基于PEV准则的D-UMOP求解方法及应用研究  

Solution method for D-UMOP based on PEV principle and its application

作　　者：孟祥飞[1] 王瑛[1] 姚頔 李超[1] Meng Xiangfei;Wang Ying;Yao Di;Li Chao(Equipment Management and Safety Engineering College,Air Force Engineering University,Xi＇an 710051,China;National Airspace Management Center of China,Beijing 100094,China)

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 [2]国家空域管理中心,北京100094

出　　处：《华中科技大学学报（自然科学版）》2018年第9期52-58,共7页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(71571190,71601183)

摘　　要：针对目标函数相关的不确定多目标规划问题提出了一种在期望-方差准则下的求解方法.首先,给出了不确定多目标规划的等价模型,基于期望-方差准则和帕累托有效解的定义,利用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,再利用该准则将不确定单目标规划问题转化为确定型单目标规划问题;其次,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,结合不确定多目标规划模型在航路网络容量评估中的应用,设计了一个具有代表性的数值算例以说明本文方法的有效性,考虑算例的特点,用遗传-粒子群算法进行了求解.A novel approach under the expected-variance value principle was proposed for dependent-uncertain multi-objective programming problem.Firstly,an equivalent model for uncertain multi-objective programming was proposed and according to the concepts of Pareto efficient solution and expected-variance value principle the original uncertain multi-objective problem was converted into an uncertain single objective programming problem by linear weighted method or ideal point method,and then it was transformed into a deterministic single objective programming problem under the expected-variance value principle.Secondly,four lemmas and two theorems were proved to illustrate that the optimal solution of the deterministic single objective programming problem was a Pareto efficient solution of the original uncertain problem.Finally,a numerical example based on air route network capacity evaluation was presented to illustrate the effectiveness of the proposed approach,and genetic-particle swarm optimization algorithm was adopted to solve it.

关 键 词：不确定理论 多目标规划 期望-方差准则 等价模型 帕累托有效解 遗传-粒子群算法 相关的不确定多目标规划问题(D-UMOP) 

分 类 号：O221.6[理学—运筹学与控制论]