Multi-objective integer programming: A general approach for generating all non-dominated solutions

Oezlen M., AZİZOĞLU M.

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, vol.199, no.1, pp.25-35, 2009 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 199 Issue: 1
  • Publication Date: 2009
  • Doi Number: 10.1016/j.ejor.2008.10.023
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.25-35
  • Keywords: Multiple objective programming, Integer programming, LINEAR-PROGRAMS, VECTORS


In this paper we develop a general approach to generate all non-dominated solutions of the multi-objective integer programming (MOIP) Problem. Our approach, which is based on the identification of objective efficiency ranges, is an improvement over classical epsilon-constraint method. Objective efficiency ranges are identified by solving simpler MOIP problems with fewer objectives. We first provide the classical epsilon-constraint method on the bi-objective integer programming problem for the sake of completeness and comment on its efficiency. Then present our method on tri-objective integer programming problem and then extend it to the general MOIP problem with k objectives. A numerical example considering tri-objective assignment problem is also provided. (C) 2008 Elsevier B.V. All rights reserved.