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

Author

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  • 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. Fred Glover, 1975. "Improved Linear Integer Programming Formulations of Nonlinear Integer Problems," Management Science, INFORMS, vol. 22(4), pages 455-460, December.
    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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    Cited by:

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    2. John Martinovic & Markus Hähnel & Guntram Scheithauer & Waltenegus Dargie, 2022. "An introduction to stochastic bin packing-based server consolidation with conflicts," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 296-331, July.

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