## 4 Proposed CB-FBC and Genetic Approach
### Optimization of \(P_{tj_{i}S}(t)\) and \(B_{Sj_{i}}(t)\)
Recharge aerial \(j\) or connect it with cluster \(i\) as follows: for\(j=1:N\)do if\(\min\left(\Gamma_{i}(t)\right)<\Gamma_{jR}(t)\)then  aerial \(j\) files back for recharging  end if else if\(\min\left(\Gamma_{i}(t)\right)\geq\Gamma_{jR}(t)\)then  a. \(\left\{i,j\right\}=\arg\min\left(\Gamma_{j_{l}}(t)\right)\)  b. \(x_{i}^{+}(t)=1\)  c. \(\Gamma_{i}(t)=\infty\forall j\in\mathcal{N}\)  d. Update \(\Gamma_{jR}(t+1)\forall j\in\mathcal{N}\)  end if
12 end for
13
14 end for
15
16 end for
```  
**Algorithm 1**Proposed CB-FBC Algorithm implemented in GBS  
```
Input:\(\mathcal{M}\), \(N\),initiated \(\delta_{i}\) using GPS localization, and \(\Omega\). Initialization: At \(t=0\), \(w_{l}(t)=0\), \(h_{l}(t)=0\), \(\hat{\gamma}_{i}(t)=0\), and \(q_{i}(t)=0\forall i\in\mathcal{M}\). 1 for\(t=1,2,\ldots,T\)do
2 for\(i=1,2,\ldots,M\)do
3 if\(h_{l}(t-1)>0\)then
4\(\hat{\gamma}_{i}(t)=\hat{\gamma}_{i}(t-1)+\sqrt{(3\log t)The output of the \"GA\" algorithm is the sub-optimum values \(P^{*}_{t|j,S}(t)\) and \(B^{*}_{S|_{l}}(t)\) as detailed in Algorithm 2. At the beginning of the algorithm, the population \"_Pop\"_ of \(P_{t|j,S}(t)\) and \(B_{S|_{l}}(t)\)\(\forall N\) is constructed randomly in the range of \([0,P_{Vmax}]\) and \([0,B_{Smax}]\), respectively, with a size of \(Ps\). Then, for \(1\leq g\leq G_{e}\), the fitness function is evaluated for all members in \"_Pop_\", and the member characterized with the highest fitness value is selected. The parents, \"_Parents_\", of size \(Pa\) are selected from \"_Pop_\" based on the calculated fitness function values. Then, a percentage of parents are crossed over to produce the children, which after mutation produces the new population, \"_NewPop_\". The generated \"_NewPop_\" are used to refine the selections of \(P^{*}_{t|j,S}(t)\) and \(B^{*}_{S|_{l}}(t)\) in the next iteration as given in Algorithm 2. This algorithm is also implemented in the terrestrial GBS as it is the most energized component in the network. Then, the adjusted values of \(P^{*}_{t|j,S}(t)\) and \(B^{*}_{S|_{l}}(t)\) are sent via control signals to LEO-Sat to adjust its bandwidth values and then relay the adjusted \(P^{*}_{t|j,S}(t)\) values to the aerials. ```
Output:\(P^{*}_{t|j,S}(t),B^{*}_{j|j}(t)\) Input:\(\textbf{Y}_{j}(t),Ps,G_{e},en_{e},\epsilon_{c},B_{Smax},P_{Vmax},\) and \(Fit\). Initialization: Construct the population \(Pop\) of size \(P_{s}\) by randomly selecting \(P_{s}\) values of \(P_{t|j,S}(t)\) in the range of \([0,P_{Vmax}]\), and \(B_{S|_{l}}(t)\) in the range of \([0,B_{Smax}]\) for \(\forall j\in N\). 1 for\(g=1,2,3\ldots,Ge\)do
2 Evaluate:\(Fit_{k}(t)\),\(k\in P_{s}\) in \(Pop\) using (16) Calculate:\([P^{*}_{t|j,S}(t),B^{*}_{t|j,S}(t)]\)= max\({}_{\forall k\in P_{s}}\{Fit_{k}(t)\}\)
3 Select: the set of Parents of size \(P_{a}\) from \(Pop\) using Roulette Wheel, Tournament based on the values of \(Fit_{k}(t)\) Set:NewPop=\(\{\}\)
4 Crossover: for\(i=1,2,\ldots,\frac{P_{a}}{2}\)do
5 Parent1=\(Parents(2i-1)\)  Parent2 = Parents(2i) ifrand \(<\epsilon_{c}\)then
6 {Child1,Child2}=**Crossover\([Parent1,Parent2]\)**
7 end if
8 {Child1,Child2}=**\([Parent1,Parent2]\)
9 end if
10 {NewPop = {NewPop,Child1,Child2}}
11 Mutation: for\(\forall Child\in NewPop\)do
12 ifrand \(<\epsilon_{m}\)then
13 MutateChild and update it in \(NewPop\)
14 end if
15 end for
16 Replace \(Pop\) by \(newPop\)
17 end
```

**Algorithm 2**Proposed GA implemented in GBS

## 5 Numerical Analysis

This section utilizes Monte-Carlo (MC) simulations to demonstrate the efficiency of the envisioned \"CB-FBC\" and \"GA\" algorithms approach. The studied post-disaster is \(1\) Km\({}^{2}\), divided into 36 clusters containing a random number of users/survivors. The LEO-Sat altitude is 550 Km, while the aerial altitude is 100 m. An assumption is made that the nearest terrestrial GBS has full connectivity with the LEO-Sat, and all aerials are within full coverage of the LEO-Sat.