There are emerging transportation problems known as the Traveling Salesman Problem with Drone (TSPD) and the Flying Sidekick Traveling Salesman Problem (FSTSP) that involve the use of a drone in conjunction with a truck for package delivery. This study represents a hybrid genetic algorithm for solving TSPD and FSTSP by combining local search methods and dynamic programming. Similar algorithms exist in the literature. Our algorithm, however, considers more sophisticated chromosomes and simpler dynamic programming to enable broader exploration by the genetic algorithm and efficient exploitation through dynamic programming and local searches. The key contribution of this paper is the discovery of how decision-making processes 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 searches to each chromosome, which is decoded by dynamic programming for fitness evaluation. Our dynamic programming algorithm merges the two sequences by determining optimal launch and landing locations for the drone to construct a TSPD solution represented by the chromosome. We propose novel type-aware order crossover operations and effective local search methods. A strategy to escape from local optima is proposed. 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 93 FSTSP instances out of 132.

翻译：新兴的运输问题——带无人机旅行商问题（TSPD）与飞行副手旅行商问题（FSTSP）——涉及卡车与无人机协同完成包裹配送。本研究提出一种混合遗传算法，通过融合局部搜索方法与动态规划来求解TSPD与FSTSP。现有文献中虽存在类似算法，但本算法采用更复杂的染色体结构与更简洁的动态规划机制，使遗传算法能够实现更广泛的探索，同时通过动态规划和局部搜索实现高效利用。本文的核心贡献在于揭示了决策过程如何在遗传算法、动态规划与局部搜索三个层面进行分工。具体而言，本算法分别生成卡车与无人机的独立任务序列，并将其编码为类型感知染色体——每个客户节点被指派给卡车或无人机。我们对每条染色体实施局部搜索，并通过动态规划解码进行适应度评估。动态规划算法通过确定无人机最优起飞与降落位置来合并两个序列，从而构建由染色体表征的TSPD解决方案。我们提出新型类型感知顺序交叉算子与高效局部搜索方法，并设计了跳出局部最优的策略。实验结果表明，本算法在大多数基准实例中在求解质量与计算时间上均优于现有算法。在920个TSPD实例中，本算法为538个实例找到新最优解；在132个FSTSP实例中，为93个实例找到新最优解。