An Evolutionary Algorithm For the Vehicle Routing Problem with Drones with Interceptions

TL;DR

This paper introduces an evolutionary algorithm to optimize last-mile delivery using trucks and drones with interception capabilities, significantly reducing total delivery time compared to existing methods.

Contribution

It proposes a novel evolutionary algorithm for the VRPDi, effectively scheduling multiple truck-drone pairs with interception, outperforming previous algorithms on benchmark datasets.

Findings

Improved total delivery time by 39-60% over baseline VRP solutions.

Successfully solved 50 and 100-node problems within reasonable computational time.

Outperformed recent algorithms in benchmark comparisons.

Abstract

The use of trucks and drones as a solution to address last-mile delivery challenges is a new and promising research direction explored in this paper. The variation of the problem where the drone can intercept the truck while in movement or at the customer location is part of an optimisation problem called the vehicle routing problem with drones with interception (VRPDi). This paper proposes an evolutionary algorithm to solve the VRPDi. In this variation of the VRPDi, multiple pairs of trucks and drones need to be scheduled. The pairs leave and return to a depot location together or separately to make deliveries to customer nodes. The drone can intercept the truck after the delivery or meet up with the truck at the following customer location. The algorithm was executed on the travelling salesman problem with drones (TSPD) datasets by Bouman et al. (2015), and the performance of the algorithm was compared by benchmarking the results of the VRPDi against the results of the VRP of the same dataset. This comparison showed improvements in total delivery time between 39% and 60%. Further detailed analysis of the algorithm results examined the total delivery time, distance, node delivery scheduling and the degree of diversity during the algorithm execution. This analysis also considered how the algorithm handled the VRPDi constraints. The results of the algorithm were then benchmarked against algorithms in Dillon et al. (2023) and Ernst (2024). The latter solved the problem with a maximum drone distance constraint added to the VRPDi. The analysis and benchmarking of the algorithm results showed that the algorithm satisfactorily solved 50 and 100-nodes problems in a reasonable amount of time, and the solutions found were better than those found by the algorithms in Dillon et al. (2023) and Ernst (2024) for the same problems.