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Reference-point-based branch and bound algorithm for multiobjective optimization

Author

Listed:
  • Wei-tian Wu

    (Sichuan University)

  • Xin-min Yang

    (National Center for Applied Mathematics of Chongqing
    Chongqing Normal University)

Abstract

In this paper, a nonconvex multiobjective optimization problem with Lipschitz objective functions is considered. A branch and bound algorithm that incorporates the decision maker’s preference information is proposed for this problem. In the proposed algorithm, a new discarding test is designed to check whether a box contains preferred solutions according to the preference information expressed by means of reference points. In this way, the proposed algorithm is able to gradually guide the search towards the region of interest on the Pareto fronts during the solution process. We prove that the proposed algorithm obtains $$\varepsilon $$ ε -efficient solutions distributed among the regions of interest with respect to the given reference points. Moreover, lower bound on the total finite number of required iterations for predefined precision is also provided. Finally, the algorithm is illustrated with a number of test problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:88:y:2024:i:4:d:10.1007_s10898-023-01306-8
    DOI: 10.1007/s10898-023-01306-8
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    References listed on IDEAS

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    1. Markus Hartikainen & Kaisa Miettinen & Margaret Wiecek, 2012. "PAINT: Pareto front interpolation for nonlinear multiobjective optimization," Computational Optimization and Applications, Springer, vol. 52(3), pages 845-867, July.
    2. Gabriele Eichfelder & Peter Kirst & Laura Meng & Oliver Stein, 2021. "Correction to: A general branch-and-bound framework for continuous global multiobjective optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 229-229, May.
    3. Ana Ruiz & Rubén Saborido & Mariano Luque, 2015. "A preference-based evolutionary algorithm for multiobjective optimization: the weighting achievement scalarizing function genetic algorithm," Journal of Global Optimization, Springer, vol. 62(1), pages 101-129, May.
    4. 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.
    5. Matthias Ehrgott & Lizhen Shao & Anita Schöbel, 2011. "An approximation algorithm for convex multi-objective programming problems," Journal of Global Optimization, Springer, vol. 50(3), pages 397-416, July.
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