## 2 Materials and Methods
### Overview of ESRO-SRO Algorithm
\begin{array}{c}\left(X_{i,j}+X_{j}^{max}\right)/2, \quad\text{if }X_{i,j}^{\prime}>X_{j}^{max}\\ \left(X_{i,j}+X_{j}^{min}\right)/2,\quad\text{if }X_{i,j}^{\prime}>X_{j}^{min} \end{array} \right.\) End For \(M_{n}=\left\{ \begin{array}{c}X_{i},\quad if\ f(X_{i}^{\prime})>f(X_{i}),\\ M_{n},\quad\quad\quad\text{otherwise}\end{array} \right.\) \(n\) randomly chosen \(X_{i}=\left\{ \begin{array}{c}X_{i}\text{if }f(X_{i}^{\prime})>f(X_{i})\\ X_{i}\text{otherwise}\end{array} \right.\) \(\text{USN}_{i}=\left\{ \begin{array}{c}\text{USN}_{i}+1,\ \text{if }f(X_{i}^{\prime})<f(X_{i})\\ 0,\text{otherwise}\end{array} \right.\) If the \(\text{USN}_{i}>\text{ MU}\)do For\(j=l\) to \(D\)do \(X_{ij}=X_{j}^{min}+\text{rand }[0,\ 1]\times\left(X_{j}^{max}-X_{j}^{min}\right)\) End for \(\text{USN}_{i}=0\) End If End for  Decide the existing finest place and upgrade Xbest End while  Return Xbest End
```

**Algorithm 1**Pseudo-code of the SRO algorithm Here, \(x_{i}\in\mathbb{R}\) and \(x_{i}\in[a_{i},\ b_{i}]\forall i\in 1,\ 2,\ \ldots,\ n\). \[x_{i}^{qo}=rand\bigg{(}\frac{a_{i}+b_{i}}{2},\ x_{i}^{o}\bigg{)} \tag{13}\]

In QOBL is exploited to the SRO algorithm to initialize the population as well as creation jumping. It generates a group of optimum outcomes for population initialization [8]. Algorithm 2 defines the QOBL pseudo-code to the novel population. ```
for\(i=1:\ Eco\_size\) for\(j=1:\ D\) \(X_{ij}^{qo}=lb_{j}+up_{j}-X_{i,j}\); \(C_{i,j}=\left(lb_{j}+up_{j}\right)/2\); if\((X_{i,j}<C_{i,j})\) \(X_{i,j}^{qo}=C_{i,j}+\left(X_{i,j}^{o}-C_{i,j}\right)\times rand\); else \(X_{i,j}^{qo}=X_{i,j}^{o}+\left(C_{i,j}-X_{i,j}^{o}\right)\times rand\); endif endfor
```

**Algorithm 2**Pseudo-code of QOBL

### Process Involved in ESRO-SRP Technique

To define an optimum group of routes, an offered function was employed to determine the following hop to destination and is represented by:

\[f(x)=\bigg{\{}i,\ for\ which\bigg{|}\bigg{(}\frac{i}{k}-X_{ij}\bigg{)}\bigg{|} \ is\ minimum,\ \forall i1\leq i\leq k \tag{14}\]

The drive is to determine an optimum group of routes from the cluster heads (CHs) to the base station (BS), employing a fitness function (FF) comprising 2 parameters such as energy and distance. Primarily, the RE of the next-hop node is determined, and a node with higher energy was provided as a relay node. To transfer data, the source node sends it to the relay node, which is further forwarded to BS utilizing inter CHs. Thus, the node with higher RE is provided as the next-hop node. A primary sub-objective \(f1\) was offered as:

\[f1=E_{CH} \tag{15}\]

In addition, the Euclidean distance was executed to define the distance from CH to BS. The minimized energy dissipation was frequently dependent on the broadcast distances. With a lesser distance, the energy was retained significantly [21]. Once the distance is improved, a further count of energy is spent. Hence, the node with lesser distances is chosen to relay nodes. So, the next sub-objective using distance is \(f2\) which is formulated as:

\[f2=\frac{1}{\sum_{i=1}^{n}d\ is(CH_{i},\ NH)+dis(NH,\ BS)} \tag{16}\]

The present research work utilized direct trust values (TVs) amongst drones, and their mathematical process was signified as:

\[f3=Trust \tag{17}\]

\[Tr_{i,j}=\left(Tr_{ij}^{Dir}+Tr_{ij}^{Indir}\right)/2. \tag{18}\]Here, \(Tr_{ij}^{dir}\) and \(Tr_{ij}^{indir}\) denotes the direct as well as indirect TVs of one node to another node correspondingly. The count of trust nodes from the cluster is attained in the group with maximal IVs, and their state value was provided by the level of confidence values suggested in one node to another node. The TV of BS was computed as:

\[Tr_{C}=\sum_{j=1}^{S-1}Tr_{C(ij)}/(S-1). \tag{19}\]

In the above formula, \(Tr_{C}\) refers to the trusted value and \(S\) represents the amount of drones. If the path trust was smaller than the trust requirement value, the path trust alert occurrence was triggered.