Multi-objective integer programming: An improved recursive algorithm

TL;DR

This paper presents an enhanced recursive algorithm for multi-objective integer programming that leverages previously solved subproblems to reduce computational effort, especially for larger problems.

Contribution

An improved recursive algorithm that efficiently generates all nondominated vectors by reusing solutions of subproblems, outperforming previous methods.

Findings

Significant reduction in computation time for larger problems

Algorithm effectively reuses solutions to avoid redundant IPs

Performance improves with increasing problem size

Abstract

This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-Objective Integer Programming (MOIP) problem. We significantly improve the earlier recursive algorithm of \"Ozlen and Azizo\u{g}lu by using the set of already solved subproblems and their solutions to avoid solving a large number of IPs. A numerical example is presented to explain the workings of the algorithm, and we conduct a series of computational experiments to show the savings that can be obtained. As our experiments show, the improvement becomes more significant as the problems grow larger in terms of the number of objectives.