## 4 Optimization Design for Satellite Game Mission Deployment Based on Co-Evolution
### Design of Co-Evolutionary Algorithm  
Co-evolution is a biological or systematics concept that describes the phenomenon where two or more interacting systems or species adapt to each other and evolve jointly during their interactions. This concept is not only widely applied in biology but has also been introduced into fields such as computer science, artificial intelligence, and optimization algorithms. In the context of satellite gaming, the co-evolutionary mechanism can be integrated with optimization algorithms like Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Zebra Optimization Algorithm (ZOA) as a strategy for cooperation and competition among multiple satellites. Each satellite in the swarm can be regarded as an individual. During the game, each satellite selects its strategy based on the strategies of others. Through multiple generations of iterations, the strategies within the satellite swarm are continuously optimized. Each generation of satellites adapts and adjusts its strategies based on the strategies of others, ultimately reaching an equilibrium state. In long-term gaming, the satellite swarm can find the optimal balance between cooperation and competition, thereby achieving complex orbital control and space missions.  
The core idea of co-evolution is the joint evolution of the mission satellite population and the target satellite population through mutual influence. For each individual mission satellite, the \(N^{O}_{best}\) individuals with the optimal loss functions are selected from the target satellite population. The mission satellite then competes against these target satellites individually, and the average value of the mission satellite's loss function is recorded as its individual loss function. Similarly, for each individual target satellite, the \(N^{A}_{best}\) individuals with the optimal loss functions are selected from the mission satellite population. The target satellite then competes against these mission satellites individually, and the average value of the target satellite's loss function is recorded as its individual loss function. Through this setup, both the target satellite and mission satellite populations update themselves based on the optimal individuals from the opposing population. The two populations compete with each other and optimize individually. Eventually, when the competition reaches a stable state, the optimal solution to the differential game model is obtained, and the iteration termination condition is met.  
The flowchart of the co-evolutionary algorithm is shown in Figure 3.  
The specific steps of the co-evolutionary algorithm are as follows:  
Step 1: Define the initial conditions and relevant parameters for the optimization process. This involves determining the initial states of the mission satellite and the target satellite, the optimization ranges of the control variables, and the initial parameters of the optimization algorithm.  
Step 2: Initialize the populations of the mission satellite and the target satellite. For the control variables of both populations, an initial position is uniformly and randomly selected within their respective optimization ranges to serve as the initial individuals.  
Step 3: Update the target satellite population using the optimization algorithm. The target satellite population is updated based on its loss function.  
Step 4: Update the mission satellite population using the optimization algorithm. The mission satellite population is updated based on its loss function.  
Step 5: Determine whether the maximum number of iterations has been reached. Check if the current iteration count has reached the preset maximum number of iterations. If not, return to Step 3 to continue the iteration process.  
Step 6: Select the optimal individuals from both populations. The finally selected optimal individuals represent the best-performing strategies during the confrontation process, ensuring that both the mission satellite and the target satellite minimize their respective losses.