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A branch-and-cut technique to solve multiobjective integer quadratic programming problems

Author

Listed:
  • Fatma Zohra Ouaïl

    (USTHB)

  • Mohamed El-Amine Chergui

    (USTHB)

Abstract

This article proposes an exact method to solve the integer programming problem featuring several convex quadratic functions to be minimized (henceforth denoted by MOIQP). The proposed algorithm is a branch and bound based technique suitable for MOIQP problems to generate the set of all efficient solutions. The features of the method are as follows. First, the branch and bound technique allows solving the relaxed problem according to any linear function and progressively generates integer solutions. Then, the efficient cut proposed reduces the search area by truncating domains containing non efficient solutions without having to enumerate them. Finally, at each node of the tree search, three fathoming rules are used to enhance the speed of the procedure. Computational experiments are presented in order to analyze the performance of the algorithm.

Suggested Citation

  • Fatma Zohra Ouaïl & Mohamed El-Amine Chergui, 2018. "A branch-and-cut technique to solve multiobjective integer quadratic programming problems," Annals of Operations Research, Springer, vol. 267(1), pages 431-446, August.
    • Handle: RePEc:spr:annopr:v:267:y:2018:i:1:d:10.1007_s10479-017-2698-6
    DOI: 10.1007/s10479-017-2698-6
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    References listed on IDEAS

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    1. Ralph Steuer & Yue Qi & Markus Hirschberger, 2007. "Suitable-portfolio investors, nondominated frontier sensitivity, and the effect of multiple objectives on standard portfolio selection," Annals of Operations Research, Springer, vol. 152(1), pages 297-317, July.
    2. Utz, Sebastian & Wimmer, Maximilian & Hirschberger, Markus & Steuer, Ralph E., 2014. "Tri-criterion inverse portfolio optimization with application to socially responsible mutual funds," European Journal of Operational Research, Elsevier, vol. 234(2), pages 491-498.
    3. Huizhen Zhang & Cesar Beltran-Royo & Liang Ma, 2013. "Solving the quadratic assignment problem by means of general purpose mixed integer linear programming solvers," Annals of Operations Research, Springer, vol. 207(1), pages 261-278, August.
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    Cited by:

    1. Lamia Zerfa & Mohamed El-Amine Chergui, 2022. "Finding non dominated points for multiobjective integer convex programs with linear constraints," Journal of Global Optimization, Springer, vol. 84(1), pages 95-117, September.
    2. Angelo Aliano Filho & Antonio Carlos Moretti & Margarida Vaz Pato & Washington Alves Oliveira, 2021. "An exact scalarization method with multiple reference points for bi-objective integer linear optimization problems," Annals of Operations Research, Springer, vol. 296(1), pages 35-69, January.

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