Luis Miguel Torres

Real-Time Dispatching of Guided and Unguided Automobile Service Units with Soft Time Windows

We investigate a real-world large scale vehicle dispatching problem with strict real-time requirements, posed by our cooperation partner, the German Automobile Association. We present computational experience on real-world data with a dynamic column generation method employing a portfolio of acceleration techniques. Our computer program ZIBDIP yields solutions on heavy-load real-world instances (215 service requests, 95 service units) in less than a minute that are no worse than 1% from optimum on state-of-the-art personal computers.

Encoding the dynamics of deterministic systems

We present a model for the dynamics of discrete deterministic systems, based on an extension of the Petri nets framework. Our model relies on the definition of a priority relation between conflicting transitions, which is encoded by orienting the edges of a transition conflict graph. We provide a characterization in terms of a local consistency condition of those deterministic systems whose dynamic behavior can be encoded using our approach. Finally, we consider the problem of recognizing when an orientation of the transition conflict graph is valid for encoding the dynamic behavior of a system.

Online-Dispatching of Automobile Service Units

We present an online algorithm for a real-world vehicle dispatching problem at ADAC; the German Automobile Association.

Model reconstruction for discrete deterministic systems

Abstract In a previous paper [Torres, L.M. and A.K. Wagler, Encoding the dynamics of deterministic systems, Preprint 09-29, Otto-von-Guericke Universitat, FMA (2009)] we proposed a compact model for encoding the dynamic behavior of certain discrete deterministic systems based on extending the widely accepted framework of Petri nets. Here, the problem of reconstructing such a model from experimental data obtained by observation of dynamic processes in the system is addressed. This is equivalent to inferring a valid orientation of a certain transition conflict graph. For a special class of systems where the corresponding valid orientations are acyclic, we present a lower bound on the number of experiments required for model reconstruction and show that it is not possible to devise a solution strategy that achieves this bound for every instance.

On the Chvátal rank of linear relaxations of the stable set polytope

We study the Chvatal rank of two linear relaxations of the stable set polytope, the edge constraint and the clique constraint stable set polytope. For some classes of graphs whose stable set polytope is given by 0/1-valued constraints only, we present either the exact value of the Chvatal rank or upper bounds (of the order of their largest cliques and stable sets), which improve the bounds previously known from the literature (of the order of the graph itself).

On the first Chvátal closure of the set covering polyhedron related to circulant matrices

Abstract We study the set covering polyhedron related to circulant matrices. In particular, our goal is to characterize the first Chvatal closure of the usual fractional relaxation. We present a family of valid inequalities that generalizes the family of minor inequalities previously reported in the literature. This family includes new facet-defining inequalities for the set covering polyhedron.

Line planning on tree networks with applications to the Quito Trolebús system

We discuss an optimization model for the line planning problem in public transport in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the computational complexity of this problem for tree network topologies as well as several categories of line operations that are important for the Quito Trolebus system. In practice, these instances can be solved quite well, and significant optimization potentials can be demonstrated.

On the Chvátal-rank of Antiwebs

Abstract We present an algorithm for computing both upper and lower bounds on the Chvatal-rank of antiwebs, starting from the edge constraint stable set polytope. With the help of this algorithm we have been able to compute the exact values of the Chvatal-rank for all antiwebs containing up to 5,000 nodes. Moreover, the algorithm can be easily adapted to start from the clique constraint stable set polytope.

Generalized minor inequalities for the set covering polyhedron related to circulant matrices

We study the set covering polyhedron related to circulant matrices. In particular, our goal is to characterize the first Chvatal closure of the usual fractional relaxation. We present a family of valid inequalities that generalizes the family of minor inequalities previously reported in the literature and includes new facet-defining inequalities. Furthermore, we propose a polynomial time separation algorithm for a particular subfamily of these inequalities.

Minor related row family inequalities for the set covering polyhedron of circulant matrices

Abstract Row family inequalities defined in [Argiroffo, G. and S. Bianchi, Row family inequalities for the set covering polyhedron, Electronic Notes in Discrete Mathematics 36 (2010), pp. 1169–1176] are revisited in the context of the set covering polyhedron of circulant matrices Q ⁎ ( C n k ) . A subclass of these inequalities, together with boolean facets, provides a complete linear description of Q ⁎ ( C n k ) . The relationship between row family inequalities and minor inequalities is further studied.