A unified solution framework for truck-and-drone routing problems

TL;DR

This paper introduces a unified three-phase framework based on the Lin-Kernighan-Helsgaun algorithm for solving various truck-and-drone routing problems, improving efficiency and solution quality across multiple delivery scenarios.

Contribution

It presents a versatile, unified solution framework that can adapt to different operational modes of truck-and-drone routing problems, maintaining structural validity and enhancing solution quality.

Findings

Framework closely matches optimal solutions on small instances

It improves best-known solutions for several medium instances

Demonstrates high flexibility across different problem variants

Abstract

Coordinated truck-and-drone routing integrates the high capacity and range of ground vehicles with the flexible routing and speed of drones, enabling simultaneous service. Increasingly applied in last-mile delivery, this synchronization helps reduce completion time and operational costs. To improve its efficiency, various coordination modes between trucks and drones have been proposed. Each mode accommodates diverse operational constraints tailored to particular delivery requirements. In existing work, a slight change in the structural framework or operational characteristics could generate a totally different problem variant, which often requires the design of specialized algorithms. Consequently, under the requirement of maintaining structural validation and adapting to multiple operational features, this paper presents a unified three-phase solution framework based on the Lin-Kernighan-Helsgaun algorithm to solve a wide family of truck-and-drone routing problems. To validate its flexibility and effectiveness, we carry out numerical experiments on three problem variants: the Flying Sidekick Traveling Salesman Problem (FSTSP), the Traveling Salesman Problem with Multiple Drones (TSP-mD), and the Vehicle Routing Problem with Drones (VRP-D), benchmarking each against an effective algorithm. Computational results show that the framework can closely match optimal solutions on small-size instances and even improve the best-known solutions for several medium-size instances. Moreover, additional extensions are discussed to further highlight its versatility.