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Adaptive direction information in differential evolution for numerical optimization

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Abstract

Differential evolution (DE) is a powerful evolutionary algorithm (EA) for numerical optimization. It has been successfully used in various scientific and engineering fields. In most of the DE algorithms, the neighborhood and direction information are not fully and simultaneously exploited to guide the search. Most recently, to make full use of these information, a DE framework with neighborhood and direction information (NDi-DE) was proposed. It was experimentally demonstrated that NDi-DE was effective for most of the DE algorithms. However, the performance of NDi-DE heavily depends on the selection of direction information. To alleviate this drawback and improve the performance of NDi-DE, the adaptive operator selection (AOS) mechanism is introduced into NDi-DE to adaptively select the direction information for the specific DE mutation strategy. Therefore, a new DE framework, adaptive direction information based NDi-DE (aNDi-DE), is proposed in this study. With AOS, the good balance between exploration and exploitation of aNDi-DE can be dynamically achieved. In order to evaluate the effectiveness of aNDi-DE, the proposed framework is applied to the original DE algorithms, as well as several advanced DE variants. Experimental results show that aNDi-DE is able to adaptively select the most suitable type of direction information for the specific DE mutation strategy during the evolutionary process. The efficiency and robustness of aNDi-DE are also confirmed by comparing with NDi-DE.

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Notes

  1. It should be noted these parameters are set different from NDi-DE in Cai and Wang (2013). From the parameter study in Cai and Wang (2013), \(F/2\) is a good choice for all the four parameters. In order to make aNDi-DE simple and easy to use, all the parameters are set to \(F/2\) in this paper. The effectiveness of the parameter setting can be verified in the following sections.

  2. Due to the space limitation, all of the experimental results for the 150 different parameter combinations are not provided in this paper. The detailed results can be obtained from the first author.

  3. When applying NDi-DE to the original DE algorithms in Cai and Wang (2013), DE/rand/1, DE/rand/2, DE/current-to-rand/1, DE/best/1, DE/current-to-best/1 and DE/rand-to-best/1 are equipped with DC, DA, DC, DR, DR and DR, respectively.

  4. When applying NDi-DE to the advanced DE variants in Cai and Wang (2013), jDE, ODE, JADE and MDE_pBX are equipped with DC, DC, DR and DR, respectively.

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Acknowledgments

This work was supported in part by the National Natural Science Foundation of China (61305085, 61202468), the Natural Science Foundation of Fujian Province of China (2014J05074, 2014J01240), the Support Program for Innovative Team and Leading Talents of Huaqiao University (2014KJTD13) and the Fundamental Research Funds for the Central Universities (12BS216).

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Authors and Affiliations

  1. College of Computer Science and Technology, Huaqiao University, Xiamen, 361021, China

    Yiqiao Cai, Yonghong Chen, Tian Wang, Hui Tian & Wei Luo

  2. Department of Computer Science, Sun Yat-sen University, Guangzhou, 510006, China

    Jiahai Wang

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  1. Yiqiao Cai
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  2. Jiahai Wang
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  3. Yonghong Chen
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  4. Tian Wang
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  5. Hui Tian
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  6. Wei Luo
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Correspondence to Yiqiao Cai.

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Communicated by V. Loia.

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Cai, Y., Wang, J., Chen, Y. et al. Adaptive direction information in differential evolution for numerical optimization. Soft Comput 20, 465–494 (2016). https://doi.org/10.1007/s00500-014-1517-0

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