The Traveling Salesman Problem with Time Windows (TSPTW) is a Vehicle Routing Problem (VRP) variant imposing time-window constraints on customer visits. The objective is to serve all customers within specified time windows while minimizing the total travel distance. Finding even a feasible solution for this problem is NP-hard. State-of-the-art local search methods typically begin with a circuit that visits all customers, possibly violating time windows, before iteratively reducing these violations through local search moves, such as shifting visits. In contrast, this paper proposes to satisfy time-window constraints while relaxing the requirement to visit all customers. It relies on constraint programming, and a model based on sequence variables for neighborhood exploration. Flexible removal and insertion-based heuristics are exploited in a large neighborhood search setting. This approach consistently yields feasible solutions in under one second for popular TSPTW benchmarks, and can be readily adapted to other routing problems.
Delecluse, A., Schaus, P., & Pascal Van Hentenryck. (2023). SEQUOIA: SEQuence-variable-based Optimization In Action for the Traveling Salesman Problem with Time Windows. Doctoral Program of CP23, Toronto. https://hdl.handle.net/2078.5/273387