2016

Heure:	10:30 - 11:30
Lieu:	Salle B107, bâtiment B, Université de Villetaneuse
Résumé:	Solving the Asymmetric Travelling Salesman Problem
Description:	Luis Gouveia There are many ways of modelling the Asymmetric Traveling Salesman Problem (ATSP) and the related Precedence Constrained ATSP (PCATSP). In this talk we present new formulations for the two problems that can be viewed as resulting from combining precedence variable based formulations, with network flow based formulations. As suggested in [1], the former class of formulations permits to integrate linear ordering constraints. The motivating formulation for this work is a complicated and "ugly" formulation that results from the separation of generalized subtour elimination constraints presented in [2] (see also [1]). This so called "ugly" formulation exhibits, however, one interesting feature, namely the "disjoint subpaths" property that is further explored to create more complicated formulations that combine two (or three) "disjoint path" network flow based formulations and have a stronger linear programming bound. Some of these stronger formulations are related to the ones presented for the PCATSP in [3] and can be viewed as generalizations in the space of the precedence based variables. Several sets of projected inequalities in the space of the arc and precedence variables and in the spirit of many presented in [1] are obtained by projection from these network flow based formulations. Computational results will be given for the ATSP and PCATSP to evaluate the quality of the new models and inequalities. References: [1] L. Gouveia and P. Pesneau. On extended formulations for the precedence constrainted asymmetric traveling salesman problem. Networks, 48(2):77{89, 2006. [2] L. Gouveia and J. M. Pires. The asymmetric travelling salesman problem: On generalizations of disaggregated Miller-Tucker-Zemlin constraints. Discrete Applied Mathematics, 112:129{145, 2001. Joint work with Pierre Pesneau (University of Bordeaux), Mario Ruthmair (University of Vienna) and Daniel Santos (University of Lisbon)

Heure:	12:30 - 13:30
Lieu:	Salle B107, bâtiment B, Université de Villetaneuse
Résumé:	Lower bounds in resource constrained shortest path algorithms
Description:	Axel Parmentier Resource constrained shortest path problems arise naturally as pricing sub-problems of column generation approaches to a wide range of routing and scheduling problems. The algorithms for these problems rely on dominance relations between paths to discard partial solutions in an enumeration of all the paths. It is well known that the use of bounds on paths resources in addition to dominance relations strongly accelerates these algorithms. Nonetheless, there is still no standard procedure to build such bounds in non-linear or stochastic settings. We provide such a bounding procedure and sho w its efficiency on several deterministic and stochastic path problems. Besides, enumeration algorithms exhibit poor performances when the number of constraints increases. We show that using sets of bounds instead of single bounds enable to discard more paths and thus to tackle better with these difficult instances. Finally, we prove the relevance of these procedures in the context of column generation on industrial instances of the airline crew pairing problem.Â