## 4 Proposed SARP Routing Protocol for BASNs
### Bio-Inspired Computing and Optimization Problems
#### 4.2.2 Multiobjective Lion Mating Optimization Algorithm (MLOA)
\begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Explanation** \\ \hline \(\mathcal{Z}_{i}(\mathbb{E}_{c})\) & \(\mathbb{E}_{c}\) is the energy consumption subject to minimization by lion \(\mathcal{Z}_{c}\). \\ \(\mathcal{Z}_{i}(\mathbb{E}_{c})\) & \(\mathbb{E}_{c}\) is the delay needing to be minimized by lion \(\mathcal{Z}_{c}\). \\ \(\mathcal{Z}_{i}(\mathcal{P}_{dr})\) & \(\mathcal{P}_{dr}\) is the packet delivery ratio leading to be increased by lion \(\mathcal{Z}_{c}\). \\ \(\mathcal{Z}_{i}(\mathcal{P}_{r})\) & \(\mathcal{J}_{p}\) is the throughput subject to being increased by lion \(\mathcal{Z}_{r}\). \\ \(\mathbb{R}_{\ell}\), \(\mathbb{R}_{\ell}\) & indicates the lower and upper bounds of the search space, respectively. \\ \(\mathcal{A}(\mathcal{C}_{i})\) & represents the matrix for saving the position of each hunter by considering the \(\mathcal{P}_{r(r)}\) position. \\ \(\mathbb{R}_{\ell}\), \(\mathbb{R}_{\ell}\) & is the value of the \(\ell\)th dimension of the thunter. \\ \(\mathbb{R}_{\ell}\) & is the number of hunters, and \(i\) is the number of variables. \\ \(\mathcal{P}_{(r)}\) & is the current location (\(\ell\)) of the prey. \\ \(\mathbb{R}_{\ell}\), \(\mathbb{R}_{\ell}\) & is the new position of the prey. \\ \(\mathbb{R}_{\ell}\) & is the current position of the hunter. \\ \(\hat{\delta}\) & is the percentage improvement in the fitness of the hunter. \\ \(\mathcal{F}_{(\ell)}\), \(\mathbb{R}_{\ell}\) & is the network position of the hunter. \\ \(\mathbb{R}_{\ell}\), \(\mathbb{R}_{\ell}\) & is the network position of the hunter. \\ \(\mathbb{R}_{\ell}\), \(\mathbb{R}_{\ell}\) & is the distance between two lions of between lions and prey in the search space. \\ \(d_{1}\), \(d_{2}\) & is the distance between the female lior's location and the certain point chosen by tournament selection among the pride’s territory. \\ \(e_{1}\), \(e_{2}\) ; \(e_{1}\) & is a vector whose start point is the previous location of the \(\mathcal{S}\mathcal{A}_{\ell}\) and its direction is toward the selected position \(\mathcal{S}\mathcal{A}_{\ell}\)(_new_), and \(e_{2}\) \\ \(r_{1}\), \(r_{2}\) & is perpendicular to \(\mathbb{R}_{\ell}\), \(e_{1}\), \(\mathbb{R}_{\ell}\) = 0 and 0 = 1. \\ \(\hat{\alpha}\) & linearly decreases from 2 to 0 over the course of iterations. \\ \(\hat{\alpha}\) & \(\hat{\alpha}\) & is a vector that generates random values in 1 or less than \(-1\). \\ \(\hat{\alpha}\) & \(\hat{\alpha}\) & is a vector that generates random values in [0, 2]. \\ \(\hat{\psi}\) & \(\hat{\psi}\) & is the number of lions in a pride \(i\in\mathbb{R}_{\ell}\)(\(\mathcal{A}_{\ell}\), \(\mathbb{R}_{\ell}\)), which improves their fitness in the last iteration. \\ \(\mathbb{R}_{\ell}^{\prime}\) & shows the position of the selected \(\ell\)th hunter at the \(\ell\)th iteration. \\ \(\mathbb{R}_{\ell}\) & is the position of the prey or a hunter in the search space. \\ \(d_{i}\), \(\mathbb{R}_{\ell}\), \(\mathbb{R}_{\ell}\), \(\mathbb{R}_{\ell}\), \(\mathbb{R}_{\ell}\) & is the distance between the male lion’s position and the selected area of territory. \\ \(\hat{\theta}\) & is the angle to search for a wide area around the current solution in the search space. \\ \(\mathbb{u}\) & is a random, uniformly distributed number between \(-\kappa\)\(\ell\) and \(\ell\). \\ \(\mathbb{B}\) & is a randomly generated number with a normal distribution with mean value 0.5 and standard deviation between 0 and 1. \\ \(\mathbb{X}_{\mathrm{E}_{\mathrm{amp}}}\) & is a shadowing factor in dB, which is a Gaussian-distributed random variable within mean zero and standard deviation \(\hat{\varsigma}\). \\ \(\mathbb{E}_{\mathrm{amp}}\) (\(\mathbb{P}\)) & is the energy required by the transmit amplifier to maintain an acceptable straight-to-ratio ratio to transfer data messages reliably. \\ \(\mathbb{u}\) & is the path loss exponent, considered as 2 in free space, and varies for different body locations. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Notations used in SARP.