## 2 Related Works  
As shown in Table 1, we sort out the network resource allocation methods applied to different optical network architectures, which provides us with ideas for studying the resource allocation problem in SCNs. RSA in EONs. The EON architecture is considered one of the most promising directions for optical networks [5]. The RSA problem of EONs refers to finding a suitable routing path for a traffic request between its source and destination nodes while satisfying both the spectrum continuity constraint and the spectrum contiguity constraint and allocating the appropriate spectrum resources to establish an optical connection based on the principle of maximizing the spectrum resource utilization [18]. Integer linear programming (ILP) models and variant forms [19; 20] have been used to solve the static RSA problem, and intelligent optimization algorithms, such as the tabu search [21], particle swarm optimization [22], differential evolution [23], simulated annealing (SA) [24], and bee colony optimization [25] have been widely adopted. Dynamically establishing and removing optical connectionsadds a great deal of difficulty to solving the dynamic RSA problem. Heuristic algorithms are frequently used to solve dynamic RSA problems [26; 27]. Meanwhile, intelligent algorithms, such as backpropagation neural networks [28], deep reinforcement learning [29], and asynchronous advantage actor-critic algorithms [30] have also been applied to solve the problem, but relatively little research has been carried out in this area. RCSA in SDM-EONs. To further increase the signal transmission rate and capacity of the network, SDM was introduced into the EONs [31; 32; 33]. Most studies have addressed the static RCSA problem in SDM-EONs by establishing mathematical models, such as the ILP model. [PERSON] et al. [34] proposed a node-arc-based ILP model which can allocate the route, the cores, and the corresponding spectrum simultaneously, by considering the inter-core crosstalk for each traffic request. An XT-aware-based mixed integer linear programming (MILP) method and a heuristic algorithm have been proposed in [34]. In [35], three algorithms have been developed to solve the RCSA problem in dynamic SDM-EONs. The MILP model and two heuristic algorithms based on the greedy approach and SA for offline survivable SDM-EONs have been proposed in [36] to ensure network survivability against a single link failure. All the above studies performed well but did not consider MFs when solving the RSA and RCSA problems. Adoption of MFs in EONs and SDM-EONs. Distance adaptive modulation was first proposed in [37], which can adaptively allocate the minimum required spectrum resources according to the end-to-end physical conditions of a light connection. The modulation format distance limit parameter has been defined considering crosstalk in [38] that was used to select the MF for a connection request, by comparing the considered routing path length. [PERSON] et al. [39] solved the static routing, modulation level, spatial mode, and spectrum assignment problem using 34 different explainable demand-prioritization strategies. MFC was not considered in all of the above strategies. Although refs. [40; 41] utilized MFC for network resource optimization, they still considered MFC as an independent optimization factor and did not jointly optimize the MFC and RMSA problems. [PERSON] et al. [42] addressed, for the first time, the joint optimization problem of selecting the signal rate, MFC nodes, spectrum allocation, and optical connections. In addition, this paper proposed a genetic algorithm to balance the contrasting objectives of minimizing MFC nodes and spectrum utilization. [PERSON] et al. have studied the routing, spectrum, transceiver, and modulation format allocation problem in EONs, by building an ILP model and designing heuristic algorithms, and also analyzed the performance gains from spectrum conversion and MFs [43; 44; 45].