# Research on Joint Resource Allocation for Multibeam Satellite Based on Metaheuristic Algorithms
## 1 Introduction  
Satellite communication systems have rapidly evolved into high-throughput satellite (HTS) systems over the past two decades, with data rates of tens or even hundreds of gigabits per second [1]. In the future, satellite communications will further develop into satellite-terrestrial networks [2], large-scale LEO constellations [3], or 6G networks [4], for which the efficient management of complex resources will be imperative [5]. Owing to the flexibility and complexity of the communication resources allocated in satellite communication systems, it is necessary to develop an automatic tool with efficient algorithms for management of dynamic resources--a problem known as dynamic resource management (DRM) [6]. In response, artificial intelligence algorithms, especially metaheuristic algorithms, are emerging as a fundamental solution to realize fully intelligent resource allocation and management [4]. Studies reported in the literature have focused on four subproblems of the DRM problem: power allocation, bandwidth allocation, joint resource allocation, and beam shape and placement. In addition, the latest research has focused on beamforming [2] and beam hopping [7], as well as their joint allocation with carriers, bandwidth, and power. The power allocation problem entails maximizing system performance under the limited power of the satellite platform while minimizing total power consumption. The studyof power allocation has practical value, as the power resources of satellite platforms are expensive and limited; increased power usage can improve signal gain and enhance user QoS. [PERSON] and [PERSON] [8] characterized the problem of power allocation as a convex optimization problem and introduced Lagrangian multipliers as a solutions, whereas [PERSON] et al. [9] calculated the capacity using satellite link budget equations, which are more practical than the Shannon capacity formula used in [8]. [PERSON] et al. [10] demonstrated that power allocation is an NP hard problem and examined the application of metaheuristic algorithms. Using the GA-SA algorithm and the NSGA-II algorithm, the authors proposed a two-stage, multiobjective optimization method to solve the Pareto front. In [11], an allocation model was created, taking interbeam interference and rain attenuation into account and solved using the PSO algorithm. [PERSON] et al. [12] used a deep reinforcement learning (DRL) technique to achieve optimal power allocation in tens of milliseconds; however, the DRL network requires pretraining and could not achieve optimal results in all scenarios. In [13], the performances of GA, SA, PSO, DRL, and hybrid approaches were compared with respect to the power allocation problem. [PERSON] et al. [14] combined power allocation with DBF (digital beamforming) to maximize the traffic accommodation rate of an HTS system by jointly optimizing the transmitted power, beam gain, and beam placement. The bandwidth allocation problem is a subproblem of the frequency assignment problem, which involves assigning the bandwidth of a satellite system to the beam and the frequency subslot of the beam to each user. In [15], it was demonstrated that frequency assignment is an NP complete problem that is difficult to approximate. As a result, some researchers have employed mathematical programming techniques to solve the bandwidth allocation problem. To determine the optimal Lagrange multiplier, [PERSON] et al. [16] used a binary search, whereas [PERSON] et al. [17] utilized subgradient algorithms. The aforementioned studies offered solutions for a small number of beams, increasing system capacity or allocation fairness, but are inapplicable to larger datasets. Several studies have been conducted on high-dimensional scenarios. A DRL framework for dynamic channel assignment problems was presented in [18], and a novel image-like tensor reformulation was designed to extract the traffic demand features.