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Optimising a nonlinear utility function in multi-objective integer programming

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Listed:
  • Melih Ozlen
  • Meral Azizoğlu
  • Benjamin Burton

Abstract

In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop a general optimisation algorithm for use with k objectives, and we illustrate our approach using a tri-objective integer programming problem. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Melih Ozlen & Meral Azizoğlu & Benjamin Burton, 2013. "Optimising a nonlinear utility function in multi-objective integer programming," Journal of Global Optimization, Springer, vol. 56(1), pages 93-102, May.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:1:p:93-102
    DOI: 10.1007/s10898-012-9921-4
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    References listed on IDEAS

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    3. Jorge, Jesús M., 2009. "An algorithm for optimizing a linear function over an integer efficient set," European Journal of Operational Research, Elsevier, vol. 195(1), pages 98-103, May.
    4. Lucie Galand & Patrice Perny & Olivier Spanjaard, 2010. "A Branch and Bound Algorithm for Choquet Optimization in Multicriteria Problems," Lecture Notes in Economics and Mathematical Systems, in: Matthias Ehrgott & Boris Naujoks & Theodor J. Stewart & Jyrki Wallenius (ed.), Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems, pages 355-365, Springer.
    5. 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.
    6. 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.
    7. 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.
    8. 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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