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Extended Linear Formulation for Binary Quadratic Problems

Fabio Furini (fabio.furini82***at***gmail.com)
Emiliano Traversi (emiliano.traversi***at***gmail.com)

Abstract: In this work we propose and test a new linearisation technique for Binary Quadratic Problems (BQP). We computationally prove that the new formulation, called Extended Linear Formulation, performs much better than the standard one in practice, despite not being stronger in terms of Linear Programming relaxation (LP). We empirically prove that this behaviour is due to the fact of having a less degenerate LP. Our tests are based on two sets of classical BQP from the literature, i.e., the unconstrained binary quadratic problem and the maximum cut of edge-weighted graphs. Finally we introduce an indicator that can be used to compare two different formulations in order to identify the less degenerate one.

Keywords: Binary Quadratic Problem; Linearization Technique; Extended Formulations; Degeneracy; Maximum Cut Problem

Category 1: Integer Programming (0-1 Programming )

Category 2: Nonlinear Optimization (Quadratic Programming )


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Entry Submitted: 06/30/2013
Entry Accepted: 06/30/2013
Entry Last Modified: 11/13/2013

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