There are emerging transportation problems known as the Traveling Salesman Problem with Drone (TSPD) and the Flying Sidekick Traveling Salesman Problem (FSTSP) that involve using a drone in conjunction with a truck for package delivery. This study presents a hybrid genetic algorithm for solving TSPD and FSTSP by incorporating local search and dynamic programming. Similar algorithms exist in the literature. Our algorithm, however, considers more sophisticated chromosomes and less computationally complex dynamic programming to enable broader exploration by the genetic algorithm and efficient exploitation through dynamic programming and local search. The key contribution of this paper is the discovery of how decision-making processes for solving TSPD and FSTSP should be divided among the layers of genetic algorithm, dynamic programming, and local search. In particular, our genetic algorithm generates the truck and the drone sequences separately and encodes them in a type-aware chromosome, wherein each customer is assigned to either the truck or the drone. We apply local search to each chromosome, which is decoded by dynamic programming for fitness evaluation. Our new algorithm is shown to outperform existing algorithms on most benchmark instances in both quality and time. Our algorithms found the new best solutions for 538 TSPD instances out of 920 and 74 FSTSP instances out of 132.

翻译：新兴的运输问题包括带无人机的旅行商问题（TSPD）和飞行搭档旅行商问题（FSTSP），这些问题涉及将无人机与卡车协同使用以完成包裹投递。本研究提出一种混合遗传算法，通过结合局部搜索和动态规划来求解TSPD和FSTSP。文献中已有类似算法，但我们的算法采用了更复杂的染色体和计算复杂度更低的动态规划，从而通过遗传算法实现更广泛的探索，并通过动态规划和局部搜索实现高效的利用。本文的关键贡献在于揭示了求解TSPD和FSTSP的决策过程应如何在遗传算法、动态规划和局部搜索的层级间进行划分。具体而言，我们的遗传算法分别生成卡车和无人机的序列，并将其编码为类型感知染色体，其中每个客户被分配给卡车或无人机。我们对每个染色体应用局部搜索，并通过动态规划解码以评估适应度。实验表明，新算法在大多数基准实例上，在求解质量和时间方面均优于现有算法。在920个TSPD实例中，我们的算法找到了538个实例的新最优解；在132个FSTSP实例中，找到了74个实例的新最优解。