## 2 Related Works
Although RDABC offers significant improvements over traditional methods, it may be faced with challenges like implementation complexity due to the dual search strategies and cross-mutation and being trapped in local optima, particularly in highly complex or multimodal optimization landscapes. The Wolf Search Algorithm (WSA) operates based on the natural behaviors of wolves during hunting, incorporating principles of individual searching, memory utilization, and threat response [12]. WSA simulates the hunting behavior of wolves, where each wolf acts as an independent searching agent. The algorithm balances exploration (searching new areas) and exploitation (refining known good areas) to find optimal solutions. Each wolf evaluates its current position and the positions of its peers within a defined visual range. The movement of a wolf is influenced by the quality of its position and the best position found by its peers; this is computed in Equation (3) as:  
\[x_{new}=x_{old}+\propto\cdot(x_{best}-x_{old})+\beta\text{-}escape() \tag{3}\]  
where \(x_{new}\) is the new position of the wolf, \(x_{old}\) is the current position of the wolf. \(x_{best}\) is the best position found by the wolf or its peers, \(\propto\) is a coefficient that controls the attraction towards the best position, \(\beta\) is a coefficient that controls the randomness of the escape movement, \(escape()\) is a function that generates a random position to jump to, simulating the wolf's response to threats. When a wolf encounters a threat (simulated as a random event), it jumps away from its current position to avoid being trapped in local optima. This is akin to a mutation in genetic algorithms. The escape movement is defined in Equation (4) as:  
\[x_{scape}=x_{old}+random(-d,d) \tag{4}\]  
where \(d\) is a predefined distance that determines how far the wolf can jump away from its current position, random \((-d,d)\) generates a random value within the range of \(-d\) to \(d\). WSA incorporates a memory mechanism where wolves remember previously visited positions. This memory helps prevent revisiting the same positions and enhances search efficiency. Each wolf evaluates the quality of its current position based on a fitness function, which is problem-specific. The fitness function determines how close the current position is to the optimal solution. The fitness function \(f(x)\) is defined in Equation (5) as:  
\[f(x)=Objective\ Function(x) \tag{5}\]  
The WSA follows the general steps outlined below:  
**Step 1:**: Initialize a population of wolves with random positions. **Step 2:**: Evaluate the fitness of each wolf's position. **Step 3:**: For each wolf, determine the best position found by itself and its peers. **Step 4:**: Update the position of each wolf using the movement formula. **Step 5:**: If a threat is encountered, apply the escape movement. **Step 6:**: Repeat the evaluation and updating process for a set number of iterations or until convergence criteria are met. [PERSON] et al. (2023) [13] proposed a scheme based on the improved Grey Wolf Optimization (EECHIGOWO) algorithm to enhance energy efficiency, average throughput, network stability, and overall network lifetime in wireless sensor networks (WSNs) through optimal selection of cluster heads (CHs). The EECHIGOWO specifically focused on addressing the challenges associated with traditional clustering methods, such as premature convergence, lack of population diversity, and the imbalance between exploration and exploitation in the optimization process. The EECHIGOWO incorporated elements of the wolf search algorithm (WSA) to improve the efficiency and effectiveness of cluster head selection in WSNs, leading to enhanced network performance and longevity. The proposed EECHIGOWO defines a fitness function that evaluates the potential CHs based on criteria such as residual energy, distance to the base station, and intra-cluster distance. The WSA uses this fitness function to guide the selection process, ensuring that the chosen CHs are optimal for energy efficiency and network stability.