## 4 Proposed CB-FBC and Genetic Approach
### Optimization of \(P_{tj_{i}S}(t)\) and \(B_{Sj_{i}}(t)\)
However, the proposed approach, named \"CB-FBC\" and the \"GA\" algorithms yield a higher mean total system rate than the other benchmark schemes. This is due to their ability to efficiently distribute the aerials across post-disaster clusters while maximizing their sum rates. Moreover, the total system rate of the proposed approach is higher than that of the basic \"UCB+GA\" MAB algorithm. This is because the proposed CB-FBC algorithm balances between the achievable data rate and the clusters' selection fairness, while UCB only maximizes the confidence of the selected clusters. It is also noteworthy that the \"Nearest\" algorithm outperforms the \"Rand\" algorithm in mean sum rate performance because it equally distributes LEO-Sat bandwidth among the aerials, whereas in the \"Rand\" scheme, they are allocated randomly. Also, Figure 3 illustrates that the proposed approach outperforms the \"UCB+GA\", \"Nearest\", and \"Rand\" methods by 1.168, 1.33 and 1.55 at \(N=2\), correspondingly. At \(N=14\), the proposed approach outperforms them by 1.14, 1.32, and 2 times, respectively. Figure 4 depicts the sum of the aerials' energy consumption in KJ. As the number of aerials increases, so does the sum of the aerials' energy consumption for all compared schemes. However, due to the proposed approach's awareness of the limited aerial battery budget and optimization of aerial TX power, it demonstrates superior performance over other benchmarks regarding aerial energy consumption. The proposed approach has lower aerial energy consumptions than the \"UCB+GA\" algorithm because it optimizes the flying, hovering, and TX powers of the aerials while UCB only optimizes the aerials' TX powers using the GA algorithm. Moreover, the \"Nearest\" algorithm shows a better aerial energy consumption achievement than the \"Rand\" algorithm as it always chooses the clusters nearest to the aerials, which significantly reduces their flying energy consumption. On the other hand, in the \"Rand\" approach, clusters are randomly selected, which increases their flying energy consumption relative to the \"Nearest\" algorithm. This is the reason why the \"Rand\" algorithm has the worst aerial energy consumption performance. Although both the proposed approach and the \"Nearest\" algorithm almost select the nearest cluster, the proposed approach has lower energy consumption. This is because the proposed approach optimizes the aerials' TX communication powers using \"GA\" algorithms, while

Figure 2: Total system rate against the number of GA generations. the \"Nearest\" approach uses fixed maximum TX power allocation. When the number of aerials is low, e.g., \(N=2\), the proposed approach has a lower sum of the aerials' energy consumption than \"UCB+GA\", the \"Nearest\" and \"Rand\" schemes by 5.2%, 42.7%, and 51.88%, respectively. However, for many aerials, e.g., \(N=14\), these values become 19.23%, 40.7%, and 71.97%, respectively. Compared to the scheme proposed in [23], the improvements over \"Rand\" and \"Nearest\" schemes were only 7% and 5%, respectively, at \(N=14\) without any improvements at \(N=2\). This superior energy consumption performance of the proposed scheme over that proposed in [23] comes from the aerial TX power optimization mechanism provided by the proposed \"GA\" algorithm, where the scheme proposed in [23] has no such functionality. Figure 5 gives the clusters selection fairness index, which is calculated as:

\[\chi=\sum_{i=1}^{M}\mathrm{abs}\bigg{|}\frac{h_{i}(T)}{\sum_{i=1}^{M}h_{i}(T)} -\delta_{i}\bigg{|} \tag{15}\]

where the term \(\frac{h_{i}(T)}{\sum_{i=1}^{M}h_{i}(T)}\) defines how many times cluster \(i\) was chosen over the time horizon \(T\) divided by the total number of clusters selected. If the clusters were drawn upon their

Figure 4: Sum of aerials energy consumption against the number of aerials. Figure 3: Total system rate against the numbers of aerials. user densities, \(\delta_{i}\), \(\chi\) reaches zero.