Many interactive approaches in multi-objective optimization assume the existence of an underlying preference function that represents the preferences of a decision maker (DM). In this paper, we develop the theory and an exact algorithm that guarantees finding the most preferred solution of a DM whose preferences are consistent with a Tchebycheff function for multi-objective integer programs. The algorithm occasionally presents pairs of solutions to the DM and asks which one is preferred. It utilizes the preference information together with the properties of the Tchebycheff function to generate solutions that are candidates to be the most preferred solution. We test the performance of the algorithm on a set of three and four-objective combinatorial optimization problems.

多目标优化中的许多交互式方法都假设存在表示决策者 (DM) 偏好的潜在偏好函数。在本文中，我们开发了理论和精确算法，以确保找到 DM 的最优选解决方案，其偏好与多目标整数规划的 Tchebycheff 函数一致。该算法偶尔会向 DM 提供成对的解决方案，并询问哪一个是首选。它利用偏好信息和 Tchebycheff 函数的属性来生成候选解决方案，成为最优选的解决方案。我们测试了算法在一组三目标和四目标组合优化问题上的性能。