On the general routing polytope

On the SQAP-Polytope

The SQAP-polytope was associated to quadratic assignment problems with a certain symmetric objective function structure by Rijal (1995) and Padberg and Rijal (1996). We derive a technique for investigating the SQAP-polytope that is based on projecting the (low-dimensional) polytope into a lower dimensional vector-space, where the vertices have a “more convenient” coordinate structure. We exploi...

General Cut-Generating Procedures for the Stable Set Polytope

We propose general separation procedures for generating cuts for the stable set polytope, inspired by a procedure by Rossi and Smriglio and applying a lifting method by Xavier and Campêlo. In contrast to existing cut-generating procedures, ours generate both rank and non-rank valid inequalities, hence they are of a more general nature than existing methods. This is accomplished by iteratively s...

Robust routing and optimal partitioning of a traffic demand polytope

In this paper we consider the problem of optimal partitioning of a traffic demand polytope using a hyperplane. In our model all possible demand matrices belong to a polytope. The polytope can be divided into parts, and different routing schemes can be applied while dealing with traffic matrices from different parts of the polytope. We consider three basic models, i.e., RobustRouting, No-Sharing...

On the Even Permutation Polytope

The mixed general routing polyhedron

In Arc Routing Problems, ARPs, the aim is to find on a graph a minimum cost traversal satisfying some conditions related to the links of the graph. Due to restrictions to traverse some streets in a specified way, most applications of ARPs must be modeled with a mixed graph. Although several exact algorithms have been proposed, no polyhedral investigations have been done for ARPs on a mixed grap...