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An Interactive Branch-and-Bound Algorithm for Multiple Criteria Optimization

Author

Listed:
  • Odile Marcotte

    (Département de mathématique et d'informatique, Université du Québec à Montréal, C.P. 8888, Succ. A, Montréal, Québec, Canada H3C 3P8)

  • Richard M. Soland

    (Department of Operations, School of Engineering and Applied Science, The George Washington University, Washington, D.C. 20052)

Abstract

We present a new interactive algorithm for multiple criteria optimization. The algorithm is of the branch-and-bound type, and differs from previous interactive algorithms in several ways. First, the field of application is wider because it applies to two important classes of multiple criteria decision problems: those for which the feasible set is convex and those for which the feasible set is discrete. Secondly, the algorithm does not require a great deal from the decision maker; he is merely required to indicate his preference between two vectors whenever the algorithm so demands.

Suggested Citation

  • Odile Marcotte & Richard M. Soland, 1986. "An Interactive Branch-and-Bound Algorithm for Multiple Criteria Optimization," Management Science, INFORMS, vol. 32(1), pages 61-75, January.
    • Handle: RePEc:inm:ormnsc:v:32:y:1986:i:1:p:61-75
    DOI: 10.1287/mnsc.32.1.61
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    Citations

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    Cited by:

    1. Francis Sourd & Olivier Spanjaard, 2008. "A Multiobjective Branch-and-Bound Framework: Application to the Biobjective Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 472-484, August.
    2. Banu Lokman & Murat Köksalan & Pekka J. Korhonen & Jyrki Wallenius, 2016. "An interactive algorithm to find the most preferred solution of multi-objective integer programs," Annals of Operations Research, Springer, vol. 245(1), pages 67-95, October.
    3. Nikolaos Argyris & José Figueira & Alec Morton, 2011. "Identifying preferred solutions to Multi-Objective Binary Optimisation problems, with an application to the Multi-Objective Knapsack Problem," Journal of Global Optimization, Springer, vol. 49(2), pages 213-235, February.
    4. 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.
    5. Zhang, Cai Wen & Ong, Hoon Liong, 2004. "Solving the biobjective zero-one knapsack problem by an efficient LP-based heuristic," European Journal of Operational Research, Elsevier, vol. 159(3), pages 545-557, December.
    6. Lourenco, Rui Pedro & Costa, Joao Paulo, 2004. "Using ELECTRE TRI outranking method to sort MOMILP nondominated solutions," European Journal of Operational Research, Elsevier, vol. 153(2), pages 271-289, March.
    7. P. Korhonen & J. Karaivanova, 1998. "An Algorithm for Projecting a Reference Direction onto the Nondominated Set of Given Points," Working Papers ir98011, International Institute for Applied Systems Analysis.
    8. Blanco, Víctor, 2011. "A mathematical programming approach to the computation of the omega invariant of a numerical semigroup," European Journal of Operational Research, Elsevier, vol. 215(3), pages 539-550, December.
    9. Alves, Maria Joao & Climaco, Joao, 2007. "A review of interactive methods for multiobjective integer and mixed-integer programming," European Journal of Operational Research, Elsevier, vol. 180(1), pages 99-115, July.
    10. Harold P. Benson & Serpil Sayin, 1997. "Towards finding global representations of the efficient set in multiple objective mathematical programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(1), pages 47-67, February.
    11. 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.
    12. Camila de Lima & Antonio Roberto Balbo & Thiago Pedro Donadon Homem & Helenice de Oliveira Florentino Silva, 2017. "A hybrid approach combining interior-point and branch-and-bound methods applied to the problem of sugar cane waste," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(2), pages 147-164, February.
    13. Mavrotas, G. & Diakoulaki, D., 1998. "A branch and bound algorithm for mixed zero-one multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 107(3), pages 530-541, June.

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    Keywords

    multicriteria optimization;

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