## 4 Proposed SARP Routing Protocol for BASNs
### Bio-Inspired Computing and Optimization Problems
#### 4.2.2 Multiobjective Lion Mating Optimization Algorithm (MLOA)
* Initialization  
In the proposed algorithm, each solution in the solution space is called 'lion'. First, an initial population is initialized randomly over the \(n\)-dimensional search space where the entire lion population (\(\mathcal{N}\)) is divided into resident lions (\(\mathcal{R}_{\mathcal{I}}\)) and nomad lions (\(\mathcal{N}_{\mathcal{I}}\)), such that \(\mathcal{N}=\mathcal{R}_{\mathcal{I}}+\mathcal{N}_{\mathcal{I}}\). The resident population lives in the form of groups \(\mathcal{Y}_{i}(\mathcal{R}_{\mathcal{I}})\) and consists of male lions (\(\mathcal{MIC}\)), female lions (\(\mathcal{F}\mathcal{L}\)), and cubs (\(\mathcal{C}_{\mathcal{U}}\)), including both male cubs (\(\mathcal{L}_{\mathcal{U}}\)) and female cubs (\(\mathcal{C}_{\mathcal{F}\mathcal{U}}\)). Similarly, the nomad population contains a set of males, females, and cubs, including both male cubs and female cubs. In each pride, the female lion population is chosen around \(\mathcal{VE}_{\mathcal{R}\mathcal{I}}\), while the rest are males \(\mathcal{VE}_{\mathcal{R}\mathcal{I}}\). However, this ratio is around \(1-(\mathcal{P}_{\mathcal{R}\mathcal{I}}+\mathcal{P}_{\mathcal{R}\mathcal{I}})\) in nomad lions and vice versa. This can be numerically indicated as  
\[\forall i=\{1,2,\ldots,x\};\;\forall j=\{1,2,\ldots,y\};\;\forall k=\{1,2, \ldots,z\};\] (2a) \[\text{Lions population}:\;\;\mathcal{N}=\big{\{}\mathcal{I}_{1}, \mathcal{I}_{2},\ldots,\mathcal{I}_{n}\big{\}}\text  
During encircling the prey, each hunter optimizes its location by considering its current and previous positions along with the positions of members of the group. Therefore, the hunters attack from opposite sites in the search space to hunt the prey. This opposition-based learning [39] makes them eligible to intelligently hunt the prey and, therefore, is an effective approach for solving optimization problems. The position of each hunter during optimization is saved in the following matrix. \[f(\mathcal{K}_{t})_{n_{near}}=\left[ \begin{array}{cccc}\mathcal{K}_{1,1}& \mathcal{K}_{1,2}&\mathcal{K}_{1,d}\\ \mathcal{K}_{2,1}&\mathcal{K}_{2,2}&\mathcal{K}_{2,d}\\ \vdots&\vdots&\vdots\\ \vdots&\vdots&\vdots\\ \mathcal{K}_{n,1}&\mathcal{K}_{n,2}&\mathcal{K}_{n,d}\end{array} \right]. \tag{3c}\]  
Consequently, the hunters, one after another, are selected randomly to attack the prey located in the center of hunters (i.e., \(\mathcal{P}_{i}=\sum\mathcal{K}_{h}\)). During hunting, if a prey escapes from the hunters, then the new position of the prey can be computed as  
\[\mathcal{P}_{i(\ell)}(new)=\mathcal{P}_{i(\ell)}+r(0,1)\times(\mathcal{P}_{i (\ell)}-\mathcal{K}_{h(\ell)})\times\delta. \tag{3d}\]  
In the hunting process, each hunter improves its own fitness value, and the new positions of the left- and right-wings of hunters can be statistically indicated as  
\[H_{\ell(i,k)}(new)=\left\{ \begin{array}{l}r(2\times\mathcal{P}_{i(\ell)}- \mathcal{K}_{i(\ell)}),\mathcal{P}_{i(\ell)}),\ (2\times\mathcal{P}_{i(\ell)}-\mathcal{K}_{i(\ell)})<\mathcal{P}_{i(\ell)}\\ r(\mathcal{P}_{i(\ell)},(2\times\mathcal{P}_{i(\ell)}-\mathcal{K}_{h(\ell)})), \ (2\times\mathcal{P}_{i(\ell)}-\mathcal{K}_{h(\ell)})>\mathcal{P}_{i(\ell)} \end{array} \right.. \tag{3e}\]  
The new positions of hunters located in the center are updated as  
\[\mathcal{K}_{j(\ell)}(new)=\left\{ \begin{array}{l}r(\mathcal{P}_{i(\ell)}, \mathcal{K}_{j(\ell)}),\ \mathcal{K}_{j(\ell)}<\mathcal{P}_{i(\ell)}\\ r(\mathcal{K}_{j(\ell)},\mathcal{P}_{i(\ell)}),\ \mathcal{K}_{j(\ell)}>\mathcal{P}_{i(\ell)} \end{array}