbin Li is a professor with the Institute of Information Security and Big Data, Central South University, China. He received the BS degree from Tsinghua University, China. His research interests include network security and big data analysis.

Han-Xiong Li received the BE degree in aerospace engineering from the National University of Defense Technology, China in 1982, the ME degree in electrical engineering from Delft University of Technology, The Netherlands in 1991, and the PhD degree in electrical engineering from the University of Auckland, New Zealand in 1997. He is currently a professor with the Department of Systems Engineering and Engineering Management, the City University of Hong Kong, China. His current research interests include system intelligence and control, process design and control integration, and distributed parameter systems with applications to electronics packaging. Dr. Li was a recipient of the Distinguished Young Scholar (overseas) by the China National Science Foundation in 2004, the Chang Jiang Professorship by the Ministry of Education, China in 2006, and the National Professorship in China Thousand Talents Program in 2010. He serves as an associate editor of IEEE Transactions on Cybernetics and IEEE Transactions on Industrial Electronics (2009–2015). He is a fellow of the IEEE.

Jiahai Wang received the PhD degree from Toyama University, Japan in 2005. In 2005, he joined Sun Yat-sen University, China, where he is currently an associate professor with the School of Data and Computer Science. His current research interests include computational intelligence and its applications.

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Cite this article

Wang, Y., Liu, ZZ., Li, J. et al. On the selection of solutions for mutation in differential evolution. Front. Comput. Sci. 12, 297–315 (2018). https://doi.org/10.1007/s11704-016-5353-5

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  • DOI: https://doi.org/10.1007/s11704-016-5353-5

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