Computer Engineering and Applications ›› 2017, Vol. 53 ›› Issue (22): 143-149.DOI: 10.3778/j.issn.1002-8331.1606-0383

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Non-dominated sorting cloud model algorithm for interval multi-objective optimization

CHEN Zhiwang1, HUANG Xingwang2, CHEN Zhixing3, ZHAO Zizheng2, HUANG Lifang4   

  1. 1.Key Lab of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao, Hebei 066000, China
    2.National Engineering Research Center for Equipment and Technology of Cold Strip Rolling, Yanshan University, Qinhuangdao, Hebei 066000, China
    3.Jiamusi Electricity Power Bureau, Jiamusi, Heilongjiang 154002, China
    4.Western Superconducting Technologies Co., Ltd., Xi’an 710018, China
  • Online:2017-11-15 Published:2017-11-29



  1. 1.燕山大学 河北省工业计算机控制工程重点实验室,河北 秦皇岛 066000
    2.燕山大学 国家冷轧板带装备及工业工程技术研究中心,河北 秦皇岛 066000
    3.佳木斯电业局,黑龙江 佳木斯 154002
    4.西部超导材料科技股份有限公司,西安 710018

Abstract: A kind of Non-dominated Sorting Cloud Model Algorithm(NSCMA) for solving interval multi-objective optimization is proposed, in which cloud model is used to improve the NSGA-II algorithm. Firstly, genetic operator such as crossover and mutation in conventional NSGA-II is replaced by normal cloud operator, and offspring cloud droplets are derived from random parent in initial cloud cluster. Secondly, generated cloud droplets are disposed and kept based on constraint conditions, so infeasible solution doesn’t be left in the next algorithm. Finally, the feasible solution is sorted by interval dominant relationship, and then the crowding distance of incomparable same order solution is calculated. The simulations results have verified the effectiveness of the designed algorithm.

Key words: multi-objective optimization, interval programming, constrained optimization problem, cloud model, NSGA-II

摘要: 针对区间多目标优化问题,利用云模型对NSGA-II算法进行改进,提出一种非支配排序云模型算法(NSCMA)。首先,从初始云团中随机选取一个云滴作为父代,通过正态云算子生成子代云滴,用来替代传统NSGA-II遗传操作中的交叉和变异;其次,用约束条件对生成的云滴进行筛选处理,避免不可行解进入下一步算法;最后,运用区间占优关系对满足约束条件的解进行占优排序,对无法比较的同序值解计算拥挤距离。仿真结果验证了所设计算法的有效性。

关键词: 多目标优化, 区间规划, 约束优化问题, 云模型, NSGA-II