An Iterated Dual Substitution Approach for Binary Integer Programming Problems under the Min-Max Regret Criterion

TL;DR

This paper introduces the iterated dual substitution (iDS) heuristic for binary integer programming problems under the min-max regret criterion, demonstrating superior performance on various combinatorial problems and benchmarks.

Contribution

The paper presents a novel iterative heuristic framework, iDS, that improves solution quality for min-max regret binary integer programming problems across multiple problem types.

Findings

iDS outperforms existing algorithms on most benchmark instances.

iDS updates best known results for several standard problems.

The approach is effective for diverse combinatorial optimization problems.

Abstract

We consider binary integer programming problems with the min-max regret objective function under interval objective coefficients. We propose a new heuristic framework, which we call the iterated dual substitution (iDS) algorithm. The iDS algorithm iteratively invokes a dual substitution heuristic and excludes from the search space any solution already checked in previous iterations. In iDS, we use a best-scenario-based lemma to improve performance. We apply iDS to four typical combinatorial optimization problems: the knapsack problem, the multidimensional knapsack problem, the generalized assignment problem, and the set covering problem. For the multidimensional knapsack problem, we compare the iDS approach with two algorithms widely used for problems with the min-max regret criterion: a fixed-scenario approach, and a branch-and-cut approach. The results of computational experiments on a broad set of benchmark instances show that the proposed iDS approach performs best on most tested instances. For the knapsack problem, the generalized assignment problem, and the set covering problem, we compare iDS with state-of-the-art results. The iDS algorithm successfully updates best known records for a number of benchmark instances.