Fabio Furini 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 … Read more
The principal idea of this paper is to exploit Semidefinite Programming (SDP) relaxation within the framework provided by Mixed Integer Nonlinear Programming (MINLP) solvers when tackling Binary Quadratic Problems (BQP). SDP relaxation is well-known to provide strong bounds for BQP in practice. However, the method is not typically implemented in many state-of-the-art MINLP solvers based … Read more
Dantzig-Wolfe decomposition (or reformulation) is well-known to provide strong dual bounds for specially structured mixed integer programs (MIPs). However, the method is not implemented in any state-of-the-art MIP solver as it is considered to require structural problem knowledge and tailoring to this structure. We provide a computational proof-of-concept that the reformulation can be automated. That … Read more
Dantzig-Wolfe decomposition is well-known to provide strong dual bounds for specially structured mixed integer programs (MIPs) in practice. However, the method is not part of any state-of-the-art MIP solver: it needs tailoring to the particular problem; the typical bordered block-diagonal matrix structure determines the decomposition; the resulting column generation subproblems need to be solved efficiently; … Read more