Mardi 12 Janvier
Heure: 
12:30  13:30 
Lieu: 
Salle B107, bâtiment B, Université de Villetaneuse 
Résumé: 
An Exact Semidefinite Programming Approach for the MaxMean Dispersion Problem 
Description: 
Michele Garraffa This work proposes an exact algorithm for the MaxMean Dispersion Problem (MaxMean DP), an NPhard combinatorial optimization problem whose aim is to select the subset of a set such that the average distance between elements is maximized. The problem admits a natural nonconvex quadratic fractional formulation from which a semidefinite programming (SDP) relaxation can be derived. In general, semidefinite relaxations have been successfully used to determine tight (but usually computationally expensive) lower/upper bounds for challenging NPhard problems, such as the Quadratic Assignment Problem and the Quadratic Knapsack Problem. The semidefinite relaxation for the MaxMean DP can be further tightened by means of a cutting plane algorithm which iteratively adds the most violated triangular inequalities. The proposed approach embeds the SDP relaxation and the cutting plane algorithm into a branch and bound framework to solve MaxMean DP instances to optimality. To authors' knowledge, this is the first exact algorithm that has been proposed for this problem. Computational experiments show that the proposed method is able to solve to optimality in reasonable time instances with up 100 elements, while standard methods for fractional combinatorial optimization manage instances whose size is less then or equal to 75. The presented approach can be generalized to other combinatorial problems with a quadratic fractional objective and linear constraints. 
Heure: 
14:00  17:00 
Lieu: 
Salle B107, bâtiment B, Université de Villetaneuse 
Résumé: 
TBC 
Description: 
Julien Courtiel 

