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Dynamic reference vectors and biased crossover use for inverse model based evolutionary multi-objective optimization with irregular Pareto fronts

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Abstract

The recently developed inverse model based multi-objective evolutionary algorithm (IM-MOEA) has been shown to be an effective methodology for solving multi-objective optimization problems (MOPs) with regular Pareto fronts (PFs). Due to the limitations of uniformly distributed reference vectors and inverse model sampling, however, the IM-MOEA is challenged when solving MOPs with irregular PFs. To alleviate these limitations, both an external elitist archive and a biased crossover operator are integrated into the IM-MOEA. The primary role of the former is to dynamically adjust the reference vectors, which encourages the IM-MOEA to explore the sparse regions. The latter is used to improve the search efficiency of the IM-MOEA. By incorporating both features into the IM-MOEA, an enhanced IM-MOEA variant (E-IM-MOEA) is presented in this paper. Experimental studies were conducted on eighteen MOPs with irregular PFs to compare the E-IM-MOEA with six state-of-the-art multi-objective evolutionary algorithms. The experimental results show that the proposed approach has better overall performance.

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Notes

  1. If fi ≤ 0, we can use fi + M to replace it, where M is an appropriate positive number such that fi + M > 0.

  2. The Matlab codes can be found in http://bimk.ahu.edu.cn/index.php?s=/Index/Software/index.html

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Acknowledgments

The authors would like to thank Dr. R. Cheng, Dr. Y. Wang, Prof. Y. C. Jin, Prof. Q. F. Zhang, and Prof. H. L. Liu for selflessly providing the source codes of IM-MOEA, IRM-MEDA, RM-MEDA, MOEA/D-DE, and MOEA/D-M2M, respectively. This work is partly supported by the National Natural Science Foundation of China under Grant 61174101, Key Project of Shaanxi Key Research and Development Program under Grant 2018YFZDGY0084, Research Program of Shaanxi Modern Equipment Green Manufacturing Co-innovation Center under Grant 304-210891704, Distinctive Research Program of Xi’an University of Technology under Grant 2016TS023, and Research Program of Shaanxi Provincial Education Department under Grant 2017JS088.

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Authors and Affiliations

  1. The Department of Automation and Information Engineering, Xi’an University of Technology, Xi’an, 710048, China

    Yanyan Lin, Han Liu & Qiaoyong Jiang

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  1. Yanyan Lin
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  2. Han Liu
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Correspondence to Han Liu.

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Lin, Y., Liu, H. & Jiang, Q. Dynamic reference vectors and biased crossover use for inverse model based evolutionary multi-objective optimization with irregular Pareto fronts. Appl Intell 48, 3116–3142 (2018). https://doi.org/10.1007/s10489-017-1133-7

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