This paper presents the first generic bi-objective binary linear branch-and-cut algorithm. Studying the impact of valid inequalities in solution and objective spaces, two cutting frameworks are proposed. The multi-point separation problem is introduced together with a cutting algorithm to efficiently generate valid inequalities violating multiple points simultaneously. The other main idea is to invoke state-of-the-art integer linear programming solver's internal advanced techniques such as cut separators. Aggregation techniques are proposed to use these frameworks with a trade-off among efficient cut separations, tight lower and upper bound sets and advanced branching strategies. Experiments on various types of instances in the literature exhibit the promising efficiency of the algorithm that solves instances with up to 2800 binary variables in less than one hour of CPU time. Our algorithms are easy to extend for more than two objectives and integer variables.

翻译：本文提出了首个通用的双目标二元线性分支切割算法。通过研究有效不等式在解空间和目标空间中的影响，提出了两种切割框架。引入了多点分离问题，并设计了一种切割算法，以高效生成同时违反多个点的有效不等式。另一核心思想是利用最先进的整数线性规划求解器的内部高级技术，如切割分离器。提出了聚合技术，以在这些框架之间实现高效切割分离、紧致的上下界集合与高级分支策略之间的权衡。对文献中多种类型实例的实验表明，该算法具有显著效率，可在不到一小时的CPU时间内解决多达2800个二元变量的实例。我们的算法易于扩展至多于两个目标及整数变量的情形。