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A branch and bound algorithm for continuous multiobjective optimization problems using general ordering cones

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  • Wu, Weitian
  • Yang, Xinmin

Abstract

Many existing branch and bound algorithms for multiobjective optimization problems require a significant computational cost to approximate the entire Pareto optimal solution set. In this paper, we propose a new branch and bound algorithm that approximates a part of the Pareto optimal solution set by introducing the additional preference information in the form of ordering cones. The basic idea is to replace the Pareto dominance induced by the nonnegative orthant with the cone dominance induced by a larger ordering cone in the discarding test. In particular, we consider both polyhedral and non-polyhedral cones, and propose the corresponding cone dominance-based discarding tests, respectively. In this way, the subboxes that do not contain efficient solutions with respect to the ordering cone will be removed, even though they may contain Pareto optimal solutions. We prove the global convergence of the proposed algorithm. Finally, the proposed algorithm is applied to a number of test instances as well as to 2- to 5-objective real-world constrained problems.

Suggested Citation

  • Wu, Weitian & Yang, Xinmin, 2025. "A branch and bound algorithm for continuous multiobjective optimization problems using general ordering cones," European Journal of Operational Research, Elsevier, vol. 326(1), pages 28-41.
    • Handle: RePEc:eee:ejores:v:326:y:2025:i:1:p:28-41
    DOI: 10.1016/j.ejor.2025.04.045
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    References listed on IDEAS

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    1. Klamroth, Kathrin & Lacour, Renaud & Vanderpooten, Daniel, 2015. "On the representation of the search region in multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 245(3), pages 767-778.
    2. Gabriele Eichfelder & Peter Kirst & Laura Meng & Oliver Stein, 2021. "A general branch-and-bound framework for continuous global multiobjective optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 195-227, May.
    3. Aliprantis, Charalambos D. & Monteiro, Paulo K. & Tourky, Rabee, 2004. "Non-marketed options, non-existence of equilibria, and non-linear prices," Journal of Economic Theory, Elsevier, vol. 114(2), pages 345-357, February.
    4. Wei-tian Wu & Xin-min Yang, 2024. "Reference-point-based branch and bound algorithm for multiobjective optimization," Journal of Global Optimization, Springer, vol. 88(4), pages 927-945, April.
    5. Julius Bauß & Michael Stiglmayr, 2024. "Augmenting bi-objective branch and bound by scalarization-based information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 85-121, August.
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    8. Daniel Scholz, 2010. "The multicriteria big cube small cube method," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 286-302, July.
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    Cited by:

    1. Yu, Fan & Chen, Qun & Zhou, Jinlong, 2026. "Decision space dynamic niching-based method for constrained multiobjective evolutionary optimization," European Journal of Operational Research, Elsevier, vol. 328(2), pages 574-590.

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