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

• Published in: European journal of operational research Vol. 326; no. 1; pp. 28 - 41
• Main Authors: Wu, Weitian, Yang, Xinmin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2025
• Subjects: 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
• DOI: 10.1016/j.ejor.2025.04.045

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.