A Hybrid Metaheuristic Solution Method to Traveling Salesman Problem with Drone

Abstract

The challenging idea of using drones in last-mile delivery systems of logistics addresses a new routing problem referred to as the traveling salesman problem with drone (TSP-D). TSP-D aims to construct a route to deliver parcels to a set of customers by either a truck or a drone, thereby minimizing operational costs. Since TSP-D is considered NP-hard, using metaheuristics is one of the most promising solutions. This paper presents a hybrid metaheuristic solution method of TSP-D based on two state-of-the-art algorithms: the genetic algorithm and ant colony optimization algorithm. Heuristics in TSP-D literature are based on two consequent decisions: truck routing and drone assignment. Unlike those in the existing literature, the proposed metaheuristic constructs both truck and drone routes simultaneously. Additionally, to the best of our knowledge, we introduce for the first time a solution method on the basis of an ant colony optimization approach to TSP-D. Additionally, we propose a binary pheromone framework for both drone and truck, diverging from the traditional pheromone structure. Computational experiments indicate that the proposed hybrid metaheuristic algorithm is able to generate optimal routes for provided instances of TSP-D benchmarking. In addition, the algorithm improves the best-known solutions of some instances found by rival heuristics.