2015

Heure:	12:30 - 13:30
Lieu:	Salle B107, bâtiment B, Université de Villetaneuse
Résumé:	EXACT APPROACHES TO THE NETWORK DESIGN PROBLEM WITH RELAYS
Description:	Ivana Ljubic This work considers the Network Design Problem with Relays (NDPR). The NDPR arises in the context of network design when given node-pairs need to communicate with each other, but, due to signal deterioration, communication paths have to respect given distance limits. To cover longer distances, equipment for signal regeneration (i.e., relays) may be required. To enable required communications, one has to upgrade the network: by installing new links, by installing relays on the existing network, or by a combination of both. Besides applications in network design, the NDPR arises in the context of e-mobility where relays model charging stations for electric cars and edge costs correspond to road tolls. In contrast to previous work on the NDPR, which was mainly focused on heuristic approaches, we propose new exact approaches based on different mixed integer linear programming formulations for the problem. We develop Branch-and-Price and Branch-Price-and-Cut algorithms that build upon models with an exponential number of constraints and variables. In a computational study, we analyze the performance of these approaches for instances with different characteristics. This is a joint work with M. Leitner, M. Riedler and M. Ruthmair

Heure:	12:30 - 13:30
Lieu:	Salle B107, bâtiment B, Université de Villetaneuse
Résumé:	Approximating the energy storage problem and other continuous dynamic programs
Description:	Giacomo Nannicini We study the problem of optimally managing a source of renewable energy connected to the power grid, a battery, and potentially a household or some other form of energy sink. This problem can be naturally cast as a dynamic program. We propose a model for this problem that subsumes other models in the literature, and we analyze its complexity, showing that in the deterministic setting the problem is solvable in polynomial time, but it becomes #P-hard in the stochastic setting. A variant of the problem that is commonly encountered in practice (i.e. the one where selling energy to the power grid is not allowed) admits a Fully Polynomial Time Approximation Scheme (FPTAS) if the energy levels are discretized; but what about the more natural case where energy is considered a continuous variable? We show that in this case, the problem belongs to a class of convex continuous dynamic programs that admits neither a multiplicative nor an additive approximation. We then show that we can construct a novel type of approximation scheme, where additive and multiplicative approximation are required at the same time but both can be arbitrarily small. We discuss a preliminary computational evaluation of this new type of approximation scheme for continuous convex dynamic programs, showing its potential.

Heure:	12:30 - 13:30
Lieu:	Salle B107, bâtiment B, Université de Villetaneuse
Résumé:	Solving the quadratic shortest path problem
Description:	Borzou Rostami Finding the shortest path in a directed graph is one of the most important combinatorial optimization problems, having applications in a wide range of fields. In its basic version, however, the problem fails to represent situations in which the value of the objective function is determined not only by the choice of each single arc, but also by the combined presence of pairs of arcs in the solution. In this paper we model these situations as a Quadratic Shortest Path Problem, which calls for the minimization of a quadratic objective function subject to shortest-path constraints. We prove strong NP-hardness of the problem and analyze polynomially solvable special cases, obtained by restricting the distance of arc pairs in the graph that appear jointly in a quadratic monomial of the objective function. Based on this special case and problem structure, we devise fast lower bounding procedures for the general problem and show computationally that they clearly outperform other approaches proposed in the literature in terms of their strength.