Научны(е)й руководител(и)ь : Philippe CHRÉTIENNE

Со-руководитель : FOUILHOUX Pierre

Conception de réseaux en anneaux-étoiles et programmation mathématique

In this document, we adress the problem of covering a graph with ring-stars. We show that designing a SDH networks reduces to solving the ring-star covering problem. We discuss the encoding of a solution and present three integer programming formulations. We study from a polyhedral point of view the dominant of the polytope associated to the natural formulation and develop a Branch-and-Cut algorithm based on these results. We also propose a set partitionning formulation containing an exponential number of variables that we solve by a column generation technique. Since the classical algorithmic approach would not lead to an efficient pricing procedure, we present a method that allows to handle set partitionning inequalities using a Branch-and-Cut algorithm to solve the auxiliary problem. The resulting Branch-and-Cut-and-Price algorithm is tested on randomly generated instances.

Публикации 2011-2014