## 3 Methods  
### Improved Cluster Algorithm Based on the Geographic Distribution of the Target  
In the initial algorithm development segment, the focus is primarily on allocating the number of drones and the optimal path for each drone within the cluster. The research is based on optimization algorithms and clustering algorithms. The entire algorithm consists of three main components, namely, sequential clustering algorithm, single\(-\)drone optimal trajectory algorithm, and cluster mission planning optimization algorithm. The clustering algorithm functions as a classification mechanism to group seemingly disordered target points, ensuring that the target points within the same group are close in position. This organization ensures that the target points within the same group are proximal to each other, reducing long\(-\)distance transfers for a single drone while keeping the target points of different groups as far apart as possible. At the same time, it avoids overlapping areas for drones, preventing resource wastage. Traditionally, k\(-\)means clustering algorithm represents classical clustering algorithms. At its core, it partitions data into 'k' groups, with 'k' entities randomly selected as the initial clustering centers. Then, the distance between each entity and the respective clustering centers is calculated to assign each entity to the nearest cluster center. Although this method boasts a high exploratory potential, it is typically marred by a considerable degree of uncertainty and extensive iterative computing time costs. Given the introduction of multiple optimizations in the proposed algorithm, the initial calculation stages strive to diminish uncertainty within the optimization process. This approach aims to yield results that are not only interpretable, but also conducive to further optimizations. To mitigate these challenges, this paper introduces a sequential clustering method that hinges on geographic coordinates, advancing from the traditional clustering approaches (Algorithm 1). During the clustering phase, two pivotal optimization parameters are highlighted: the cluster circle diameter \(D\) and the cluster circle positioning distance \(\Delta d\)The former parameter, \(D\), signifies the cluster circle's diameter, influencing the cluster count and the number of clustered target parcels. Conversely, \(\Delta d\) denotes the minimum positional shift between the starting point of a new cluster and the center of the preceding cluster during a cluster transition. This parameter influences the relative positioning amongst the cluster circles to adjust the relative position between the cluster circles, thereby improving the uniformity of clustering in densely targeted areas and reducing the spatial overlap of clusters. In the sequential clustering process, each cluster's target points, which correlate to the tasks assigned to each drone, need to be traversed. This problem is akin to the classic _TSP_ in mathematics. It dictates that each drone tasked with visiting 'n' target points must define a path encompassing all designated points, with the stipulation that each target is visited only once before returning to the initial starting position. This path selection aims to minimize the overall journey length amongst all potential paths. Recognized as a quintessential combinatorial optimization issue, _TSP_ falls under the category of \(NP-\)complete problems. As of now, no flawless solution has been identified. In this paper, the ant colony optimization (ACO) algorithm is employed to solve the shortest path problem for drones, approximating the optimal solution. The basic principle of the ACO algorithm is derived from nature's shortest path principle for foraging. According to entomologists, ants can find the shortest path from food sources to their nests without any hints, even in complex environments (Figure 3). 1. The coordinates of the target point set \(\{P_{int}\}\), the assembly point coordinate \(\{P_{j\mu}\}\), and the reference point coordinate \(P_{0}\);
2. Initialize parameters;
3.