# Multi-Satellite Observation-Relay Transmission-Downloading Coupling Scheduling Method
## 1 Introduction
The exact method [30; 31; 32; 33] can obtain the optimal solution, but the efficiency of the algorithm is significantly reduced when the task size is increased [29], which is not suitable for the large-scale multi-satellite observation-relay transmission-download coupling scheduling problem. The heuristic method [34; 35; 36] has high problem-solving efficiency; however, it is only suitable for specific scenarios due to fixed rules. The multi-satellite observation-relay transmission-download coupling scheduling problem is affected by multiple factors such as observation, data transmission, and multi-subsystem constraints. Changes in the scenario may lead to suboptimal algorithmic results. Metaheuristic methods use a search-based approach, achieving a balance between efficiency and obtaining better results. Common metaheuristic approaches for satellite mission planning include genetic algorithms, simulated annealing algorithms, ant colony optimization, tabu search, etc. A genetic algorithm [37; 38] uses genetic operators to achieve optimization by imitating the process of population reproduction and has strong global search ability. Traditional genetic algorithms have a low convergence speed, and blind searches easily result in low efficiency or repeated searches. This phenomenon is more obvious when genetic algorithms solve large-scale problems [25]. Slow convergence is exacerbated in the context of entire process coupling planning and intricate subsystem interactions. Using a genetic algorithm in the multi-satellite observation-relay transmission-download coupling scheduling problem will also result in low convergence speed, as this is a large-scale problem that contains complex processes and numerous subsystem constraints. Ant colony optimization [39; 40] has the advantage of fast convergence brought by positive feedback, but due to the accumulation of pheromones, it can easily fall into local optimization [41]. Because of the complexity of the multi-satellite observation-relay transmission-download coupling scheduling problem, the disadvantage that the ant colony algorithm is easy to fall into the local optimum will also be aggravated here. The simulated annealing method [42; 43] has both global search ability and local search ability by controlling the temperature-decreasing speed. However, a very slow decrease in temperature gives the best results but is also computationally costly. If the temperature is decreased too rapidly, the system is likely to become trapped in a local minimum [44]. The solution process for the multi-satellite observation-relay transmission-download coupling scheduling problem is related to the target distribution, the ground station distribution, the number, and the states of satellites. When using the simulated annealing method in the multi-satellite observation-relay transmission-download coupling scheduling problem, it is required to set reasonable parameters for different scenarios, bringing difficulties to applying this method. Tabu search [45; 46; 47; 48] avoids cycling by storing the information of the past in the search. It usually reaches local minima since a single candidate solution is used to generate offspring [49]. It is also highly inclined to fall into the local optimum in the multi-satellite observation-relay transmission-download coupling scheduling problem. The multi-satellite observation-relay transmission-download coupling scheduling problem brings challenges to solution searching, but the rational use of the coupling law between the subsystems can also play a role in guiding the search process. By guiding the search direction to change the states of the satellite subsystem and reasonably allocating the missions, the resources of the subsystems of the satellite can be reasonably used to complete more target observations and data transmission. The key to solving the problem lies in reasonable neighborhood design and the formulation of the neighborhood search strategy.