Fix-and-optimize metaheuristics for minmax regret binary integer programming problems under interval uncertainty

The Binary Integer Programming problem (BIP) is a mathematical optimization problem, with linear objective function and constraints, on which the domain of all variables is {0, 1}. In BIP, every variable is associated with a determined cost coefficient. The Minmax regret Binary Integer Programming p...

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Bibliographic Details
Published in:R.A.I.R.O. Recherche opérationnelle Vol. 56; no. 6; pp. 4281 - 4301
Main Authors: Carvalho, Iago A., Noronha, Thiago F., Duhamel, Christophe
Format: Journal Article
Language:English
Published: 01.11.2022
ISSN:0399-0559, 2804-7303
Online Access:Get full text
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Summary:The Binary Integer Programming problem (BIP) is a mathematical optimization problem, with linear objective function and constraints, on which the domain of all variables is {0, 1}. In BIP, every variable is associated with a determined cost coefficient. The Minmax regret Binary Integer Programming problem under interval uncertainty (M-BIP) is a generalization of BIP in which the cost coefficient associated to the variables is not known in advance, but are assumed to be bounded by an interval. The objective of M-BIP is to find a solution that possesses the minimum maximum regret among all possible solutions for the problem. In this paper, we show that the decision version of M-BIP is Σ p 2 -complete. Furthermore, we tackle M-BIP by both exact and heuristic algorithms. We extend three exact algorithms from the literature to M-BIP and propose two fix-and-optimize heuristic algorithms. Computational experiments, performed on the Minmax regret Weighted Set Covering problem under Interval Uncertainties (M-WSCP) as a test case, indicates that one of the exact algorithms outperforms the others. Furthermore, it shows that the proposed fix-and-optimize heuristics, that can be easily employed to solve any minmax regret optimization problem under interval uncertainty, are competitive with ad-hoc algorithms for the M-WSCP.
ISSN:0399-0559
2804-7303
DOI:10.1051/ro/2022198