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Branch and cut method for solving integer indefinite quadratic bilevel programs

Author

Listed:
  • Nacéra Maachou

    (USTHB)

  • Mustapha Moulaï

    (USTHB)

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.

Suggested Citation

  • Nacéra Maachou & Mustapha Moulaï, 2022. "Branch and cut method for solving integer indefinite quadratic bilevel programs," Annals of Operations Research, Springer, vol. 316(1), pages 197-227, September.
    • Handle: RePEc:spr:annopr:v:316:y:2022:i:1:d:10.1007_s10479-021-04387-4
    DOI: 10.1007/s10479-021-04387-4
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    References listed on IDEAS

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    3. C. Bector, 1972. "Indefinite quadratic fractional functional programming," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 18(1), pages 21-30, December.
    4. Arora, S.R. & Gupta, Ritu, 2009. "Interactive fuzzy goal programming approach for bilevel programming problem," European Journal of Operational Research, Elsevier, vol. 194(2), pages 368-376, April.
    5. Yasmine Cherfaoui & Mustapha Moulaï, 2021. "Generating the efficient set of MultiObjective Integer Linear plus Linear Fractional Programming Problems," Annals of Operations Research, Springer, vol. 296(1), pages 735-753, January.
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