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Theoretical and computational study of several linearisation techniques for binary quadratic problems

Author

Listed:
  • Fabio Furini

    (Université Paris Dauphine)

  • Emiliano Traversi

    (Université de Paris 13)

Abstract

We perform a theoretical and computational study of the classical linearisation techniques (LT) and we propose a new LT for binary quadratic problems (BQPs). We discuss the relations between the linear programming (LP) relaxations of the considered LT for generic BQPs. We prove that for a specific class of BQP all the LTs have the same LP relaxation value. We also compare the LT computational performance for four different BQPs from the literature. We consider the Unconstrained BQP and the maximum cut of edge-weighted graphs and, in order to measure the effects of constraints on the computational performance, we also consider the quadratic extension of two classical combinatorial optimization problems, i.e., the knapsack and stable set problems.

Suggested Citation

  • Fabio Furini & Emiliano Traversi, 2019. "Theoretical and computational study of several linearisation techniques for binary quadratic problems," Annals of Operations Research, Springer, vol. 279(1), pages 387-411, August.
    • Handle: RePEc:spr:annopr:v:279:y:2019:i:1:d:10.1007_s10479-018-3118-2
    DOI: 10.1007/s10479-018-3118-2
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    References listed on IDEAS

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    5. Caprara, Alberto, 2008. "Constrained 0-1 quadratic programming: Basic approaches and extensions," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1494-1503, June.
    6. Billionnet, Alain & Soutif, Eric, 2004. "An exact method based on Lagrangian decomposition for the 0-1 quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 157(3), pages 565-575, September.
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