## 1 Introduction
### Related Work  
Several studies have investigated various methods for optimizing the antenna parameters for both satellite and terrestrial communications. [PERSON] et al. [4] proposed a dynamic coverage adjustment method that optimizes the beam size and resource allocation based on user distribution using two types of coverage patterns. [PERSON] et al. [5] proposed an optimization method to cover all users while minimizing the number of beams based on user distribution. [PERSON] et al. [6; 7; 8] proposed an optimization method to maximize the sum rate in a satellite-terrestrial integrated network while satisfying the transmission power and quality of service constraints. However, because the user distribution in satellite communications may hardly change, there is minimal consideration for handling various user distributions. Conversely, terrestrial network communications, which have narrower coverage areas and different user distribution patterns than satellite network communications, are likely  
Figure 1: Concept diagram of the HAPS mobile communication infrastructure. to benefit from an optimization algorithm that can handle various problems. The methods frequently employed in this field are reinforcement learning (RL) [9; 10; 11; 12; 13; 14; 15; 16] and heuristic algorithms [17; 18; 19; 20; 21]. A detailed survey of additional studies involving machine learning can be found in [22]. In RL algorithms, an agent acts based on the reward it will receive. [PERSON] et al. [9] proposed a solution using RL for the intercell interference coordination problem in orthogonal frequency-division multiple access (OFDMA) systems. [PERSON] et al. [10] resolved the carrier allocation problem for femto BSs using RL. Deep Reinforcement Learning (DRL), which is a more advanced RL technique and can handle complex states and actions, has also been adopted. Methods based on DRL have contributed to autonomous and dynamic beam optimization in both single-sector and multiple-sector environments [11], as well as in a heterogeneous cellular network [12]. In [13; 14], DRL has been employed for power allocation and modulation and coding scheme (MCS) selection in a cellular network. Recently, DRL-based methods have been extended to HAPSs. [PERSON] et al. have proposed a HAPS user scheduling algorithm using channel state information (CSI) in massive MIMO systems [15]. [PERSON] et al. have proposed a HAPS power control algorithm for spectrum sharing with existing systems [16]. Although these RL-based methods provide useful algorithms that can be finely tuned to fit the environment, given the limited combinations of states and actions in these studies, achieving convergence in these approaches can become more difficult as the number of user distribution patterns increases. Furthermore, to improve the learning performance, many DRL algorithms require consideration of methods for updating the target function weights and, in some cases, policy optimization. Such requirements often lead to increased complexity in the algorithm's architecture, thus making their practical implementation challenging. Meanwhile, a heuristic algorithm consists of simple algorithms that follow predefined rules to search for the best possible solution at a given time. [PERSON] et al. [17] proposed a heuristic-based algorithm for optimizing vertical tilt angles to maximize user spectral efficiency considering LTE network scenarios. [PERSON] et al. [18] proposed a new multi-objective optimization model based on a metaheuristic approach that considers fairness and throughput. In [19; 20; 21], load-balancing problems, such as traffic or power problems, are resolved following a heuristic approach. However, these search methods struggle to promptly adapt to sudden distribution shifts, such as those resulting from natural disasters or major events, due to the high computational cost. Furthermore, these methods cannot utilize the results from previous calculations, necessitating calculations each time.