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.

中文翻译：

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使用一般排序锥的连续多目标优化问题的分支定界算法

许多现有的多目标优化问题分支和定界算法需要大量的计算成本来近似整个 Pareto 最优解集。在本文中，我们提出了一种新的分支和定界算法，该算法通过以排序锥的形式引入额外的偏好信息来近似 Pareto 最优解集的一部分。基本思想是在丢弃测试中用较大的有序锥引起的锥优势替换非负 orthant 诱导的 Pareto 优势。特别是，我们考虑了多面体和非多面体锥，并分别提出了相应的基于锥优势的丢弃测试。这样，不包含与排序锥有关的有效解的子框将被删除，即使它们可能包含 Pareto 最优解。我们证明了所提算法的全局收敛性。最后，将所提出的算法应用于许多测试实例以及 2 到 5 目标的真实世界约束问题。