## 3 Utilized Meta-Heuristic Algorithms
### Standard Genetic Algorithm
Cuckoos typically deposit their fertilized eggs in the nests of other cuckoos, hoping that their offspring will be raised by surrogate parents. There are instances when cuckoos realize that the eggs in their nests do not belong to them, leading to either the removal of foreign eggs from the nests or the complete abandonment of the nests. Levy flights are stochastic walks where both direction and step lengths are determined by the Levy distribution. These flights are observed in various animals and insects and are characterized by sequences of straight flights followed by sudden 90-degree turns. Compared to standard random walks, Levy flights are more efficient for exploring large-scale search areas. This increased efficiency is mainly attributed to the fact that the variances of Levy flights increase much more rapidly than those of normal random walks [11]. The algorithm, shown in Algorithm 5, is governed by three fundamental rules:

1. Each cuckoo lays one egg at a time and places it in a randomly selected nest. 2. Nests with high-quality eggs are preserved and passed on to the next generations. 3. There is a fixed number of available host nests, and the likelihood of a cuckoo's egg being discovered by the host bird is determined by a probability parameter, \(p_{a}\), within the range of \([0,1]\). In such cases, the host bird has the option to either discard the egg or abandon the nest entirely and construct a brand-new one. ```
Objective function f(x) where \(x=(x_{1},x_{2},...,x_{d})^{T}\) Generate an initial population of n host nests from \(x_{i}\) where i = 1, 2,... n \(count\gets 1\) while\(count\leq The\ number\ of\ iteration\) or stopping criteria do  Randomly get a cuckoo by Levy flights  Evaluate the fitness value of the cuckoo, \(F_{i}\)  Randomly select a nest (say, j) from the host nest % For a minimization problem if\(F_{i}\leq F_{j}\)then  Replace j by the new solution endif  A fraction (\(p_{a}\)) of the worst nests are abandoned and new ones are built  Keep the best solutions  Rank the solutions and find the current best \(count=count+1\) endwhile
```

**Algorithm 5** Cuckoo Search

### Grey Wolf Optimizer

GWO drew its inspiration from the hunting tactics observed in grey wolf packs and the intricate dynamics of their hierarchical structure [14]. Within this hierarchy, four distinct wolf roles emerge: alpha, beta, omega, and delta. Alpha wolves assume leadership within the pack, tasked with pivotal decisions such as hunting strategies, choice of resting grounds, and determining the optimal time to rouse the pack. Betas play a supportive role, aiding alphas in decision-making processes. Deltas, however, encompass a diverse array of functions including scouting (alerting the pack to potential threats), sentineling (guarding the pack), elders (seasoned wolves, formerly alpha or beta), hunters (actively pursuing prey or procuring sustenance), and caretakers (attending to the needs of the infirm or injured). Omegas, often designated as scapegoats, are obliged to defer to the directives of all other ranks. It is upon this intricate social framework that GWO finds its conceptual basis. GWO initiates its procedures by generating an initial population (referred to as a swarm) through randomization. Following this, it sets in motion its core parameters: \(\overrightarrow{A}\) and \(\overrightarrow{C}\), see Algorithm 6. \(\overrightarrow{A}\) comprises a vector of randomly selected values, falling in the range of [\(-1\), \(1\)], encouraging search agents to diverge from their target. On the other hand, \(\overrightarrow{C}\) is also a vector, populated with random values within the range of [\(0\), \(2\)], thereby imbuing GWO with an element of stochastic behavior throughout its runtime [14]. Subsequent to this initialization phase, the positions of grey wolves are established, thereby designating them as alpha, beta, or delta based on their proximity to the prey.