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A trust-region approach for computing Pareto fronts in multiobjective optimization

Author

Listed:
  • A. Mohammadi

    (NOVA School of Science and Technology)

  • A. L. Custódio

    (NOVA School of Science and Technology)

Abstract

Multiobjective optimization is a challenging scientific area, where the conflicting nature of the different objectives to be optimized changes the concept of problem solution, which is no longer a single point but a set of points, namely the Pareto front. In a posteriori preferences approach, when the decision maker is unable to rank objectives before the optimization, it is important to develop algorithms that generate approximations to the complete Pareto front of a multiobjective optimization problem, making clear the trade-offs between the different objectives. In this work, an algorithm based on a trust-region approach is proposed to approximate the set of Pareto critical points of a multiobjective optimization problem. Derivatives are assumed to be known, allowing the computation of Taylor models for the different objective function components, which will be minimized in two main steps: the extreme point step and the scalarization step. The goal of the extreme point step is to expand the approximation to the Pareto front, by moving towards the extreme points of it, corresponding to the individual minimization of each objective function component. The scalarization step attempts to reduce the gaps on the Pareto front, by solving adequate scalarization problems. The convergence of the method is analyzed and numerical experiments are reported, indicating the relevance of each feature included in the algorithmic structure and its competitiveness, by comparison against a state-of-art multiobjective optimization algorithm.

Suggested Citation

  • A. Mohammadi & A. L. Custódio, 2024. "A trust-region approach for computing Pareto fronts in multiobjective optimization," Computational Optimization and Applications, Springer, vol. 87(1), pages 149-179, January.
    • Handle: RePEc:spr:coopap:v:87:y:2024:i:1:d:10.1007_s10589-023-00510-2
    DOI: 10.1007/s10589-023-00510-2
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    References listed on IDEAS

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    1. Konstantinos Anagnostopoulos & Georgios Mamanis, 2011. "Multiobjective evolutionary algorithms for complex portfolio optimization problems," Computational Management Science, Springer, vol. 8(3), pages 259-279, August.
    2. Kely D. V. Villacorta & Paulo R. Oliveira & Antoine Soubeyran, 2014. "A Trust-Region Method for Unconstrained Multiobjective Problems with Applications in Satisficing Processes," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 865-889, March.
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