2015

Heure:	12:30 - 13:30
Lieu:	Salle B107, bâtiment B, Université de Villetaneuse
Résumé:	Multiband Robust Optimization: theory and applications
Description:	Fabio D'Andreagiovanni Over the last years, Robust Optimization (RO) has emerged as an effective and efficient methodology to tackle data uncertainty in real-world optimization problems. RO takes into account data uncertainty in the shape of hard constraints that restrict the feasible set and maintain only robust solutions, i.e. solutions that remain feasible even when the values of the input data change. In this talk, we provide an overview of our research about theory and applications of RO. Specifically, we present Multiband Robustness, a new model for RO that we recently proposed to generalize and refine the classical Gamma-robustness model by Bertsimas and Sim. The main aim of our new model is to provide a refined representation of arbitrary non- symmetric distributions of the uncertainty, that are commonly present in real-world applications. Such refined representation grants a reduction in conservatism of robust solutions, while maintaining the accessibility and computational tractability that have been a key factor of success of Gamma-robustness. We also provide an overview of applications of the Multiband model to real-world problems that we have considered in past and ongoing research and industrial projects.

Heure:	12:30 - 13:30
Lieu:	Salle B107, bâtiment B, Université de Villetaneuse
Résumé:	Unit Commitment problems: approaches and solution algorithms
Description:	Claudio Gentile The Unit Commitment is a the problem to manage a set of power generating units of different types over a short time horizon. Unit Commitment is formulated as a Mixed Integer Nonlinear Programming problem. It requires special techniques to handle both the large size of the instances to be solved and the nonlinearity of the objective function. Two main approaches have been used in its solution: the Lagrangian Relaxation coupled with primal heuristics and MILP approximations. We discuss some new advancements for both approaches.

Heure:	12:30 - 13:30
Lieu:	Salle B107, bâtiment B, Université de Villetaneuse
Résumé:	Exact Algorithms for Nonconvex Quadratic Integer Optimization
Description:	Christoph Buchheim The talk addresses the problem of minimizing a quadratic objective function over integer variables. Even in the most simple case of binary or box-constrained integer variables, such problems are very hard to solve in theory and in practice. In fact, the problem remains NP-hard both in the case of a convex objective function over binary variables (then being equivalent to max-cut) and in the case of a non-convex objective function over the unit cube (the so-called BoxQP). After shortly reviewing some classical approaches for quadratic discrete optimization, we present two recent methods that are specifically designed for the nonconvex case, aiming at relaxations that jointly address the nonconvexity of the objective function and the nonconvexity of the discrete variable domains. While the first approach results in a semidefinite relaxation of the problem, the second approach uses ellipsoidal relaxations; both approaches can be embedded into branch-and-bound schemes. We present experimental results for the resulting algorithms, showing that the SDP-based approach yields very strong dual bounds that however take more time to be computed, while the second approach based on ellipsoidal relaxations is able to enumerate a large number of nodes in a short time due to a sophisticated preprocessing phase. The resulting total running times are comparable; both approaches however significantly outperform standard software such as Couenne or BARON.