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求解约束高维多目标问题的分解约束支配NSGA-Ⅱ优化算法

顾清华1,2 莫明慧2 卢才武1 陈露2

(1.西安建筑科技大学资源工程学院, 西安 710055)
(2.西安建筑科技大学管理学院, 西安 710055)

【摘要】针对多目标进化算法处理约束高维多目标优化问题时出现解的分布性和收敛性差、易陷入局部最优解问题,采用Pareto支配、分解与约束支配融合的方法,提出一种基于分解约束支配NSGA-Ⅱ优化算法(DBCDP-NSGAⅡ).该算法在保留NSGA-Ⅱ中快速非支配排序的基础上,首先采用Pareto支配对种群进行支配排序;然后根据解的性质采用分解约束支配(DBCDP)惩罚等价解,保留稀疏区域的可行解和非可行解,提高种群的分布性、多样性和收敛性;最后采用个体到权重向量的垂直距离和拥挤度距离对临界值进行再排序,直到选出N个最优个体进入下一次迭代.以约束DTLZ问题中C-DTLZ1、C-DTLZ2、DTLZ8、DTLZ9测试函数为例,将所提出的算法与C-NSGAⅡ、C-NSGA-Ⅲ、C-MOEA/D和C-MOEA/DD进行对比分析.仿真结果表明, DBCDP-NSGA-Ⅱ所得最优解分布更加均匀,具有更好的全局收敛性.

【关键词】 约束高维多目标;Deb约束支配;MOEA/D;NSGA-Ⅱ;分布性;收敛性;

【DOI】

【基金资助】 国家自然科学基金项目(51774228,51404182); 陕西省自然科学基金项目(2017JM5043); 陕西省教育厅专项科研计划项目(17JK0425);

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;

【DOI】

【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

ISSN:1001-0920

CN: 21-1124/TP

Vol 35, No. 10, Pages 2466-2474

October 2020

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Article Outline

Abstract

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