# Research on Joint Resource Allocation for Multibeam Satellite Based on Metaheuristic Algorithms
## 1 Introduction
In [3], a fast heuristic assignment algorithm for the frequency assignment problem of LEO constellations was proposed, which can achieve the goal of serving a greater number of users with fewer beams. The joint resource allocation problem is an optimization problem that simultaneously allocates power and bandwidth, typically continuing to develop based on a single resource allocation and achieving increased allocation fairness or communication service capability than single resource allocation. [PERSON] et al. [19] designed an objective function that combines fairness and demand fit and proposed a stochastic optimization algorithm based on simulated annealing to solve the joint allocation of bandwidth and power. In [20], a link budget model considering interference between beams was proposed based on [10], as well as a GA-based joint resource allocation algorithm, which improved the USC (unmet system capacity) results of the fixed average algorithm by 55.7%. In [21], the PSO-GA and NSGA-II algorithms were used to examine the multiobjective optimization of power and carrier bandwidth for a scenario in which hundreds of beams serve a highly volatile demand. [PERSON] et al. [22] decomposed the JRA problem into two non-convex subproblems, i.e., carrier and power allocation, and solved them using a continuous convex approximation. [PERSON] et al. [23] and [PERSON] et al. [24] studied multiobjective optimization with respect to the JRA problem, with the difference that literature [23] used DRL, whereas literature [24] used a metaheuristic multiobjective algorithm, i.e., CMOPSO (multi-objective PSO algorithm with competition mechanism). In summary, the power allocation and bandwidth allocation problems have been intensively studied, whereas the number of studies on joint resource allocation remains limited. Although DRL [12; 18; 25] has gradually spread in various satellite resource allocation scenarios, pretraining, generalization, and scenario dependency limit its versatility. Metaheuristic algorithms (e.g., GA, SA, PSO, etc.) are the main methods currently used owing to their speed, ease of encoding, and optimization performance. Nonetheless, the existingresearch is subject to some limitations: (1) As bandwidth can be used with reuse patterns in multibeam scenarios, any metaheuristic algorithm must deal with overlapping bandwidth constraints. A method called unused bandwidth allocation (UBA) has been proposed in the literature [20] to handle invalid solutions that do not satisfy the bandwidth constraint by repairing the beams one by one, simultaneously increasing the algorithm's computational complexity and decreasing its exploration capability. (2) Different metaheuristic algorithms have varying convergence times, which are significant in actual operational situations. In addition to the currently studied algorithms, such as GA and PSO, it is necessary to investigate additional metaheuristic algorithms with quicker convergence. We address these issues by focusing on a typical subproblem of the DRM problem, namely the joint resource allocation problem (JRA) for HTS. Based on the literature [13; 20; 21; 26; 27], we construct a link budget model that takes into account interbeam interference and signal modulation patterns, approaching an actual scenario. Then, a non-dominated beam coding (NDBC) method is proposed to address the shortcomings of the UBA method. We label adjacent rows of beams as dominant and non-dominant beams. The algorithm only encodes and optimizes the bandwidth of the non-dominated beams, and there is no bandwidth overlap constraint between them, such that they can be freely taken in the value domain, which effectively increases the search flexibility and improves the optimization quality of the algorithm. The bandwidths of the dominant beams are then obtained based on the non-dominant beams through a simple calculation. The computational complexity is also reduced, as invalid solutions are no longer repaired. Finally, the NDBC method is applied to four common metaheuristic algorithms.