Divergence Behaviour of the Successive Geometric Mean Method of Pairwise Comparison Matrix Generation for a Multiple Stage, Multiple Objective Optimization Problem

作     者：Tarun, Prashant K. Chen, Victoria C. P. Corley, H. W. 

作者机构：Missouri Western State Univ Steven L Craig Sch Business St Joseph MO 64507 USA Univ Texas Arlington Ind & Mfg Syst Engn Arlington TX 76019 USA 

出 版 物：《JOURNAL OF MULTI-CRITERIA DECISION ANALYSIS》 (多标准决策分析杂志)

年 卷 期：2014年第21卷第3-4期

页      面：197-208页

学科分类：0402[教育学-心理学(可授教育学、理学学位）] 04[教育学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 

基　　金：Dallas-Fort Worth International Airport 

主　　题：divergence pairwise comparison matrix analytic hierarchy process multiple stage multiple objective successive geometric mean three-phase methodology stochastic dynamic programming 

摘      要：This paper focuses on the divergence behaviour of the successive geometric mean (SGM) method used to generate pairwise comparison matrices while solving a multiple stage, multiple objective (MSMO) optimization problem. The SGM method can be used in the matrix generation phase of our three-phase methodology to obtain pairwise comparison matrix at each stage of an MSMO optimization problem, which can be subsequently used to obtain the weight vector at the corresponding stage. The weight vectors across the stages can be used to convert an MSMO problem into a multiple stage, single objective (MSSO) problem, which can be solved using dynamic programming-based approaches. To obtain a practical set of non-dominated solutions (also referred to as Pareto optimal solutions) to the MSMO optimization problem, it is important to use a solution approach that has the potential to allow for a better exploration of the Pareto optimal solution space. To accomplish a more exhaustive exploration of the Pareto optimal solution space, the weight vectors that are used to scalarize the MSMO optimization problem into its corresponding MSSO optimization problem should vary across the stages. Distinct weight vectors across the stages are tied directly with distinct pairwise comparison matrices across the stages. A pairwise comparison matrix generation method is said to diverge if it can generate distinct pairwise comparison matrices across the stages of an MSMO optimization problem. In this paper, we demonstrate the SGM method s divergence behaviour when the three-phase methodology is used in conjunction with an augmented high-dimensional, continuous-state stochastic dynamic programming method to solve a large-scale MSMO optimization problem. Copyright (C) 2013 John Wiley & Sons, Ltd.