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The Robust Set Covering Problem with interval data

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Abstract

We study the Set Covering Problem with uncertain costs. For each cost coefficient, only an interval estimate is known, and it is assumed that each coefficient can take on any value from the corresponding uncertainty interval, regardless of the values taken by other coefficients. It is required to find a robust deviation (also called minmax regret) solution. For this strongly NP-hard problem, we present and compare computationally three exact algorithms, where two of them are based on Benders decomposition and one uses Benders cuts in the context of a Branch-and-Cut approach, and several heuristic methods, including a scenario-based heuristic, a Genetic Algorithm, and a Hybrid Algorithm that uses a version of Benders decomposition within a Genetic Algorithm framework.

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Authors and Affiliations

  1. Escola Tècnica Superior d’Enginyers Industrials de Barcelona, Universitat Politècnica de Catalunya, Avda. Diagonal 647, 7th floor, 08028, Barcelona, Spain

    Jordi Pereira

  2. Department of Management, University of Toronto Scarborough, 1265 Military Trail, Toronto, Ontario, M1C 1A4, Canada

    Igor Averbakh

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  1. Jordi Pereira
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  2. Igor Averbakh
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Correspondence to Igor Averbakh.

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Pereira, J., Averbakh, I. The Robust Set Covering Problem with interval data. Ann Oper Res 207, 217–235 (2013). https://doi.org/10.1007/s10479-011-0876-5

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