# A Heterogeneous Multi-Satellite Dynamic Mission Planning Method Based on Metaheuristic Algorithms
## 3 Algorithm Design  
The algorithm proposed in this paper comprises two parts, with the first being a discretely improved PSO algorithm. Typically, PSO is used for continuous problems; however, because our optimization objective is to select the most suitable satellite for each user, we have adaptively modified the PSO algorithm. Specifically, we eliminated the velocity component and incorporated a mechanism that combines the updates of local best and global best positions in each iteration, along with random factors. This mechanism ensures the accuracy of the local search while expanding the breadth of the global search, making it more suitable for solving such problems. In the initialization phase, the algorithm generates initial positions for each particle and records the local best positions and fitness values for each user. During the iterative update phase, each particle updates its position based on the current local best and global best positions, evaluates its fitness, and updates the local best and global best positions according to the new fitness values. Ultimately, after reaching the preset number of iterations, the algorithm returns the best global position found, as illustrated in Algorithm 1. In the specific computational process, to enhance user satisfaction, we need to consider the following factors. User Priority: User priority is represented by a numerical value \(P_{u}=\{1,2,3,4,5\}\) indicating the priority of user \(u\). This priority can serve as a weighting factor for adjusting the allocation of satellite resources. A higher \(P_{u}\) signifies a higher priority for user \(u\), thus necessitating the prioritization of \(u\)'s needs. This prioritization is essential in a multi-user environment, where resource allocation can become competitive. \(P_{u}\) ensures that the optimization algorithm focuses on fulfilling the most critical demands first, thereby enhancing user satisfaction and service quality. Figure 3: Illustrative diagram of the PSO. User Preference: The preference of users for different satellite types can be represented by a number \(H_{u}\) between 0 and 1. When \(H_{u}=1\), it indicates a complete preference for GEO satellites, which require broader coverage. Conversely, \(H_{u}=0\) signifies a complete preference for MEO satellites, which require lower latency. The interaction between \(H_{u}\) and the choice of satellite type influences the overall communication experience, as users' satisfaction can significantly improve when their preferences are taken into account. This preference informs the algorithm's decision making, allowing it to assign users to the satellite type that best aligns with their requirements. Capacity Satisfaction: The capacity required by the user is denoted as \(C_{R}^{u}\), while the capacity provided by the satellite is denoted as \(C_{O}^{u}\). The capacity matching rate can be calculated as \(\frac{C_{R}^{u}}{C_{R}^{u}}\). This matching rate is integral to the fitness function, as it drives the optimization process to ensure the efficient use of resources while maximizing user satisfaction.