Sequential and Parallel Local Search for the Time-Constrained Traveling Salesman Problem

In memory ofPaolo Camerini Local search is a well-known and a well·investigated solution approach for the traveling salesman problem. It is not obvious, however, how local search for the TSP has to be implemented efficiently when each city has to be visited within one or more given time windows.1bis is particularly true when parallel computer architectures are available. We consider these questions. Sequential and parallel local search for the time-constrained traveling salesman problem In memory ofPaolo Camerini 1. Introduction Like so many other approaches in combinatorial optimization, local search was first seriously investigated in the context of the traveling salesman problem. Lin [1965] calls a traveling salesman tour k-optimal when it cannot be improved by replacing a set of k of its edges by another set of k edges. It is not known whether, for any fixed value of k"?2, a k-optimal tour can be generated in polynomial time. However, it is trivial to observe that the k-optimality of a given tour through n