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

Furini, Fabio; Traversi, Emiliano (2018), Theoretical and computational study of several linearisation techniques for binary quadratic problems, Annals of Operations Research, p. 1-25. 10.1007/s10479-018-3118-2

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Type
Article accepté pour publication ou publié
Date
2018
Journal name
Annals of Operations Research
Publisher
Springer
Pages
1-25
Publication identifier
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Author(s)
Furini, Fabio
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Traversi, Emiliano
Laboratoire d'Informatique de Paris-Nord [LIPN]
Abstract (EN)
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.
Subjects / Keywords
Linearisation techniques; Binary quadratic problems; Max cut problem; Quadratic knapsack problem; Quadratic stable set problem