## 1 Introduction  
With the development of space technology and the popularity of satellite applications, the number and types of Earth observation satellites are increasing, playing quite an important role in the fields of economy, military and people's livelihood [1]. Facing the growing demand for large-scale and diversified tasks of users from all walks of life, multi-satellite scheduling for constellations has become a hot research issue at home and abroad. The Multi-Satellite Scheduling Problem (MSSP) refers to the process by which the satellite control department allocates resources, including satellites, payloads and ground stations, etc., to meet the routine needs or urgent requests of earth observation. The process must satisfy various constraints, maximizing the benefits of satellite missions during the satellite in-orbit operation [2, 3]. Obviously, multi-satellite scheduling involves not only satellite payload resources but also ground management resources to ensure their normal operation. It can be seen that there are many constraints in multi-satellite scheduling. Therefore, reasonable models and efficient scheduling methods are of great significance for describing and solving problems such as the MSSP. As for the multi-satellite scheduling methods, due to the Non-deterministic Polynomial (NP) characteristics of scheduling problems, most of the current research uses heuristic methods to solve the problem [4], mainly including Tabu Search (TS) [5], AntColony Optimization (ACO) [6], Genetic Algorithm (GA) [7; 8], Particle Swarm Optimization (PSO) [9; 10] and the Multi-Objective Evolutionary Algorithm (MOEA) [11; 12], etc. These heuristic optimization methods are easy to implement and widely used. [PERSON] [5] applied the new Tabu Search (TS) algorithm to solve the problem of low-orbit satellite scheduling by considering the priority of the task and satisfying the time and resource constraints. However, the limiting factors considered only include coverage rate, data storage capacity and battery capacity in that paper. [PERSON] et al. [8] used the improved Genetic Algorithm (GA) to solve the satellite scheduling problem and proposed a Hybrid Dynamic Mutation (HDM) strategy, which overcomes the early convergence and long calculation time to some extent. However, the simulation model did not consider the constraints adequately; only the limits of satellite data transmission were taken into account. [PERSON] et al. [1] proposed a complete search algorithm, heuristic search algorithm and swarm intelligence optimization algorithm for the observation of task-oriented satellite cluster scheduling problems on different scales. As mentioned above, these heuristic optimization methods are easy to implement and efficient to solve satellite scheduling problems with specific constrains. However, when we encounter complex satellite scheduling problems in real time, the constraints of the model should be considered adequately; the computational complexity and efficiency of the algorithm are considered the most important aspects of multi-satellite scheduling. [PERSON] [13] first proposed an evolutionary algorithm based on Population-Based Incremental Learning (PBIL) in 1996. The basic idea of the algorithm is to regard the evolution process as a learning process. The knowledge, also called the probability of learning, is obtained by learning to guide the generation of offspring. This probability is the accumulation of information throughout the evolutionary process, and it will guide more effective directions for the offspring (compared to GA's parental genetic recombination strategy), which results in faster convergence and better optimizations. Inspired by this PBIL, called the traditional PBIL, we propose a real-coding PBIL that has a better performance both in efficiency and quality for multi-satellite scheduling with complex constrains close to reality. In this paper, we discuss modeling and algorithms for the Multi-satellite Scheduling Problem (MSSP).