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A Novel Fitness Function Based on Decomposition for Multi-objective Optimization Problems

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Intelligent Computing Theories and Application (ICIC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9772))

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Abstract

Research on multi-objective optimization problems (MOPs) becomes one of the hottest topics of intelligent computation. The diversity of obtained solutions is of great importance for multi-objective evolutionary algorithms. To this end, in this paper, a novel fitness function based on decomposition is proposed to help solutions converge toward to the Pareto optimal solutions and maintain the diversity of solutions. First, the objective space is decomposed in a set of sub-regions based on a set of direction vectors and obtained solutions are classified. Then, for an obtained solution, the size of the class which contains the solution and an aggregation function value of the solution are used to calculate the fitness value of the solution. Aggregation function which decides whether the target space is divided evenly plays a very important role in the fitness function. A hyperellipsoidal function is designed for any-objective problems. The proposed algorithm has been compared with NSGAII and MOEA/D on various continuous test problems. Experimental results show that the proposed algorithm can find more accurate Pareto front with better diversity in most problems, and the hyperellipsoidal function works better than the weighted Tchebycheff.

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Acknowledgments

This work was supported by National Natural Science Foundation of China (no. 61502290), China Postdoctoral Science Foundation (no. 2015M582606), Industrial Research Project of Science and Technology in Shaanxi Province (no. 2015GY016), Fundamental Research Funds for the Central Universities (no. GK201603094) and Natural Science Basic Research Plan in Shaanxi Province of China (no. 2016JQ6045).

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Authors and Affiliations

  1. College of Computer Science, Shaanxi Normal University, Xi’an, 710062, China

    Cai Dai & Xiujuan Lei

  2. School of Science, Xi’an Technological University, Xi’an, Shaanxi, China

    Xiaofang Guo

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  1. Cai Dai
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  2. Xiujuan Lei
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  3. Xiaofang Guo
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Correspondence to Xiujuan Lei .

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Editors and Affiliations

  1. Tongji University , Shanghai, China

    De-Shuang Huang

  2. University of Ulsan , Ulsan, Korea (Republic of)

    Kang-Hyun Jo

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Dai, C., Lei, X., Guo, X. (2016). A Novel Fitness Function Based on Decomposition for Multi-objective Optimization Problems. In: Huang, DS., Jo, KH. (eds) Intelligent Computing Theories and Application. ICIC 2016. Lecture Notes in Computer Science(), vol 9772. Springer, Cham. https://doi.org/10.1007/978-3-319-42294-7_2

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  • DOI: https://doi.org/10.1007/978-3-319-42294-7_2

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