A Beam Search Heuristic for the Traveling Salesman Problem with Time Windows

Abstract

The traveling salesman problem with time windows (TSPTW) is a variety of the traveling salesman problem. In practice, temporal aspect is a necessary constraint with respect to the routing problems. TSPTW is a NP-hard problem, and computational time of exact algorithm increases exponentially as the number of customers increases. Hence, we present a beam search (BS) algorithm which is a heuristic based on breadth-first branch-and-bound without backtracking to solve the TSPTW. BS filters out worse nodes by a local evaluation and only keeps β (called beam width) nodes according to global evaluation at each level. In our BS, both one-step local evaluation and global evaluation are applied to estimate cost of nodes by inserting unvisited nodes of a given initial solution. The computational results on test instances from the literature show that our beam search can obtain good solutions with effective computational times for TSPTW.