## 1 Introduction  
Sudden and frequent natural disasters (such as earthquakes, mudslides, infectious diseases, etc.) have damaged the economy and society of all countries worldwide, making people suffer double losses of life and property. In the initial stage of a disaster, the key to rescue operations is how to quickly make rescue action plans, meet the needs of the public for emergency materials to the greatest extent, and reduce the losses caused by disasters. Due to the suddenness and unpredictability of a disaster, the materials in the disaster area are often insufficient to ensure the development of emergency relief work, and emergency materials need to be transported from outside the disaster area to the disaster area in a short time. However, due to the damage to the road network and the poor environment in the disaster area, it is difficult for traditional truck transportation to meet the needs of each disaster-stricken area in time. Meanwhile, the timeliness and effectiveness of the distribution of emergency materials also enhance the difficulty of emergency logistics. It is of great practical significance to study the problem of multi-UAV cooperative delivery under such circumstances. Amazon first introduced the concept of drone delivery in 2013. In recent years, UAV equipment has been used to distribute emergency materials at home and abroad. Google X LABS first experimented with using drones for disaster relief and delivering aid to remote areas in 2014 and completed its first real-world delivery in rural Queensland, Australia, where it successfully delivered first aid kits, food, and water to local farmers. In the early days of the COVID-19 outbreak, Google used drones to provide contactless delivery of medicines and food to customers [1], and achieved good results. In China, Jingdong delivered supplies to sealed towns through drones [2], and the drones developed by SF Express also successfully delivered epidemic prevention supplies to hospitals [3]. With the continuous development of intelligent manufacturing and UAV technology, the wide application of UAVs has become the focus of researchers. Many studies have highlighted the critical role of drones in delivering medical supplies, helping to save more lives and reduce emergency response times [4; 5]. [PERSON] et al. [6] evaluated the efficiency of UAVs in different application scenarios, such as medical equipment delivery, blood transportation, and drug distribution. According to [PERSON] et al. [7], using drones to deliver small packages is more efficient than traditional trucking methods in terms of cost and total service time. Current research on the distribution of emergency materials includes the location of the distribution center, task allocation, flight path planning, and so on. Researchers are generally keen on mathematical modeling and model optimization, mainly focusing on time, cost, efficiency, and other factors as goals, paying more attention to an intelligent optimization algorithm to propose new solutions that will be applied to practical transportation problems. For example, [PERSON] et al. [8] propose a multi-period formula for facility locations to maximize coverage while meeting reliability constraints. [PERSON] et al. [9] consider simultaneously optimizing site selection and path planning and developing a joint model to minimize disaster losses and rescue time. [PERSON] et al. [10] solved the facility location problem and online demand allocation by dividing UAVs into two phases. Various constraints, such as vehicle capacity, time window, route length, etc., usually accompany the material distribution problem. To ensure that the generated solution can meet these constraints, researchers usually introduce penalty functions in the model to improve the feasibility and operability of the solution. For example, [PERSON] et al. [11] proposed an improved genetic tabu search algorithm and introduced the penalty factor into the fitness function. [PERSON] et al. [12] and [PERSON] et al.