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Interactive resolution of multiobjective combinatorial optimization problems by incremental elicitation of criteria weights

Author

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  • Nawal Benabbou

    (National University of Singapore)

  • Patrice Perny

    (Sorbonne Université)

Abstract

We propose an introduction to the use of incremental preference elicitation methods in the field of multiobjective combinatorial optimization. We consider three different optimization problems in vector-valued graphs, namely the shortest path problem, the minimum spanning tree problem and the assignment problem. In each case, the preferences of the decision-maker over cost vectors are assumed to be representable by a weighted sum but the weights of criteria are initially unknown. We then explain how to interweave preference elicitation and search to quickly determine a near-optimal solution with a limited number of preference queries. This leads us to successively introduce an interactive version of dynamic programming, greedy search, and branch and bound to solve the problems under consideration. We then present numerical tests showing the practical efficiency of these algorithms that achieve a good compromise between the number of queries asked and the solution times.

Suggested Citation

  • Nawal Benabbou & Patrice Perny, 2018. "Interactive resolution of multiobjective combinatorial optimization problems by incremental elicitation of criteria weights," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 6(3), pages 283-319, November.
    • Handle: RePEc:spr:eurjdp:v:6:y:2018:i:3:d:10.1007_s40070-018-0085-4
    DOI: 10.1007/s40070-018-0085-4
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    References listed on IDEAS

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    1. Kaddani, Sami & Vanderpooten, Daniel & Vanpeperstraete, Jean-Michel & Aissi, Hassene, 2017. "Weighted sum model with partial preference information: Application to multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 260(2), pages 665-679.
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    Cited by:

    1. Arwa Khannoussi & Alexandru-Liviu Olteanu & Patrick Meyer & Nawal Benabbou, 2024. "A regret-based query selection strategy for the incremental elicitation of the criteria weights in an SRMP model," Operational Research, Springer, vol. 24(2), pages 1-21, June.
    2. Özgür Özpeynirci & Selin Özpeynirci & Vincent Mousseau, 2023. "A decomposition based minimax regret approach for inverse multiple criteria sorting problem," 4OR, Springer, vol. 21(1), pages 125-149, March.
    3. Ali Tlili & Oumaima Khaled & Vincent Mousseau & Wassila Ouerdane, 2023. "Interactive portfolio selection involving multicriteria sorting models," Annals of Operations Research, Springer, vol. 325(2), pages 1169-1195, June.

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