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A branch and bound algorithm for Holder bi-objective optimization. Implementation to multidimensional optimization

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  • Ammar, Hamadi
  • Naffeti, Bechir

Abstract

In the present paper, we put forward and explain the branch and bound method to solve Holder multidimensional bi-objective optimization problems. We start by considering the one-dimensional case and developing an optimization algorithm based on parabolic under-estimators. Those under-estimators generate a sequence of points that will contribute in the identification of the Pareto front of the problem being raised. When seeking these points, we have to solve nonlinear equations that are difficult to solve. Besides, we develop a recursive method suitable for solving such nonlinear equations. Then we widen our focus to deal with Holder multidimensional bi-objective optimization problems. We illustrate how to implement the proposed algorithm in the multidimensional case using α-dense space filling curves. In the last section, we implement the proposed algorithm to solve some numerical examples in the one-dimensional and the multidimensional cases.

Suggested Citation

  • Ammar, Hamadi & Naffeti, Bechir, 2023. "A branch and bound algorithm for Holder bi-objective optimization. Implementation to multidimensional optimization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 181-201.
    • Handle: RePEc:eee:matcom:v:204:y:2023:i:c:p:181-201
    DOI: 10.1016/j.matcom.2022.08.003
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    References listed on IDEAS

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    1. Naffeti, Bechir & Ammar, Hamadi, 2021. "A new trisection method for solving Lipschitz bi-objective optimization problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1186-1205.
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    Cited by:

    1. Naffeti, Bechir & Ammar, Hamadi & Aribi, Walid Ben, 2024. "A Branch and Bound algorithm for multidimensional Holder optimization: Estimation of the age-dependent viral hepatitis A infection force," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 311-326.

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