Effective Neighborhood Structures for the Generalized Traveling Salesman Problem Bin Hu and G¨ unther R. Raidl Institute of Computer Graphics and Algorithms Vienna University of Technology Favoritenstraße 9–11/1861, 1040 Vienna, Austria {hu|raidl}@ads.tuwien.ac.at Abstract. We consider the generalized traveling salesman problem in which a graph with nodes partitioned into clusters is given. The goal is to identify a minimum cost round trip visiting exactly one node from each cluster. For solving difficult instances of this problem heuristically, we present a new Variable Neighborhood Search (VNS) approach that utilizes two complementary, large neighborhood structures. One of them is the already known generalized 2-opt neighborhood for which we pro- pose a new incremental evaluation technique to speed up the search significantly. The second structure is based on node exchanges and the application of the chained Lin-Kernighan heuristic. A comparison with other recently published metaheuristics on TSPlib instances with geo- graphical clustering indicates that our VNS, though requiring more time than two genetic algorithms, is able to find substantially better solutions. Key words: Network Design, Generalized Traveling Salesman Problem, Variable Neighborhood Search 1 Introduction The Generalized Traveling Salesman Problem (GTSP) extends the classical Traveling Salesman Problem (TSP) and is defined as follows. We consider an undirected weighted complete graph G = 〈V,E,c〉 with node set V , edge set E, and edge cost function c : E → R + . Node set V is partitioned into r pairwise disjoint clusters V 1 ,V 2 ,...,V r ,  r i=1 V i = V, V i ∩ V j = ∅, i,j =1,...,r, i = j . V1 V2 V3 V4 V5 p1 p2 p4 p5 p3 Fig. 1. Example for a GTSP solution.