An improved epsilon constraint-handling method in MOEA/D for CMOPs with large infeasible regions


This paper proposes an improved epsilon constraint-handling mechanism and combines it with a decomposition-based multi-objective evolutionary algorithm (MOEA/D) to solve constrained multi-objective optimization problems (CMOPs). The proposed constrained multi-objective evolutionary algorithm (CMOEA) is named MOEA/D-IEpsilon. It adjusts the epsilon level dynamically according to the ratio of feasible to total solutions in the current population. In order to evaluate the performance of MOEA/D-IEpsilon, a new set of CMOPs with two and three objectives is designed, having large infeasible regions (relative to the feasible regions), and they are called LIR-CMOPs. Then, the 14 benchmarks, including LIR-CMOP1-14, are used to test MOEA/D-IEpsilon and four other decomposition-based CMOEAs, including MOEA/D-Epsilon, MOEA/D-SR, MOEA/D-CDP and CMOEA/D. The experimental results indicate that MOEA/D-IEpsilon is significantly better than the other four CMOEAs on all of the test instances, which shows that MOEA/D-IEpsilon is more suitable for solving CMOPs with large infeasible regions. Furthermore, a real-world problem, namely the robot gripper optimization problem, is used to test the five CMOEAs. The experimental results demonstrate that MOEA/D-IEpsilon also outperforms the other four CMOEAs on this problem.

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This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grants 61300159, 75661473241 and 61332002, by the Natural Science Foundation of Jiangsu Province of China under Grant SBK2018022017, by the Project of International as well as Hong Kong, Macao & Taiwan Science and Technology Cooperation Innovation Platform in Universities in Guangdong Province under Grant 2015KGJH2014, by China Postdoctoral Science Foundation under Grant 2015M571751, by the Science and Technology Planning Project of Guangdong Province of China under Grant 2013B011304002, by Educational Commission of Guangdong Province of China under Grant 2015KGJHZ014, by the Fundamental Research Funds for the Central Universities of China under Grant NZ2013306, by the Guangdong High-Level University Project “Green Technologies” for Marine Industries, by the Scientific Startup Research Foundation of Shantou University under Grant NTF12024 and by the State Key Lab of Digital Manufacturing Equipment & Technology under grant DMETKF2019020.

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Correspondence to Xinye Cai.

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Table 8 Objectives and constraints of LIR-CMOP1-14

In this section, the detailed definitions of LIR-CMOP1-14 are listed in Table 8. The source codes of MOEA/D-IEpsilon and LIR-CMOPs can be found in the Web site.Footnote 2

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Fan, Z., Li, W., Cai, X. et al. An improved epsilon constraint-handling method in MOEA/D for CMOPs with large infeasible regions. Soft Comput 23, 12491–12510 (2019).

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  • Constrained multi-objective evolutionary algorithms
  • Epsilon constraint handling
  • Constrained multi-objective optimization
  • Robot gripper optimization