基于PEV准则的I-UMOP问题求解方法

针对传统方法在求解不确定多目标规划问题过程中存在的不足,提出了该问题在新准则下的求解方法。首先,提出了求解方法的基本框架,并通过引入不确定变量之间的序关系定义了不确定多目标规划的帕累托有效解;其次,根据线性加权或理想点法将原问题转化为不确定单目标规划问题,再利用期望方差准则将不确定单目标规划问题转化为确定的单目标规划问题;再次,通过相关理论推导证明了在该准则下转化后的问题求得的最优解是原不确定问题的帕累托有效解;最后,设计了决策变量分别为连续型和离散型的数值算例对该方法的有效性加以说明,考虑算例的复杂度,分别采用遗传粒子群算法和二进制狼群算法进行了求解。

New method for I-UMOP problem based on PEV principle

Aiming at the deficiencies of traditional solution methods of independent-uncertain multi-objective programming problems, a novel solution approach under a new principle is proposed. Firstly, the basic framework of the approach is proposed and the concepts like Pareto efficient solution and expected-variance value principle are defined using the order relationship between different uncertain variables. Secondly, the original uncertain multi-objective problem is converted into an uncertain single objective programming problem by the linear weighted method or the ideal point method, and then it is transformed into a deterministic single objective programming problem under the expected-variance value principle. Thirdly, four lemmas and two theorems are proved to illustrate that the optimal solution of the deterministic single objective programming problem is an efficient solution of the original uncertain problem. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed approach, and the genetic-particle swarm optimization algorithm and the binary wolf pack algorithm are adopted to solve them respectively.