## 1 Introduction  
With rapid developments of communication technologies, satellite communications have attracted a lot of attention in academia and industry. Especially, with the advent of many commercial satellite constellations, e.g., Starlink, OneWeb and O3b, many topics of satellite technologies have become the key research of 6G communications [1, 2]. Compared with the terrestrial-network, the non-terrestrial-satellite-network (NTSN) has many advantages, such as global coverage and network security. These features can make up for the shortcomings of the traditional mobile communication. Numerous studies imply that the non-terrestrial-network (NTN) contains Geo-synchronous Earth Orbit (GEO), Medium Earth Orbit (MEO), Low Earth Orbit (LEO) and High Altitude Platform (HAP) [3]. GEO and MEO apply a higher altitude orbit. They can not only realize the data transfer function, but also realize the network management function. HAP is applied as an auxiliary platform for LEO. As the primary data transfer medium, LEO can realize both access services and data bearer services. All data flows are processed and transmitted by LEO nodes. Low orbit satellite behaves many special characteristics: frequent topology variation, dynamic link state and limited power resources [4]. In particular, the lack of energy would lead to not only mission failure but also devastating damage to satellites. By a lot of research, many scholars indicate that an excellent routing strategy can solve those problems [5]. In order to achieve load balancing and energy optimization, routing strategies are an important research direction. In addition, the routing strategy is also a key technology to improve network performance. From the basic principle, NTSN routing strategies can be divided into centralized routing and distributed routing. In the former, the calculation of the routing path is concentrated in a single satellite node, e.g., the source node and the head of satellitescluster. [PERSON] [6] proposed a satellite network task deployment method based on the information centric network (ICN). The specific routing strategy is based on source routing architecture. [PERSON] [7] proposed a centralized quality-of-service (QoS)aware routing algorithm for beyond 5G NTN. A modified [PERSON]'s algorithm and [PERSON]'s algorithm are running in a calculating node. However, all centralized routing schemes suffer from sudden failure and congestion, because the centralized routing calculation cannot be changed once finished. In addition, the resource balancing also cannot be achieved by it. [PERSON] [8] present three basic cooperative models about the hybrid satellite-terrestrial network (HSTN). In it, a survey of the state-of-the-art technologies is provided. However, the relevant content of the energy balance is not covered. In the latter, each satellite node calculates the next hop node independently, according to the least state. [PERSON] [9] proposed a distributed congestion control routing protocol based on traffic classification in LEO satellite networks. A low-overhead distributed scheme was used to compute the routing. [PERSON] [10] proposed a distributed routing algorithm for the mega satellite constellation network. A Longer Side Priority strategy aims at maximizing the path searching space. Although the recovery of failure can be achieved in the above distributed schemes, they are difficult to take into account in resource balancing at the same time. With the gradual increase in traffic density, network congestion and energy shortage cause the network performance to drop sharply. A lot of novel QoS-oriented routing schemes have been developed to improve the network performance. [PERSON] [11] proposed a QoE-aware algorithm to enhance the user satisfaction by constructing QoE factors. A taboo list is introduced to optimize the latency. [PERSON] [12] proposed a bee colony algorithm optimization based on the link cost. Many constraints are taken into account, e.g., Doppler wavelength drift, transmission delay, wavelength consistency and continuity.