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Many-objective optimization based on information separation and neighbor punishment selection

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Abstract

Many-objective optimization refers to optimizing a multi-objective optimization problem (MOP) where the number of objectives is more than 3. Most classical evolutionary multi-objective optimization (EMO) algorithms use the Pareto dominance relation to guide the search, which usually perform poorly in the many-objective optimization scenario. This paper proposes an EMO algorithm based on information separation and neighbor punishment selection (ISNPS) to deal with many-objective optimization problems. ISNPS separates individual’s behavior in the population into convergence information and distribution information by rotating the original coordinates in the objective space. Specifically, the proposed algorithm employs one coordinate to reflect individual’s convergence and the remaining \(m-1\) coordinates to reflect individual’s distribution, where m is the number of objectives in a given MOP. In addition, a neighborhood punishment strategy is developed to prevent individuals from being crowded. From a series of experiments on 42 test instances with 3–10 objectives, ISNPS has been found to be very competitive against six representative algorithms in the EMO area.

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Notes

  1. Here the binary tournament selection (Miller and Goldberg 1995) is used as the mating selection.

  2. For MOEA/D, we adopt the original C++ code, which can be obtained at http://dces.essex.ac.uk/staff/zhang/webofmoead.htm.

  3. For NSGA-III, the C++ implemention (version 1.1) from professor Chiang is used in our study, which can be downloaded at web.ntnu.edu.tw/ tcchiang/publications/nsga3cpp/nsga3cpp.htm.

  4. For \(\epsilon \)-MOEA, we adopt the C implemention from KanGAL, which can be downloaded at www.iitk.ac.in/kangal/index.shtml.

  5. For MSOPS, the original MATLAB code is adopted, which can be found at .

  6. For IBEA, the Java implementation in jMetal (Durillo et al. 2010; Durillo and Nebro 2011) project (version 4.5) is utilized, which can be downloaded at .

  7. As suggested by Gómez and Coello Coello (2013), the Monte Carlo simulation is utilized to accelerate the calculation of hypervolume contribution of SMS-EMOA.

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Acknowledgments

The authors wish to thank the support of the National Natural Science Foundation of China (Grant Nos. 61379062, 61372049, 61403326), the Science Research Project of the Education Office of Hunan Province (Grant Nos. 12A135, 12C0378), the Hunan Province Natural Science Foundation (Grant Nos. 14JJ2072, 13JJ8006), the Science and Technology Project of Hunan Province (Grant No. 2014GK3027), the Construct Program of the Key Discipline in Hunan Province, and the Hunan Provincial Innovation Foundation For Postgraduate (Grant No. CX2013A011).

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, China

    Ruimin Shen

  2. Department of Xiangtan University, Institute of Information Engineering, Xiangtan, Hunan, China

    Jinhua Zheng, Miqing Li & Juan Zou

  3. Key Laboratory of Intelligent Computing and Information Processing, (Xiangtan University) Ministry of Education, Xiangtan, Hunan, China

    Jinhua Zheng

  4. Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom

    Miqing Li

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  1. Ruimin Shen
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Correspondence to Jinhua Zheng.

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Shen, R., Zheng, J., Li, M. et al. Many-objective optimization based on information separation and neighbor punishment selection. Soft Comput 21, 1109–1128 (2017). https://doi.org/10.1007/s00500-015-1842-y

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