Some Interval Approximation Techniques for MINLP

Nicolas Berger (1) , Laurent Granvilliers (1)

1 LINA - Laboratoire d'Informatique de Nantes Atlantique

MINLP problems are hard constrained optimization problems, with nonlinear constraints and mixed discrete continuous variables. They can be solved using a Branch-and-Bound scheme combining several methods, such as linear programming, interval analysis, and cutting methods. Our goal is to integrate constraint programming techniques in this framework. Firstly, global constraints can be introduced to reformulate MINLP problems thus leading to clean models and more precise computations. Secondly, interval-based approximation techniques for nonlinear constraints can be improved by taking into account the integrality of variables early. These methods have been implemented in an interval solver and we present experimental results from a set of MINLP instances.

Domaines: Intelligence artificielle [cs.AI]

Nicolas Berger, Laurent Granvilliers. Some Interval Approximation Techniques for MINLP. SARA 2009: The Eighth Symposium on Abstraction, Reformulation and Approximation, Jul 2009, Lake Arrowhead, California, United States. pp.26-33. ⟨hal-00462786⟩