Exact and heuristic approaches for traveling salesman problems with drones.

Abstract

The technological advances concerning drones have encouraged the market to consider drone applications in different areas including last mile delivery. However, limitations due to battery capacity, maximum weight, and legal regulations restrict the effective operational range of drones in many practical applications. To overcome the battery issue, hybrid operations involving one or more drones launching from a larger vehicle have emerged, in which the larger vehicle operates as a mobile depot and a recharging platform. In this dissertation, we describe a routing model that leverage the drone and truck working as a synchronized unit. The Flying Sidekick Traveling Salesman Problem (FSTSP) considers a delivery system composed by a truck and a drone. The drone launches from the truck with a single package to deliver to a customer. Each drone must return to the truck to recharge batteries, pick up another package, and launch again to a new customer location. This work proposes two novel Mixed Integer Programming (MIP) formulations and a heuristic approach to address the problem. The proposed MIP formulations yields better linear relaxation bounds than previously proposed formulations for all instances, and was capable of optimally solving several unsolved instances from the literature. We developed a hybrid heuristic based on the General Variable Neighborhood Search metaheuristic to tackle a generalization of the FSTSP called Multiple Traveling Salesman Problem with Drones, in which multiple trucks and drones are considered as part of the delivery system. The heuristic obtained high-quality solutions for large-size instances. The efficiency of the algorithm was evaluated on 410 benchmark instances from the literature, and over 80% of the best known solutions were improved.