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

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...

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Vydané v:European journal of operational research Ročník 326; číslo 1; s. 28 - 41
Hlavní autori: Wu, Weitian, Yang, Xinmin
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.10.2025
Predmet:
Branch and bound algorithm
Efficient solution
Global optimization
Multiple objective programming
Ordering cone
Global optimization
90C30
Efficient solution
Multiple objective programming
90C29
Branch and bound algorithm
90C26
Ordering cone
ISSN:0377-2217
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Popis
Shrnutí: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. •A multiobjective branch and bound algorithm using general ordering cones is proposed.•Polyhedral cones and ice cream cones are studied.•The algorithm computes the efficient solutions corresponding to the cones.•The algorithm has global convergence.•Numerical experiments demonstrate the efficiency of the algorithm.
ISSN:0377-2217
DOI:10.1016/j.ejor.2025.04.045