An exact algorithm for biobjective integer programming problems

TL;DR

This paper introduces an exact algorithm for biobjective integer programming that efficiently finds the set of nondominated solutions using scalarization techniques, outperforming existing methods especially under time constraints.

Contribution

The paper presents a novel exact algorithm based on Pascoletti-Serafini scalarizations for biobjective integer programming, with analysis of different strategies and computational comparisons.

Findings

The algorithm effectively finds the nondominated set with fewer scalarizations.

Different strategies excel in speed or solution quality under time limits.

The proposed method outperforms existing algorithms in coverage and efficiency.

Abstract

We propose an exact algorithm for solving biobjective integer programming problems, which arise in various applications of operations research. The algorithm is based on solving Pascoletti-Serafini scalarizations to search specified regions (boxes) in the objective space and returns the set of nondominated points. We implement the algorithm with different strategies, where the choices of the scalarization model parameters and splitting rule differ. We then derive bounds on the number of scalarization models solved; and demonstrate the performances of the variants through computational experiments both as exact algorithms and as solution approaches under time restriction. The experiments demonstrate that different strategies have advantages in different aspects: while some are quicker in finding the whole set of nondominated solutions, others return good-quality solutions in terms of representativeness when run under time restriction. We also compare the proposed approach with existing algorithms. The results of our experiments show the satisfactory behaviour of our algorithm, especially when run under time limit, as it achieves better coverage of the whole frontier with a smaller number of solutions compared to the existing algorithms.