A flexible variable neighbourhood search algorithm for different variants of the Electric Vehicle Routing Problem

This manuscript presents a flexible variable neighbourhood search (VNS)-based (Flexi-VNS) algorithm to tackle both the classical Electrical Vehicle Routing Problem (EVRP) and the Battery Swap Station Location -routing Problem with Capacitated Electric Vehicles (BSS-EV-LRP). The latter has been addressed in just a few studies. It incorporates into the EVRP the battery swapping stations (BSS) location requirement to be jointly taken with decisions on the routing of electric vehicles. The Flexi-VNS algorithm includes a Randomised Variable Neighbourhood Descent (RVND) method as the local search procedure, which incorporates a new intra-RVND procedure called every time a solution is modified and applied only to those routes that have been modified. We assess the performance of Flexi-VNS on EVRP and BSS-EV-LRP benchmark instances and compare it with some algorithms in the literature. The statistical test did not guarantee the existence of a statistical difference between the proposed algorithm and the best algorithm from the literature for each problem, considering a 95% confidence level. However, despite this, computational results showed the Flexi-VNS efficiency. It improved several of the best-known solutions and reduced the number of constructed battery swap stations. More specifically, Flexi-VNS was able to equal or improve the BKS values of 15 out of a total of 20 instances with available results in the literature for BSS-EV-LRP and 47 out of 52 instances available for the EVRP, totalling 75% of the BSS-EV-LRP instances and 90.38% of the EVRP instances. Furthermore, compared to the exact algorithms, the optimal solutions were found using only a fraction of the computational times reported. Additionally, Flexi-VNS was the first to provide solutions for some BSS-EV-LRP instances.