An approach for finding efficient points in multiobjective linear programming

This paper presents a complete procedure for solving Multiple Objective Linear Programming Problems. The approach generates the whole efficient set and all extreme efficient points. The algorithm is based on a new characterization of efficient face incident to a given extreme point and the connectedness property of the set of ideal tableaux associated to a degenerated point to handle degenerated problems. A numerical example is given to illustrate the proposed algorithm.

[1]  Joseph G. Ecker,et al.  Finding all efficient extreme points for multiple objective linear programs , 1978, Math. Program..

[2]  Masahiro Inuiguchi,et al.  A fuzzy satisficing method for large-scale multiobjective linear programming problems with block angular structure , 1996, Fuzzy Sets Syst..

[3]  Willem J. Selen,et al.  A simplified molp algorithm: The MOLP-S procedure , 1991, Comput. Oper. Res..

[4]  Paul Armand,et al.  Programmation lineaire multicritere et problemes de la degenerescence , 1991 .

[5]  J. Ecker,et al.  Generating all maximal efficient faces for multiple objective linear programs , 1980 .

[6]  T. Gal A general method for determining the set of all efficient solutions to a linear vectormaximum problem , 1977 .

[7]  P. Armand,et al.  Determination of the efficient set in multiobjective linear programming , 1991 .

[8]  Johan Philip,et al.  Algorithms for the vector maximization problem , 1972, Math. Program..

[9]  P. Yu,et al.  The set of all nondominated solutions in linear cases and a multicriteria simplex method , 1975 .

[10]  Serpil Sayin,et al.  An algorithm based on facial decomposition for finding the efficient set in multiple objective linear programming , 1996, Oper. Res. Lett..

[11]  Heinz Isermann,et al.  The Enumeration of the Set of All Efficient Solutions for a Linear Multiple Objective Program , 1977 .

[12]  Paul Armand,et al.  Finding all maximal efficient faces in multiobjective linear programming , 1993, Math. Program..

[13]  Hong Yan,et al.  Constructing efficient solutions structure of multiobjective linear programming , 2005 .