Piecewise w∞-equitable Efficiency in Multiobjective Programming  

作　　者：D.FOROUTANNIA A.MAHMODINEJAD 

机构地区：[1]Department of Mathematics,Vali-e-Asr University of Rafsanjan,Rafsanjan,Iran [2]Department of Mathematics,Sirjan University of Technology,Sirjan,Iran

出　　处：《Acta Mathematicae Applicatae Sinica》2017年第3期825-836,共12页应用数学学报（英文版）

摘　　要：In equitable multiobjective optimization all the objectives are uniformly optimized, but in some cases the decision maker believes that some of them should be uniformly optimized according to the importance of objectives. To solve this problem in this paper, the original problem is decomposed into a collection of smaller subproblems, according to the decision maker, and the subproblems are solved by the concept of wr- equitable efficiency, where w ∈ R＋ m is a weight vector. First some theoretical and practical aspects of Pwr- equitably efficient solutions are discussed and by using the concept of Pwr-equitable efficiency one model is presented to coordinate weakly wr-equitable efficient solutions of subproblems. Then the concept of Pw ∞- equitable is introduced to generate subsets of equitably efficient solutions, which aims to offer a limited number of representative solutions to the decision maker.In equitable multiobjective optimization all the objectives are uniformly optimized, but in some cases the decision maker believes that some of them should be uniformly optimized according to the importance of objectives. To solve this problem in this paper, the original problem is decomposed into a collection of smaller subproblems, according to the decision maker, and the subproblems are solved by the concept of wr- equitable efficiency, where w ∈ R＋ m is a weight vector. First some theoretical and practical aspects of Pwr- equitably efficient solutions are discussed and by using the concept of Pwr-equitable efficiency one model is presented to coordinate weakly wr-equitable efficient solutions of subproblems. Then the concept of Pw ∞- equitable is introduced to generate subsets of equitably efficient solutions, which aims to offer a limited number of representative solutions to the decision maker.

关 键 词：PARETO nondominated EQUITABILITY DECOMPOSITION COORDINATION multiobjective programming 

分 类 号：O221.6[理学—运筹学与控制论]