Decremental State-Space Relaxations for the Basic Traveling Salesman Problem with a Drone

Abstract

Truck-and-drone routing problems have become an important research topic in the last decade because of their applications for last-mile deliveries. Despite the many publications in this area, the most efficient exact algorithms designed thus far struggle to solve the benchmark instances with 39 or more customers. This fact holds even for one of the simplest variants involving one truck and one drone whose routes must synchronize at customers’ locations: the basic traveling salesman problem with a drone (TSP-D). In this article, we devise a new algorithm for the TSP-D that solves every benchmark instance with up to 59 customers, and it scales up to 99 customers when the drone is much faster than the truck. The core of our method is a dynamic programming algorithm that is applied for column generation and variable fixing within tailored decremental state-space relaxation strategies. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This work was supported by Fondo para la Investigación Científica y Tecnológica [Grant PICT-2018-2961] (Ministry of Science, Argentina). Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0390 .