An adaptive VNS algorithm for vehicle routing problems with intermediate stops

Abstract

There are numerous practical vehicle routing applications in which vehicles have to stop at certain facilities along their routes to be able to continue their service. At these stops, the vehicles replenish or unload their cargo or they stop to refuel. In this paper, we study the vehicle routing problem with intermediate stops (VRPIS), which considers stopping requirements at intermediate facilities. Service times occur at these stops and may depend on the load level or fuel level on arrival. This is incorporated into the routing model to respect route duration constraints. We develop an adaptive variable neighborhood search (AVNS) to solve the VRPIS. The adaptive mechanism guides the shaking step of the AVNS by favoring the route and vertex selection methods according to their success within the search. The performance of the AVNS is demonstrated on test instances for VRPIS variants available in the literature. Furthermore, we conduct tests on newly generated instances of the electric vehicle routing problem with recharging facilities, which can also be modeled as VRPIS variant. In this problem, battery electric vehicles need to recharge their battery en route at respective recharging facilities.

Appendix: Influence of problem-specific components

Table 12 shows a comparison of our AVNS to an AVNS without the problem-specific components addressing intermediate stops (denoted as $\text {AVNS-without}$) on the VRPIRF instances of Crevier et al. (2007). For each instance, we report the instance name and the BKS. Moreover, we provide the average solution found in the ten runs ($L^\mathrm{{avg}}$), the gap of the average solution to the BKS ($\Delta ^\mathrm{{avg}}$) and the average runtime in minutes ($t^\mathrm{{avg}}$) for both methods. Finally, averages of the runtimes and the gaps to the BKS over the complete set of instances are given at the end of the table. Results show that adding the problem-specific components clearly improves the solution quality while notably reducing runtimes.

Table 12 Comparison of the results of our final AVNS implementation to those obtained by our AVNS without the problem-specific methods explicitly addressing intermediate stops ($\text {AVNS-without}$) on the VRPIRF instances of Crevier et al. (2007)