## 1 Introduction  
Nowadays, society is in a rapidly developing information age, and the development of new broadband-intensive industries, such as the internet of things, cloud services, and data centers not only prompt network traffic requests to grow at a high rate but also place higher requirements on the flexible and dynamic transmission capability of optical networks. Moreover, assuming that router blade capacities grow steadily at 40% per year, then a single transceiver could carry \(\sim\)100 terabit per second (Tb/s) of such extra-bitrate traffic requests by 2030, and the entire fiber would be equivalent to a logical point-to-point interface at that time [1]. Elastic optical networks (EONs) divide the fixed wavelengths in traditional wavelength division multiplexing (WDM) optical networks into frequency slots (FSs) of finer granularity [2, 3, 4, 5], which can effectively improve network flexibility and spectrum resource utilization, thus increasing the throughput of the network. Nevertheless, EONs are still based on single-core fibers (SMFs), and the transmission capacity of existing SMFs is close to the Shannon capacity. It is difficult for EONs to cope with such extra-bitrate traffic requests. Multi-core fibers (MCFs) use the technology of embedding multiple single-mode fiber cores into the fiber cladding, an MCF is equivalent to a corresponding number of SMFs, so it can carry more service requirements without much increase in network costs, and it is easy to achieve exponential growth in the network capacity. Researchers have introduced space division multiplexing-based technology into EONs, which have the advantages of a high throughput, high flexibility, low crosstalk, and core independence. Although SDM-EONs can significantly increase the network capacity, the use of SDM fibers meansultra-scale deployment of very large-size scalable reconfigurable optical add-drop multiplexers (ROADMs), which implies higher costs and more complex network node structures. Furthermore, new optical node technologies are still limited to solving problems from a single WDM layer perspective, using fine-granular key technologies, such as wavelength switching. Taking these considerations into account, spatial channel networks (SCNs) have been creatively proposed to address these aforementioned problems [6; 7]. In [6; 7], the idea of introducing optical bypass into optical networks to build hierarchical IP-over-WDM network architectures based on ROADMs/WXCs, is borrowed by SCNs. Hierarchical IP-over-WDM-over-SDM network architectures are built by introducing spatial bypass based on spatial channel cross-connects (SXCs) into the SDM layer. SCNs replace wavelength switching with spatial switching of coarser granularity, evolve the optical layer explicitly into a WDM layer and an SDM layer, and transform optical nodes into hierarchical optical cross-connects (HOXCs) consisting of SXCs and WXCs. The spatial switching of coarser granularity indicates that SCNs have a large network capacity. The use of HOXCs can reduce the cost and simplify the network node structure. [PERSON] et al. have conducted serious studies on SCN architectures and the enabling technologies [8; 9; 10; 11; 12; 13; 14; 15; 16] as well as evaluated scalability, reliability, and techno economics [10; 11; 12; 13] to ensure SCNs be promising for reliable and cost-effective optical architectures toward the forthcoming SDM era. Since SCNs are highly promising optical network architectures, it is necessary to further study the network resource allocation problem in SCNs. With the evolution of optical networks from WDM networks to EONs, SDM-EONs, and then to SCNs, network resource units that need to be allocated have also changed accordingly. The routing and wavelength assignment (RWA) problem is the key issue of resource allocation in WDM networks. Network resource units to be allocated in EONs are changed from wavelengths of WDM to FSs, and the key problem is converted from the RWA problem to the routing and spectrum assignment (RSA) problem [17].