Decomposition-based constrained dominance principle NSGA-Ⅱ for constrained many-objective optimization problems

GU Qing-hua1,2 MO Ming-hui2 LU Cai-wu1 CHEN Lu2

(1.School of Resources Engineering, Xi’an University of Architecture and Technology, Xi’an, Shaanxi Province, China 710055)
(2.School of Management, Xi’an University of Architecture and Technology, Xi’an, Shaanxi Province, China 710055)

【Abstract】The distribution and convergence of solutions are poor when constrained many-objective optimization problems are solved with many-objective evolutionary algorithm, which tends to fall into local optimal solutions. We propose a decomposition-based constrained dominance principle NSGA-II (DBCDP–NSGA-II) based on the fusion of Pareto dominance, decomposition, and constraint dominance. In the study, based on retaining the fast non-dominant ranking in NSGA-II, Pareto dominance is employed firstly to dominate the population. Then according to the nature of the solution, the DBCDP is adopted to punish the equivalent solutions. The feasible and infeasible solutions in sparse regions are preserved to improve the distribution, diversity, and convergence of the population. Finally, the critical values are reordered by the vertical distance and the crowding distance from the individual to the weight vector until N optimal individuals are selected for the next iteration. With constrained DTLZ taken as an example, the algorithm is compared with C–NSGA-II, C–MOEA/D, C–MOEA/DD, and C–NSGA-Ⅲ. The results show that it has a more uniform distribution and better global convergence than the other four algorithms.

【Keywords】 constrained many-objective optimization; Deb constrained dominance; MOEA/D; NSGA-II; distribution; convergence;


【Funds】 National Natural Science Foundation of China (51774228, 51404182) Natural Science Foundation of Shaanxi Province (2017JM5043) Special Scientific Research Project of Shaanxi Provincial Department of Education (17JK0425)

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This Article


CN: 21-1124/TP

Vol 35, No. 10, Pages 2466-2474

October 2020


Article Outline


  • 0 Introduction
  • 1 Basic definitions
  • 2 DBCDP–NSGA-II algorithm
  • 3 Experimental simulation and analysis
  • 4 Conclusions
  • References