A column generation algorithm for the team orienteering problem with time windows

un algorithme de génération de colonnes pour la résolution du problème de tournées sélectives avec fenêtres de temps

Racha El-Hajj (1, 2, 3) , Aziz Moukrim (2, 3) , B Chebaro (1) , M Kobeissi (1)

1 UNIVERSITE LIBANAISE Faculté de Sciences II
2 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]
3 Labex MS2T - Laboratoire d'Excellence "Maîtrise des Systèmes de Systèmes Technologiques"

The Team Orienteering Problem with Time Windows (TOPTW) is a well-known variant of the Vehicle Routing Problem (VRP) whose aim is to maximize the total amount of profit collected from the visited customers while taking into consideration some resource limitations. In this variant, customers must be served at most once in their time windows while respecting the predefined maximum travel time limit of each vehicle. In this paper we propose a column generation based algorithm to solve the linear relaxation of TOPTW. A dynamic programming algorithm is used to solve the subproblems in order to generate additional columns. Experiments conducted on the benchmark of TOPTW show the effectiveness of our algorithm and the strengthen of our formulation since we were able to prove the optimality of several instances by finding their integer solutions at the root node while solving the linear relaxation of the model.

Mots clés: Column Generation; Dynamic Programming; Vehicle Routing Problem with profit; Time Windows

Domaines: Recherche opérationnelle [math.OC]

Racha El-Hajj, Aziz Moukrim, B Chebaro, M Kobeissi. A column generation algorithm for the team orienteering problem with time windows. The 45th International Conference on Computers & Industrial Engineering (CIE45), Oct 2015, Metz, France. ⟨hal-01261179⟩