Branch and cut method for solving integer indefinite quadratic bilevel programs

Nacéra Maachou () and Mustapha Moulaï ()
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Nacéra Maachou: USTHB
Mustapha Moulaï: USTHB

Annals of Operations Research, 2022, vol. 316, issue 1, No 9, 197-227

Abstract: 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.

Keywords: Bilevel programming; Integer programming; Quadratic programming; 90C30; 90C10; 90C20 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10479-021-04387-4

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