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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| Vydané v: | R.A.I.R.O. Recherche opérationnelle Ročník 56; číslo 6; s. 4281 - 4301 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
01.11.2022
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| ISSN: | 0399-0559, 2804-7303 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | 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. |
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| ISSN: | 0399-0559 2804-7303 |
| DOI: | 10.1051/ro/2022198 |