A Study on Optimization of Truck-Drone Parcel Delivery Using Metaheuristics

Abstract

This research addresses a variant of the traveling salesman problem in drone-based delivery systems known as the TSP-D. The TSP-D is a combinatorial optimization problem in which a truck and a drone collaborate to deliver parcels to customers, with the objective of minimizing the total delivery time. Determining the optimal solution is NP-hard; thus, the size of the problems that can be solved optimally is limited. Therefore, metaheuristics are used to solve the problem. Metaheuristics are adaptive and intelligent algorithms that have proved their success in many similar problems. This study proposes a hybrid meta-heuristic solution to the TSP-D problem, where the solution is initialized from the optimal TSP solution reached by the Concorde TSP solver. Next, the delivery routes for the truck and the drone are obtained using the greedy, randomized adaptive search procedure (GRASP) with two local search alternatives. The main contribution of this work is the application of self-adaptive selection when searching the neighbourhood in GRASP. The proposed approach was tested on 200 instances with different properties from the publicly available ”Instances of TSP with Drone” benchmark. Results were evaluated against state-of-the-art algorithms. Nonparametric statistical tests concluded that the proposed approach has comparable performance to the rival algorithms (p = 0:074) in terms of tour duration. The proposed approach has better or similar performance in instances where the drone and truck have the same speed (\(\alpha\) = 1).