多目标决策下Pareto非支配解的快速构造方法  

Fast construction method of Pareto non-dominated solution for multi-objective decision-making problem

作　　者：王芳[1,2] 饶运清[1] 唐秋华[3] 何晓霞[4] 张利平[3] 

机构地区：[1]华中科技大学数字制造装备与技术国家重点实验室,武汉430074 [2]武汉科技大学管理学院,武汉430081 [3]武汉科技大学机械学院,武汉430081 [4]武汉科技大学理学院,武汉430081

出　　处：《系统工程理论与实践》2016年第2期454-463,共10页Systems Engineering-Theory & Practice

基　　金：湖北省教育厅青年项目(Q20151104);国家自然科学基金面上项目(51275366);国家自然科学基金青年项目(51305311);国家重点基础研究发展计划项目(973计划)(2014CB046705)~~

摘　　要：有效构造非支配解集可加快Pareto前沿的求解速度,提升多目标决策的质量和效率.在非支配解定义和性质分析基础上,推导出支配关系传递性引理,非支配解集构造定理及引理,并据此提出一种基于性质定理的非支配解集构造方法.基于所提方法,分析其循环次数和比较次数,推导出在最坏情况下能算出确定值的复杂度计算公式.最后证明该方法的正确性与完备性,分析最坏情形下其构造集的结构特征,并通过ZDT1~ZDT3测试函数进行检验.结果表明：所提方法比排除法和选举法的计算复杂度更低,构造速度更快.Formulating non-dominated solution set effectively can speed up the solving process of the Pareto front,and can improve the quality and efficiency of multi-objective decision-making.Therefore,based on the definition and feature of the non-dominated solutions,the lemma of dominations relation transitivity,the theorems and lemma of non-dominated solution set construction are deduced.Depending upon the proposed theorems and lemmas,a novel non-dominated solution set construction method is first proposed.Then the frequency of the comparison and the number of iteration in the new method are counted,and a novel formula is put forward to calculate the deterministic value of computational complexity in the worst case.Finally,the correctness and completeness of the new method are proved in theory,and the structural features of the construction set at the maximum degree of complexity are given,what’s more,the performance test of the new method is carried out through the ZDT1 ~ ZDT3 test functions.The results show that the new method is lower in computational complexity and faster in construction speed than the exclusions method and electoral law method.

关 键 词：多目标决策 Pareto非支配解 构造方法 复杂度 

分 类 号：N945.25[自然科学总论—系统科学]