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Branch and cut method for solving integer indefinite quadratic bilevel programs

  • S.I.: Scalable Optimization and Decision Making in OR
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Abstract

The paper tackles a class of bilevel programming where the upper level problem and the lower level problem are integer indefinite quadratic programs. This article presents a new algorithm for solving the integer indefinite quadratic bilevel problem, say IIQBP. Indeed, the upper level indefinite quadratic problem is solved, the optimal solution of which belongs to the efficient solutions set of the corresponding bicriteria problem. The set of efficient solutions is determined by branch and bound method with cuts. The found integer optimal solution is tested for optimality of the main problem by solving the lower level problem. If this solution is non optimal of IIQBP problem, a cut is added to the upper level problem and a new efficient solutions set is determined then a new integer solution of the upper level problem is found. After the presentation and validation of the algorithm, two examples are provided to better visualize the proposed algorithm.

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Acknowledgements

Authors are grateful to doctor Hadjer Moulai and anonymous reviewers whose comments allowed us to improve the manuscript significantly. Authors work was supported by the Direction Générale de la Recherche Scientifique et du Développement Technologique (DGRSDT) Grant ID: C0656104.

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Authors and Affiliations

  1. Department of Operations Research, Faculty of Mathematics, USTHB, BP 32, Bab Ezzouar, 16111, Algiers, Algeria

    Nacéra Maachou

  2. LaROMaD Laboratory, Faculty of Mathematics, USTHB, BP 32, Bab Ezzouar, 16111, Algiers, Algeria

    Mustapha Moulaï

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  1. Nacéra Maachou
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  2. Mustapha Moulaï
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Correspondence to Nacéra Maachou.

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Maachou, N., Moulaï, M. Branch and cut method for solving integer indefinite quadratic bilevel programs. Ann Oper Res 316, 197–227 (2022). https://doi.org/10.1007/s10479-021-04387-4

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