# Fault Reconstruction for a Giant Satellite Swarm Based on Hybrid Multi-Objective Optimization
## 1 Introduction  
In recent years, satellite systems have shown a trend of clustering [1]. For example, SpaceX plans to launch tens of thousands of low-Earth orbit satellites to achieve global high-speed internet coverage as part of its Starlink project [2]. The rapid increase in micro- and nanosatellites has made many tasks easier. Moreover, system complexity and fault risk have increased, which has led to higher requirements for the on-orbit maintenance and health management of ultra-large-scale satellite swarm systems [3]. The definition of an ultra-large-scale satellite cluster is not consistent throughout academia. To avoid confusion, this paper refers to satellite clusters consisting of more than 1000 satellites as ultra-large-scale satellite swarms. To improve the ability of ultra-large-scale satellite swarms to handle and tolerate faults autonomously, scholars have carried out research on satellite swarm reconstruction technology. [PERSON] et al. [4] proposed a decentralized formation control scheme based on couplings within the satellite system and maintained the stable operation of the entire tethered satellite system by adjusting the controller of the faulty satellite itself. [PERSON] et al. [5] considered the problem of spacecraft formation reconfiguration under directed and undirected communication. They proposed that the faulty satellite and the reconfigured healthy satellite cooperate to compensate for controller faults and synchronize the system attitude. [PERSON] et al. [6] introduced a fuzzy logic system to solve the problem of tracking inconsistency among multiple satellites under fault conditions by cutting off the communication between faulty satellites and healthy satellites. From the perspective of fault-tolerant control, the above scheme focuses on the situation in which a single satellite fault has little impact on the entire system. To study the problem of mission failure causedby multi-satellite failure, [PERSON] et al. [7] proposed a state-switching multibody satellite formation failure reconstruction method, which has faulty satellites leave the formation and healthy satellites compensate to achieve reconstruction. The above fault reconstruction techniques have been developed over many years. However, for ultra-large-scale satellite clusters, factors such as the complexity of satellite coordination, task diversity, and uncertainty of reconstruction indicators introduce challenges to the satellite swarm reconstruction task. Since fault satellite swarm reconstruction is usually based on system redundancy and reconfiguration of the system structure [8], there may be multiple reconstruction control strategies. However, for different satellite swarm systems, there are differences in their reconstruction strategies in terms of energy consumption, health state, reliability, etc. Therefore, the problem of satellite swarm fault reconstruction is a kind of multi-objective optimization problem. Multi-objective optimization problems play an important role both in theory and in engineering applications. In the 1960s, [PERSON] [9] first tried to use genetic algorithms to solve multi-objective optimization problems, and gradually multi-objective optimization problems came to the public's attention. In the 1980s, [PERSON] [10] designed the first multi-objective evolutionary algorithm, the vector-evaluated genetic algorithm. Since then, the multi-objective optimization algorithm has gone through two periods, from the initial development with simple rules to the current second stage with efficiency as the evolutionary goal. According to the different ways of solving multi-objective problems, refactoring methods can be divided into system-model-based and transformation-based methods. The former needs to establish an accurate system model and use inference diagnosis to solve the strategy, which cannot deal with large and complex systems and is not efficient. The latter converts the problem to other well-studied domain problems, such as the planning field [11; 12; 13].