We propose a heuristic algorithm capable of handling multiple variants of the vehicle routing problem with drones (VRPD). Assuming that the drone may be launched from a node and recovered at another, these variants are characterized by three axes, (1) minimizing the transportation cost or minimizing the makespan, (2) the drone is either allowed or not allowed to land while awaiting recovery, and (3) single or multiple trucks each equipped with a drone. In our algorithm, we represent a VRPD solution as a set of customer sequences and evaluate it via local search procedures solving for each sequence a problem that we refer to as the fixed route drone dispatch problem (FRDDP). Given a sequence of customers to be served by a single truck and its drone, the FRDDP selects a subset of customers to be served by the drone and determines drone launch and recovery nodes, while ensuring that each such customer is positioned between two nodes in the initial sequence. We introduce a heuristic dynamic program (HDP) to solve the FRDDP with reduced computational complexity compared to an exact solution algorithm for the problem. We reinforce our algorithm by developing filtering strategies based on the HDP. We benchmark the performance of our algorithm on nine benchmark sets pertaining to four VRPD variants resulting in 932 instances. Our algorithm computes 651 of 680 optimal solutions and identifies 189 new best-known solutions.

中文翻译：

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无人机车辆路径问题的竞争启发式算法


我们提出了一种启发式算法，能够处理无人机车辆路径问题的多种变体（VRPD）。假设无人机可以从一个节点发射并在另一个节点回收，这些变体具有三个轴的特征，（1）最小化运输成本或最小化完工时间，（2）无人机在等待时允许或不允许着陆回收，以及 (3) 单辆或多辆卡车，每辆卡车配备一架无人机。在我们的算法中，我们将 VRPD 解决方案表示为一组客户序列，并通过本地搜索程序对其进行评估，解决每个序列的问题，我们将其称为固定路线无人机调度问题 (FRDDP)。给定由单辆卡车及其无人机服务的一系列客户，FRDDP 选择由无人机服务的客户子集并确定无人机发射和回收节点，同时确保每个此类客户位于系统中的两个节点之间初始序列。我们引入启发式动态程序（HDP）来求解 FRDDP，与该问题的精确求解算法相比，其计算复杂度降低。我们通过开发基于 HDP 的过滤策略来强化我们的算法。我们在与 4 个 VRPD 变体相关的 9 个基准集上对算法的性能进行了基准测试，产生了 932 个实例。我们的算法计算 680 个最佳解决方案中的 651 个，并识别出 189 个新的最知名解决方案。