Title: Generating efficient faces for multiobjective linear programming problems

Authors: Hela Masri; Saoussen Krichen; Adel Guitouni

Addresses: Larodec Laboratory, Institut Supérieur de Gestion de Tunis, 2000 Bardo, Tunisia ' Faculty of Law, Economics and Management, University of Jendouba, Avenue de l'UMA, 8189 Jendouba, Tunisia, and Larodec Laboratory, Institut Superieur de Gestion de Tunis, 2000 Bardo, Tunisia ' Command and Control Decision Support System Section, Defence Research and Development Canada (DRDC) Valcartier, 2459 Pie-XI North, Quebec (Quebec), G3J 1X5, Canada; Peter B. Gustavson School of Business, University of Victoria, Victoria, British-Columbia, Canada

Abstract: In this paper, we propose a new method for generating the efficient solutions in multiobjective linear programming (MOLP) problems. An exact tree-based method is proposed to generate all the pareto set by adopting a bottom-up approach. This method is suitable for small- and medium-sized problems. For large-scaled problems, we develop a tabu search-based heuristic combined with a dichotomic exploration of the efficient set. This method generates potentially maximal efficient faces. The two methods are empirically compared. Experimental results show that the tree-based method ensures finding the entire efficient set in a reasonable central processing unit (CPU) time. Furthermore, the dichotomic TS method has a significant advantage for solving large-scaled instances of MOLP problems. It features good compromise between the central processing unit (CPU) time and the size of the generated efficient set.

Keywords: MOPL; multiobjective linear programming; efficient faces; efficient sets; decision space; tabu search.

DOI: 10.1504/IJOR.2012.048288

International Journal of Operational Research, 2012 Vol.15 No.1, pp.1 - 15

Published online: 11 Jan 2015 *

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