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Optimizing Over the Efficient Set Using a Top-Down Search of Faces

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  • Serpil Sayin

    (Koç University, College of Administrative Sciences and Economics, Istinye, 80860 Istanbul, Turkey)

Abstract

The problem of optimizing a linear function over the efficient set of a multiple objective linear programming problem is studied. The decomposition of the efficient set into efficient faces is used as the basis of a search-based algorithm to solve this problem. The faces of the feasible region are characterized by the set of constraints that hold as equality in that face. The search is conducted over the indices of the constraints in a way that explores faces of possibly higher dimension first. Computational tests are performed to establish the behavior of the algorithm when the objective function is built according to different schemes that have received attention in the literature. The results indicate that different objective function types may lead to varying computation time requirements. In general, computational requirements of the algorithm increase significantly with problem size. A heuristic modification of the algorithm is proposed to solve large problems within reasonable time limits. Tests to measure the quality of the heuristic solutions show that the heuristic approach constitutes a practical alternative for finding good solutions for the problem.

Suggested Citation

  • Serpil Sayin, 2000. "Optimizing Over the Efficient Set Using a Top-Down Search of Faces," Operations Research, INFORMS, vol. 48(1), pages 65-72, February.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:1:p:65-72
    DOI: 10.1287/opre.48.1.65.12449
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    References listed on IDEAS

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    1. Dessouky, M. I. & Ghiassi, M. & Davis, W. J., 1986. "Estimates of the minimum nondominated criterion values in multiple-criteria decision-making," Engineering Costs and Production Economics, Elsevier, vol. 10(2), pages 95-104, June.
    2. Pekka Korhonen & Seppo Salo & Ralph E. Steuer, 1997. "A Heuristic for Estimating Nadir Criterion Values in Multiple Objective Linear Programming," Operations Research, INFORMS, vol. 45(5), pages 751-757, October.
    3. Harold P. Benson & Serpil Sayin, 1993. "A face search heuristic algorithm for optimizing over the efficient set," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(1), pages 103-116, February.
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    1. Kahina Ghazli & Nicolas Gillis & Mustapha Moulaï, 2020. "Optimizing over the properly efficient set of convex multi-objective optimization problems," Annals of Operations Research, Springer, vol. 295(2), pages 575-604, December.
    2. Jornada, Daniel & Leon, V. Jorge, 2016. "Biobjective robust optimization over the efficient set for Pareto set reduction," European Journal of Operational Research, Elsevier, vol. 252(2), pages 573-586.
    3. Sauli Ruuska & Kaisa Miettinen & Margaret M. Wiecek, 2012. "Connections Between Single-Level and Bilevel Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 60-74, April.
    4. Vahid Mahmoodian & Iman Dayarian & Payman Ghasemi Saghand & Yu Zhang & Hadi Charkhgard, 2022. "A Criterion Space Branch-and-Cut Algorithm for Mixed Integer Bilinear Maximum Multiplicative Programs," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1453-1470, May.
    5. J. Glackin & J. G. Ecker & M. Kupferschmid, 2009. "Solving Bilevel Linear Programs Using Multiple Objective Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 197-212, February.
    6. Alvaro Sierra Altamiranda & Hadi Charkhgard, 2019. "A New Exact Algorithm to Optimize a Linear Function over the Set of Efficient Solutions for Biobjective Mixed Integer Linear Programs," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 823-840, October.
    7. S.T. Hackman & U. Passy, 2002. "Maximizing a Linear Fractional Function on a Pareto Efficient Frontier," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 83-103, April.
    8. Daniel Jornada & V. Jorge Leon, 2020. "Filtering Algorithms for Biobjective Mixed Binary Linear Optimization Problems with a Multiple-Choice Constraint," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 57-73, January.

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