## 5 The Hybrid White Shark Optimizer and Whale Optimization Algorithm (WSO-WOA)
### White Shark Optimizer (WSO)  
The WSO, created by [PERSON] et al. [34] in 2022 was inspired by the natural behaviors of great white sharks. The optimizer's mathematical framework is based on the sharks' exceptional hearing and smelling capabilities, which they use for navigation and hunting. These behaviors are integrated into the algorithm to balance exploration and exploitation, allowing search agents to efficiently investigate different areas of the search space. This approach enhances the optimization process, helping to identify the best possible solutions. The WSO operates through a systematic, iterative process aimed at solving optimization problems efficiently. Initially, the parameters of the problem and the algorithm are set, followed by the random generation of initial positions and velocities for the population of white sharks. The positions of the sharks are evaluated to establish a baseline for the optimization process. As the algorithm progresses through iterations, the following shark behaviors are utilized to update the shark positions:  
1. A white shark determines the position of its prey by sensing a disruption in the water's waves, which is caused by the movements of prey. This behavior is known as the speed of movement toward prey. Each shark's velocity is adjusted based on the difference between its current position and the best-known positions within the swarm. It is guided by random factors to introduce variability, as illustrated in (38). \[v_{i}^{t+1}=\epsilon\bigg{(}v_{i}^{t}+P_{1}\Big{(}x_{gbest}^{t}-x_{i}^{t}\Big{)} \times c_{1}+P_{2}\bigg{(}x_{gbest}^{t^{\prime}}-\omega_{i}^{t}\bigg{)}\times c _{2}\bigg{)}\] (38) In the expression \(\epsilon=\frac{2}{\left|2-\tau-\sqrt{\tau^{2}-4\tau}\right|}\), the variable \(\epsilon\) is determined, with \(\tau\) denoting the acceleration factor, which is fixed at 4.125. The notation \(v_{i}^{t}\) represents the velocity vector associated with the _ith_ white shark in the _tth_ iteration. Furthermore, \(x_{gbest}^{t^{\prime}}\) refers to the best-known position vector for the ith white shark in the swarm. The parameters c1 and c2 are random values that are uniformly distributed within the interval [0, 1]. \(P_{1}\) and \(P_{2}\) are computed (39). The minimum and maximum values for P (\(P^{min}\) and \(P^{max}\)) are set at 0.5 and 1.5, respectively. \[ \begin{cases}P_{1}=P^{max}+\big{(}P^{max}-P^{min}\big{)}\times e^{-(4t/iter^{ max})^{2}}\\ P_{2}=P^{min}+\big{(}P^{max}-P^{min}\big{)}\times e^{-(4t/iter^{max})^{2}}\end{cases} \] (39) 2. Sharks then update their positions according to these velocities, with two possible strategies: one that applies when the randomly generated number is less than the sensory intensity factor (\(mv\)), and another when it is greater. This behavior is known as the progression towards the ideal white shark. In this scenario, the behavior of white sharks as they close in on their prey is modelled using the following position-update strategy: \[x_{i}^{t+1}=\left\{ \begin{aligned} x_{i}^{t}\rightarrow\oplus x_{o}+u. a+l.b\,;if\,rand<mv\\ x_{i}^{t}+\frac{v_{i}^{t}}{f}\,;if\,rand\geq mv\end{aligned} \right.\] (40)  
Here, \(\oplus\) denotes the bitwise XOR. The variable f corresponds to the frequency of the white shark's oscillatory motion, and \"rand\" denotes a randomly generated number that is uniformly distributed between 0 and 1. The parameter mv is introduced to assess the growing intensity of the white shark's sensory perception, specifically its hearing and olfactory senses, which become increasingly refined with each iteration. Further elaboration is provided in [PERSON] et al. [34]. 1. Great white sharks are adept at sustaining their location near the most favorable solution in relation to their prey. When the randomly generated number is less than the sensory sensitivity parameter (\(s_{\text{s}}\)), each shark's movement towards the prey is fine-tuned using additional calculations to precisely determine direction and magnitude,as detailed in (41) and (42).