A memetic algorithm with a large neighborhood crossover operator for the generalized traveling salesman problem

Boris Bontoux (1) , Christian Artigues (2) , Dominique Feillet (3)

1 LIA - Laboratoire Informatique d'Avignon
2 LAAS-MOGISA
3 SFL-ENSMSE - Département Sciences de la Fabrication et Logistique

The Generalized Traveling Salesman Problem (GTSP) is a generalization of the well-known Traveling Salesman Problem (TSP), in which the set of nodes is divided into mutually exclusive clusters. The objective of the GTSP consists in visiting each cluster exactly once in a tour, while minimizing the sum of the routing costs. This paper addresses the solution of the GTSP using a Memetic Algorithm procedure. The originality of our approach rests on the crossover procedure that uses a large neighborhood search. This algorithm is compared with other algorithms on a set of 41 standard test problems with up to 442 nodes. The obtained results show that our algorithm is efficient in both solution quality and computation time.

Domaines: Recherche opérationnelle [math.OC]

Boris Bontoux, Christian Artigues, Dominique Feillet. A memetic algorithm with a large neighborhood crossover operator for the generalized traveling salesman problem. Computers and Operations Research, 2010, 37 (11), pp.1844-1852. ⟨10.1016/j.cor.2009.05.004⟩. ⟨hal-00238472v2⟩