A branch-and-cut-and-price framework for convex MINLP applied to a stochastic network design problem

Bernard Fortz (1) , Martine Labbé (2) , Michael Poss (3)

1 GOM - Graphes et Optimisation Mathématique [Bruxelles]
2 CESP - Centre de recherche en épidémiologie et santé des populations
3 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]

Many convex linearly constrained programs and mixed integer programshave a large number of variables, so that the variables shouldbe generated dynamically throughout the solution algorithm. Thisyields to the well known “branch-and-price algorithm” and “simplicialdecomposition”. We present a novel “branch-and-cut-and-pricealgorithm” to extend this idea to certain classes of convex linearly constrainedMINLP. Our algorithm incorporates the variables generationinto the “LP/NLP algorithm” introduced by Quesada and Grossman.We detail our framework for the stochastic network design problemwith simple recourse and present preliminary computational results.Keywords: convex MINLP, branch-and-price, stochastic programming,network design.

Domaines: Recherche opérationnelle [math.OC]

Bernard Fortz, Martine Labbé, Michael Poss. A branch-and-cut-and-price framework for convex MINLP applied to a stochastic network design problem. Proceedings of the European Workshop on Mixed Integer Nonlinear Programming, 2010, Unknown, Unknown Region. pp.131-138. ⟨hal-01255269⟩