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

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 gen...

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Bibliographic Details
Published in:Mathematics and computers in simulation 2023-02, Vol.204, p.181-201
Main Authors: Ammar, Hamadi, Naffeti, Bechir
Format: Article
Language:English
Subjects:
Alienor technical
Bi-objective optimization
Branch and bound methods
Holder functions
Optimization algorithms
Pareto front
Trisection methods
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Summary: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.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2022.08.003