## 2 Dynamic Area Optimization Using Search Methods
### Dynamic Area Optimization Using GA: An Overview and Challenges  
The application of search methods for dynamic area optimization offers an effective way to explore better antenna parameters that improve communication quality for user distribution. In this study, we choose GA as the search method and utilize the generated solutions as our training data. The focus of this study is to optimize the horizontal beam directions exclusively, as an initial investigation, specifically for the three-cell and six-cell scenarios. Figure 3 illustrates the heatmap of the GA-optimized beam accounting for the user distribution in a three-cell scenario. The red dots are the user position, and the yellow regions indicate areas with high beam power. In GA, based on the value of the fitness function, the top individuals are preserved as elites, and the others undergo crossover and mutation to generate the next generation. In this study, we assigned each individual a horizontal beam direction for each cell and set the rate of the elites, crossover, and mutation to 5%, 80%, and 15%, respectively. The implementation of crossover and mutation is based on the literature [28]. Other GA parameters, i.e., the population size, convergence generation, and maximum generation are set to 100, 100, and 1000, respectively, to ensure sufficient exploration during the GA search process. Furthermore, based on [29], the fitness function is defined as a penalty function that combines the objective function and the amount of violation for constraint conditions. We essentially used the settings for GA that delivered good outcomes in an earlier study [23; 24], where they evaluated and discussed these parameters in detail. The implementation of the GA was primarily facilitated using MATLAB's Global Optimization Toolbox. For further details regarding the GA methodology, reference is made to MATLAB's comprehensive documentation.  
In our approach, we enforce constraints to maintain a basic level of communication quality to ensure full coverage of the service area. Specifically, we employ the constraint conditions for SNR and SINR in studies [23; 24], which are defined as follows:  
\[\begin{split} DLSNR_{1\%}>8\;\mathrm{dB},\\ DLSNR_{1\%}>-7\;\mathrm{dB},\\ ULSNR_{1\%}>11\;\mathrm{dB}.\end{split} \tag{12}\]  
Here, \(DLSNR_{1\%}\), \(DLSNR_{1\%}\), and \(ULSNR_{1\%}\) represent the first percentile thresholds of the DL SNR, DL SINR, and UL SNR for users in the area. These are calculated in Equation (7), Equation (8) and Equation (11), respectively. The DL SINR value given here is under full buffer conditions. A safety margin of 15 dB from the required SNR and SINR is included within these constraints. When evaluating these constraints, a uniform user distribution is assumed to ensure that coverage standards are met even in user-absent regions.  
In defining the objective function, we utilize an indicator (\(I\)) that factors in proportional fairness (PF) [30] across users on a per cell basis. It is represented as follows:  
\[I=\sum_{u=1}^{N_{u}}\frac{B}{N_{C_{u}}}\log\Big{(}\log_{2}\Big{(}1+10^{\frac{7 \mathrm{SNR}_{1\%}}{10}}\Big{)}\Big{)}, \tag{13}\]  
where \(B\  
Here, \(\omega\) and \(\Omega\) mean the horizontal beam directions for each cell and all possible combinations of them, respectively. The optimization based on the search algorithm efficiently obtains near-optimal parameters. However, as mentioned in Section 1, the frequent optimization by the search methods and the growing search space proportional to cells or parameters induce an increase in the computational cost of the searches, which hinders the prompt adaptation to sudden distribution changes resulting from natural disasters or major events.