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Diversity-maintained differential evolution embedded with gradient-based local search

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Abstract

Differential evolution (DE) has been used to solve real-parameter optimization problems with nonlinear and multimodal functions for more than a decade of years. However, it is pointed out that this classical DE harbors restricted efficiency and limited local search ability. Inspired by that gradient-based algorithms have powerful local search ability, we propose a new algorithm, which is diversity-maintained DE based on gradient local search (namely, DMGBDE), by incorporating approximate gradient-based algorithms into the DE search while maintaining the diversity of the population. The primary novelties of the proposed DMGBDE are the following: (1) the gradient-based algorithm is embedded into DE in a different manner and (2) a diversity-maintained mutation is introduced to slow down the learning procedure from the searched best individual. We conduct numerical experiments with a number of benchmark problems to measure the performance of the proposed DMGBDE. Simulation results show that the proposed DMGBDE outperforms classical DE and variant without gradient local search or diversity-based mutation. Moreover, comparison with some other recently reported approaches indicates that our proposed DMGBDE is rather competitive.

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Acknowledgments

The authors thank the anonymous reviewers for their helpful comments and suggestions, and also would like to thank Dr. Ponnuthurai Nagaratnam Suganthan in Nanyang Technological University, Singapore, Dr. Yong Wang in Central South University, China, Dr. Janez Brest in University of Maribor, Slovenia, and Dr. Rammohan Mallipeddi in Nanyang Technological University, Singapore, for providing the source codes of their algorithms SaDE, CoDE, jDE, and EPSDE, respectively, on the websites. This work was supported by the Chinese National Natural Science Foundation under Grant 61173060 and the Major Research Plan of National Natural Science Foundation of China under Grant 91230118.

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  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Weicheng Xie, Wei Yu & Xiufen Zou

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  1. Weicheng Xie
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  2. Wei Yu
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  3. Xiufen Zou
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Correspondence to Xiufen Zou.

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Communicated by F. Herrera.

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Xie, W., Yu, W. & Zou, X. Diversity-maintained differential evolution embedded with gradient-based local search. Soft Comput 17, 1511–1535 (2013). https://doi.org/10.1007/s00500-012-0962-x

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