基于P_(EV)准则的I-UMOP问题求解方法  

New method for I-UMOP problem based on P_(EV) principle

作　　者：孟祥飞[1] 王瑛[1] 亓尧 吕茂隆 李超[1] 

机构地区：[1]空军工程大学装备管理与安全工程学院,陕西西安710051

出　　处：《系统工程与电子技术》2018年第2期338-345,共8页Systems Engineering and Electronics

基　　金：国家自然科学基金(71601183)资助课题

摘　　要：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。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 frame- work of the approach is proposed and the concepts like Pareto efficient solution and expected-variance value prin- ciple are defined using the order relationship between different uncertain variables. Secondly, the original uncer- tain 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 pro- gramming 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 effi- cient 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.

关 键 词：不确定理论 多目标规划 期望方差准则 遗传-粒子群算法 二进制狼群算法 

分 类 号：O221.6[理学—运筹学与控制论]