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

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  • Özlen, Melih
  • Azizoglu, Meral

Abstract

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.

Suggested Citation

  • Özlen, Melih & Azizoglu, Meral, 2009. "Multi-objective integer programming: A general approach for generating all non-dominated solutions," European Journal of Operational Research, Elsevier, vol. 199(1), pages 25-35, November.
    • Handle: RePEc:eee:ejores:v:199:y:2009:i:1:p:25-35
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    References listed on IDEAS

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    1. Laumanns, Marco & Thiele, Lothar & Zitzler, Eckart, 2006. "An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method," European Journal of Operational Research, Elsevier, vol. 169(3), pages 932-942, March.
    2. Matthias Ehrgott, 2006. "A discussion of scalarization techniques for multiple objective integer programming," Annals of Operations Research, Springer, vol. 147(1), pages 343-360, October.
    3. Sylva, John & Crema, Alejandro, 2007. "A method for finding well-dispersed subsets of non-dominated vectors for multiple objective mixed integer linear programs," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1011-1027, August.
    4. Matthias Ehrgott & Xavier Gandibleux, 2004. "Approximative solution methods for multiobjective combinatorial optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 1-63, June.
    5. Klein, Dieter & Hannan, Edward, 1982. "An algorithm for the multiple objective integer linear programming problem," European Journal of Operational Research, Elsevier, vol. 9(4), pages 378-385, April.
    6. Sylva, John & Crema, Alejandro, 2004. "A method for finding the set of non-dominated vectors for multiple objective integer linear programs," European Journal of Operational Research, Elsevier, vol. 158(1), pages 46-55, October.
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