In this article, an exact method is proposed to optimize two preference functions over the efficient set of a multiobjective integer linear program (MOILP). This kind of problems arises whenever two associated decision-makers have to optimize their respective preference functions over many efficient solutions. For this purpose, we develop a branch-and-cut algorithm based on linear programming, for finding efficient solutions in terms of both preference functions and MOILP problem, without explicitly enumerating all efficient solutions of MOILP problem. The branch and bound process, strengthened by efficient cuts and tests, allows us to prune a large number of nodes in the tree to avoid many solutions. An illustrative example and an experimental study are reported.

中文翻译：

---

有效集多目标整数规划问题的双目标优化

在本文中，提出了一种在多目标整数线性程序（MOILP）的有效集上优化两个偏好函数的精确方法。每当两个相关的决策者必须通过许多有效的解决方案优化其各自的偏好功能时，都会出现此类问题。为此，我们开发了一种基于线性规划的分支切算法，用于在偏好函数和MOILP问题方面找到有效的解决方案，而无需明确枚举MOILP问题的所有有效解决方案。有效的剪切和测试加强了分支和绑定过程，使我们可以修剪树中的大量节点，从而避免许多解决方案。报告了说明性实例和实验研究。