The increasing use of drones to perform various tasks has motivated an exponential growth of research aimed at optimizing the use of these means, benefiting both military and civilian applications, including logistics delivery. In this sense, the combined use of trucks and drones has been explored with great interest by Operations Research. This work presents mathematical formulations in Mixed Integer Linear Programming and proposes a hybrid Genetic Algorithm (HGenFS) for optimizing a variation of the Traveling Salesman Problem (TSP) called Flying Sidekick TSP (FSTSP), in which truck and drone cooperate. The results obtained confirmed that the adopted formulation for the exact solution is suitable for solving problems up to ten customers, and the HGenFS proved to be capable of finding optimal solutions for the FSTSP in a few seconds by incorporating specific heuristics and a local search phase.

翻译：无人机在多种任务中的日益普及，激发了旨在优化其使用的研究呈指数增长，这既有利于军事和民用应用，也包括物流配送。在此背景下，卡车与无人机的协同使用已成为运筹学领域备受关注的研究方向。本文提出了混合整数线性规划的数学公式，并设计了一种混合遗传算法（HGenFS），用于优化旅行商问题（TSP）的一种变体——飞行副手旅行商问题（FSTSP），其中卡车与无人机协同工作。研究结果表明，所采用的精确求解公式适用于解决最多十名客户的问题，而HGenFS通过融入特定启发式算法和局部搜索阶段，能够在几秒内找到FSTSP的最优解。