A generic Branch-and-Cut algorithm for bi-objective binary linear programs

TL;DR

This paper introduces a novel generic branch-and-cut algorithm for bi-objective binary linear programs, utilizing new cutting frameworks and multi-point separation techniques to efficiently solve large instances.

Contribution

It presents the first generic bi-objective binary linear branch-and-cut algorithm with innovative cutting frameworks and multi-point separation, enhancing solution efficiency and scalability.

Findings

Successfully solves instances with up to 2800 variables in under an hour.

Demonstrates the effectiveness of the proposed cutting frameworks.

Shows potential for extension to more objectives and variables.

Abstract

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.