Iterated Maximum Large Neighborhood Search for the Traveling Salesman Problem with Time Windows and its Time-dependent Version

Abstract

This article introduces a new algorithm for finding feasible or makespan-optimal solutions of Traveling Salesman Problems with Time Windows (TSPTWs) and Time-Dependent TSPTWs (TDTSPTWs). The algorithm starts from a sequence of visits of the customers involved in the problem, uses destroy and repair operations to iteratively improve this sequence, and applies perturbations to diversify search. For the destroy phase, customers are removed from the current sequence of visits as long as a parameter called the insertion-width is not too high. For the repair phase, the customers removed are reinserted for the best based on a dynamic programming procedure whose complexity is only linear in the number of customers. For the perturbation phase, some customers are randomly shifted in the sequence of visits. The algorithm obtained is called Iterated Maximum Large Neighborhood Search (ImaxLNS). On seven standard TSPTW benchmarks, it returns the best-known solution for each instance in less than one second on average. On two TDTSPTW benchmarks related to urban logistics, it provides new feasible solutions and best solutions. On a TDTSPTW benchmark related to Earth observing satellites, it solves most of the instances in less than a second.