A new Branch and Bound algorithm for MIQPs

Alain Billionnet (1) , Sourour Elloumi (1) , Amélie Lambert (2)

1 CEDRIC - Centre d'études et de recherche en informatique et communications
2 CEDRIC - OC - CEDRIC. Optimisation Combinatoire

Let (MQP) be a MIQP that consists in minimizing a quadratic function subject to linear constraints. Our approach to solve (MQP) is first to consider (MQP'), an equivalent MIQP that has a convex objective function, additional variables and constraints, and additionnal quadratic constraints. Then, we propose a new Branch and Bound based on the relaxation of the quadratic constraints to solve (MQP'). We perform experiments on pure-and mixed-integer instances of medium size, and show that their solution times are improved by our Branch and Bound in comparison with two existing approaches.

Keywords: General mixed-integer quadratic programming; experiments; Branch and Bound; quadratic convex relaxation

Keywords: Branche et lié aux; relaxation convexe quadratique; Générale mixte-entier quadratique; expériences

Domains: Operations Research [math.OC]

Alain Billionnet, Sourour Elloumi, Amélie Lambert. A new Branch and Bound algorithm for MIQPs. EURO 2012, Jul 2012, Vilnius, Liechtenstein. pp.57. ⟨hal-01126099⟩