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ε Constrained differential evolution using halfspace partition for optimization problems

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Abstract

There are many efficient and effective constraint-handling mechanisms for constrained optimization problems. However, most of them evaluate all the individuals, including the worse individuals, which waste a lot of fitness evaluations. In this paper, halfspace partition mechanism based on constraint violation values is proposed. Since constraint violation information of individuals in current generation are already known, the positive side of tangent line of one point as positive halfspace is defined. A point is treated as potential point if it locates in the intersect region of two positive halfspaces. Hence, the region includes all these points has greater possibility to obtain smaller constraint violation. Only when the offspring locates in this area, the actual objective function value and constraint violation will be calculated. The estimated worse individuals will be omitted without calculating actual constraint violation and fitness function value. Four engineering optimization and a case study with the grinding optimization process are studied. The experimental results verify the effectiveness of the proposed mechanism.

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Acknowledgement

This research work is supported by financial support from the National Natural Science Foundation for Distinguished Young Scholars of China under Grant No. 51825502, National Natural Science of China under Grant Nos. 71371170, 71871203, L1924063. Foundation of Zhejiang Education Committee under Grant No. Y201840056. Zhejiang Natural Science Foundation of China under Grant No. LY18G010017.

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Authors and Affiliations

  1. School of Mechanical Engineering, Zhejiang University of Technology, Hangzhou, 310041, People’s Republic of China

    Wenchao Yi, Zhi Pei, Jiansha Lu & Yong Chen

  2. The State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, People’s Republic of China

    Liang Gao

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  1. Wenchao Yi
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Yi, W., Gao, L., Pei, Z. et al. ε Constrained differential evolution using halfspace partition for optimization problems. J Intell Manuf 32, 157–178 (2021). https://doi.org/10.1007/s10845-020-01565-2

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