Abstract
Multi-objective evolutionary algorithm based on decomposition (MOEA/D) has been proved competitive in tackling complex multi-objective optimization problems. However, the performance of MOEA/D is very sensitive to its parameter settings. Differential evolutionary (DE) operator is the most widely used operator in MOEA/D while generating new solutions and the parameters of DE (scaling factor F and crossover rate CR) could influence the performance of MOEA/D significantly. In this paper, a distance-dependent parameter adaption mechanism for MOEA/D (MOEA/D-DPA) is proposed to adapt the DE parameters. Similarity information of the DE parents is considered in MOEA/D-DPA, and this is expected to benefit the balance between exploration and exploitation. In the proposed algorithm, the distance space, which is defined based on the distance between two subproblems in MOEA/D, is firstly divided into several levels. Then the successful parameters (Fs and CRs) that belong to the same level of distance are further used to generate new parameters for that level of distance adaptively. Besides, the neighborhood size for each subproblem is also sampled from a specific distance level with a probability. Five adaptive MOEA/Ds proposed recently are adopted as a comparison. The algorithms in comparison are tested on nine WFG test problems and ten unconstrained test problems proposed in CEC-2009 Special Session and Competition. Experimental results indicate that MOEA/D-DPA is competitive when compared with five adaptive MOEA/Ds, especially on the WFG test suite.
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Notes
ENS-MOEA/D is implemented by our own and the source code of the other four algorithms is obtained from its original authors.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China under Grant Nos. 61571346, 61305041 and 61305040. The authors gratefully acknowledge the kind help of Xin Qiu and Qiuzhen Lin for providing the source code. The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.
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Communicated by A. Di Nola.
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Ning, W., Guo, B., Yan, Y. et al. Distance-dependent parameter adaption for multi-objective evolutionary algorithm based on decomposition. Soft Comput 22, 6845–6859 (2018). https://doi.org/10.1007/s00500-017-2980-1
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DOI: https://doi.org/10.1007/s00500-017-2980-1