On the Impact of Local Search Operators and Variable Neighbourhood Search for the Generalized Travelling Salesperson Problem

The generalized travelling salesperson problem is an important NP-hard combinatorial optimization problem where local search approaches have been very successful. We investigate the two hierarchical approaches of Hu and Raidl (2008) for solving this problem from a theoretical perspective. We examine the complementary abilities of the two approaches caused by their neighbourhood structures and the advantage of combining them into variable neighbourhood search. We first point out complementary abilities of the two approaches by presenting instances where they mutually outperform each other. Afterwards, we introduce an instance which is hard for both approaches, but where a variable neighbourhood search combining them finds the optimal solution in polynomial time.