## 1 Introduction
In recent years, there has been a significant advancement in satellite technology, leading to a growing desire among people to customize satellite orbit designs for specific tasks, rather than relying on traditional, general designs [16; 17]. The optimization of satellite orbits allows for simultaneous observations of the satellite by multiple ground laser stations, significantly extending the common-view observation time and reducing observation noise. The development of spacecraft trajectory optimization techniques has arisen from the need to strategically shape a spacecraft's trajectory in order to efficiently achieve mission objectives in an optimal or near-optimal manner [18]. There are two main categories of numerical trajectory optimization methods: indirect methods (\"optimize and then discretize\") and direct methods (\"discretize and then optimize\") [19]. Currently, direct methods are more commonly used, involving the examination of state and input parameters to determine the minimum (or maximum) value of the objective function. This approach results in a static nonlinear optimization problem [20]. Simulated Annealing (SA) is an effective and versatile metaheuristic for searching, particularly in cases involving large discrete or continuous spaces [21]. In SA, the likelihood of considering a low-value solution decreases as the algorithm runs. This adjustment increases the probability of finding the global optimum. Algorithms in this category primarily use stochastic methods that combine local and global search techniques. Additionally, the theoretical and mathematical foundations provide strong justifications for the effectiveness of these algorithms in real-world applications [22]. This paper introduces a model for optimizing satellite orbits in order to maximize the probability of ground-based laser stations in the common view. The model uses a simulated annealing algorithm with an improved annealing strategy to achieve optimization. Two sets of experiments were conducted to validate the practicality and effectiveness of the algorithm. After modeling and optimizing the algorithm, the improved annealing strategy generates optimal satellite orbits for multiple stations within the specified model. Thispaper presents an optimization model and methods for adjusting satellite orbit designs to achieve observational objectives. It is specifically designed for satellite missions that involve laser retroreflector arrays and tasks that focus on laser time transfer comparisons within specific regions. The subsequent sections of the paper are organized as follows: Section 2 explains the Ground-to-Ground laser time transfer principle, which is based on Space-to-Ground time transfer, and introduces the multi-station satellite orbit design model for the common view. Section 3 describes the methodology, including an analysis of the improved simulated annealing algorithm and the process of optimizing satellite orbits in the common view. Section 4 investigates the minimum satellite orbit altitude between two stations in the common-view mode, and presents a comprehensive analysis of the optimization of optimal satellite orbits between two and multiple Satellite Laser Ranging (SLR) stations using the improved simulated annealing algorithm. Finally, Section 5 concludes the discussion.