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Global maximization of UTA functions in multi-objective optimization

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  • Nguyen, Duy Van

Abstract

The UTAs (UTilité Additives) type methods for constructing nondecreasing additive utility functions were first proposed by Jacquet-Lagrèze and Siskos in 1982 for handling decision problems of multicriteria ranking. In this article, by UTA functions, we mean functions which are constructed by the UTA type methods. Our purpose is to propose an algorithm for globally maximizing UTA functions of a class of linear/convex multiple objective programming problems. The algorithm is established based on a branch and bound scheme, in which the branching procedure is performed by a so-called I-rectangular bisection in the objective (outcome) space, and the bounding procedure by some convex or linear programs. Preliminary computational experiments show that this algorithm can work well for the case where the number of objective functions in the multiple objective optimization problem under consideration is much smaller than the number of variables.

Suggested Citation

  • Nguyen, Duy Van, 2013. "Global maximization of UTA functions in multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 228(2), pages 397-404.
    • Handle: RePEc:eee:ejores:v:228:y:2013:i:2:p:397-404
    DOI: 10.1016/j.ejor.2012.06.022
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    References listed on IDEAS

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    1. Bous, Géraldine & Fortemps, Philippe & Glineur, François & Pirlot, Marc, 2010. "ACUTA: A novel method for eliciting additive value functions on the basis of holistic preference statements," European Journal of Operational Research, Elsevier, vol. 206(2), pages 435-444, October.
    2. Jacquet-Lagreze, E. & Siskos, J., 1982. "Assessing a set of additive utility functions for multicriteria decision-making, the UTA method," European Journal of Operational Research, Elsevier, vol. 10(2), pages 151-164, June.
    3. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, December.
    4. Greco, Salvatore & Mousseau, Vincent & Slowinski, Roman, 2008. "Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions," European Journal of Operational Research, Elsevier, vol. 191(2), pages 416-436, December.
    5. Figueira, José Rui & Greco, Salvatore & Slowinski, Roman, 2009. "Building a set of additive value functions representing a reference preorder and intensities of preference: GRIP method," European Journal of Operational Research, Elsevier, vol. 195(2), pages 460-486, June.
    6. R. Horst & N. V. Thoai, 1997. "Utility Function Programs and Optimization over the Efficient Set in Multiple-Objective Decision Making," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 605-631, March.
    7. Jacquet-Lagreze, Eric & Meziani, Rachid & Slowinski, Roman, 1987. "with an interactive assessment of a piecewise linear utility function," European Journal of Operational Research, Elsevier, vol. 31(3), pages 350-357, September.
    8. H. P. Benson & E. Sun, 2000. "Outcome Space Partition of the Weight Set in Multiobjective Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 17-36, April.
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