Algorithms the min-max regret 0-1 Integer Linear Programming Problem with Interval Data

TL;DR

This paper introduces a Benders-like decomposition and two metaheuristics to solve the min-max regret 0-1 Integer Linear Programming problem with interval data, demonstrating their effectiveness through computational experiments.

Contribution

The paper presents novel decomposition and metaheuristic methods specifically designed for the MMR-ILP with interval data, improving solution efficiency.

Findings

Metaheuristics outperform the Benders-like algorithm in computational time.

Metaheuristics achieve good solutions within reasonable time.

Decomposition method provides a benchmark for comparison.

Abstract

We address the Interval Data Min-Max Regret 0-1 Integer Linear Programming problem (MMR-ILP), a variant of the 0-1 Integer Linear Programming problem where the objective function coefficients are uncertain. We solve MMR-ILP using a Benders-like Decomposition Algorithm and two metaheuristics for min-max regret problems with interval data. Computational experiments developed on variations of MIPLIB instances show that the heuristics obtain good results in a reasonable computational time when compared to the Benders-like Decomposition algorithm.