AN EFFICIENT COMPOSITE HEURISTIC FOR THE SYMMETRIC GENERALIZED TRAVELING SALESMAN PROBLEM Jacques Renaud and Fayez F. Boctor Télé-Université, Université du Québec, Canada, and Université Laval, Canada. ABSTRACT The main purpose of this paper is to introduce a new composite heuristic for solving the generalized traveling salesman problem. The proposed heuristic is composed of three phases: the construction of an initial partial solution, the insertion of a node from each non-visited node-subset, and a solution improvement phase. We show that the heuristic performs very well on thirty six TSPLIB problems which have been solved to optimality by other researchers. We also propose some simple heuristics that can be used as basic blocks to construct more efficient composite heuristics. Keywords: Generalized traveling salesman problem, heuristics. 1- INTRODUCTION This paper deals with the problem known as the generalized traveling salesman problem (GTSP); a special case of the well known traveling salesman problem (TSP). In this case, the salesman must pass through a number of predefined subsets of customers, visiting at least one customer in each subset while minimizing the sum of traveling costs. Thus, in addition to determining the order in which the subsets should be visited, the salesman should choose the customer or the customers to be visited in each subset. The GTSP may be defined on either a directed graph or an undirected graph and may be either symmetric or asymmetric. The most studied version of this problem is the one where the salesman should visit exactly one customer in each subset. Obviously, even if it is not required explicitly, the optimal tour will visit only one customer in each subset when travel costs are symmetrical and satisfy the triangle inequality (see Laporte and Nobert 1983).