Abstract: After a major disaster occurs, it is often accompanied by the destruction of transportation infrastructure such as roads and bridges, which will seriously hinder the transportation of materials and further increase the losses in the disaster-stricken areas. In addition, during the rescue process, it is often difficult to accurately determine the demand in the disaster-stricken area. This uncertainty may make it difficult for rescue workers to effectively assess the required supplies, thus endangering life safety and recovery efforts in the disaster-stricken area. At the same time, ensuring equity in disaster-stricken areas is also crucial. If fairness is not guaranteed, this may lead to problems such as low rescue efficiency and negative social and psychological impacts. Such emotions may trigger mass incidents and social instability, thereby hampering the normal progress of rescue efforts.
To effectively solve these problems, a collaborative delivery model of trucks and drones is proposed to improve the flexibility and efficiency of material delivery. In this context, this study proposes the Multi-Visit Vehicle Routing Problem with Drones (MVVRPD), and introduces road resistance coefficient, triangular fuzzy number and time comparison function to measure the degree of road damage, the quantity of material requirements and the fairness of arrival time. This paper establishes a mixed integer programming model that aims to minimize the latest time and total time comparison functions of vehicles returning to the depot. Furthermore, a hybrid chimp optimization algorithm is designed to solve this problem. The optimization strategy of this algorithm includes improving the quality and diversity of the initial population, using genetic algorithm operations to update the position of individuals, and combining sine-cosine operators, nonlinear learning factors, and simulated annealing acceptance criteria for local search to further optimize the solution.
Since there is no standard data test for the MVVRPD, this paper improves it based on the Solomon standard example. By adding information related to demand uncertainty and road damage, the calculation accuracy and calculation speed experiments of the MVVRPD model and HChoA algorithm are conducted. The experimental results verify the correctness of the MVVRPD model and the effectiveness of the HChoA algorithm. Finally, a sensitivity analysis is performed on road damage and fairness.

Key words: emergency logistics, truck-drone, fairness, road damage, uncertain demand, hybrid chimp optimization algorithm

摘要： 应急物流系统面临着很多的挑战,如道路受损、需求量不确定和受灾地区的“不公平感”。在这种复杂情形下,选择恰当的运输方式和科学规划路径成为亟需解决的问题之一。为了应对这一挑战,本文建立了考虑受灾点公平性的卡车和无人机协同配送路径优化模型,提出了一种混合黑猩猩优化算法(Hybrid Chimp Optimization Algorithm, HChoA)求解,并通过算例进行了仿真实验。结果表明,HChoA算法相比Gurobi在运行时间上有明显优势,且达到了相同甚至更好的结果。HChoA算法在局部搜索能力和计算精度方面都有所提高,算法的有效性得以验证。最后,对两个关键参数进行了灵敏度分析。

关键词: 应急物流, 卡车和无人机, 公平性, 道路受损, 不确定需求量, 混合黑猩猩优化算法