## 3 Utilized Meta-Heuristic Algorithms
### Standard Genetic Algorithm
Similar to GAs, DE begins its procedure by creating the first population (called initial). Unlike GAs, DE advances to the mutation step instead of proceeding with the selection step. While the algorithm is in this step, it generates a vector, known as the _donor vector_, for each individual in the population. The donor vector is composed using three randomly chosen individuals from the population. In the mutation step, the scaling factor \(F\), a crucial parameter controlling differential variation [33], plays a significant role. It is essential that \(F\) falls within the range [0, 2][6]. Following the creation of the donor vector, the recombination (crossover) step commences. This step determines whether the individual or its donor vector is sent for the selection step, resulting in the creation of a _trial vector_. The crossover rate value \(CR\) guides this decision-making process. It is recommended to take the value in the range [0, 1][6]. Finally, the selection process is carried out by comparing the fitness value of each individual with the trial vector. Whichever of these two compared values is better, the individual continues to the next generation with that value (see Algorithm 3). ```
Population size = N; Specify CR (crossover rate) and F (scaling factor) values Randomly create the initial population Evaluate the fitness value of individuals in the population \(count\gets 1\) while\(count\leq The\ number\ of\ iteration\)do for\(i=1:N\)do  Randomly choose three individuals \(i_{1},i_{2},i_{3}\) where \(i_{1}\
eq i_{2}\
eq i_{3}\) Generate a random integer \(I_{rand}=\{0,1,2,...,D\}\) where D is dimension % Trial Vector for\(j=1:D\)do if\(rand(0,1)\leq CR\) or \(j==I_{rand}(i,j)\)then \(trial_{i}=F*|i_{1}-i_{2}|+i_{3}\) else \(trial_{i}=pop_{i}\) endif endfor Replace \(trial_{i}\), if it is better than \(pop_{i}\) endfor Evaluate the fitness value of individuals in the new population \(count=count+1\) endwhile
```

**Algorithm 3** Differential Evolution

### Particle Swarm Optimization

Originally, PSO was not conceptualized for optimization; rather, its inception aimed to emulate the collective behavior of bird flocks and fish swarms in nature [9]. Upon examining how PSO behaved, it became clear that the algorithm was actually performing optimization. By creating an initial population (swarm), where each member (particle) has a velocity to explore the search space, PSO begins its process, shown in Algorithm 4. On the other hand, two significant positions, the best position called pbest and the global best position called gbest, are also directly affect the movement of particles. pbest, gbest, or both are improved if a particle finds a better position than before. The velocity vector for the ith individual can be computed as in Equation (4). \[v_{i}(t+1)=w.v_{i}(t)+c_{1}.r_{1}.(p_{Best}-x_{i}(t))+c_{2}.r_{2}.(g_{Best}-x_{i}(t)) \tag{4}\]

where \(c_{1}\) and \(c_{2}\) are acceleration coefficients, \(w\) is the inertia weight, \(r_{1}\) and \(r_{2}\) are real values from the range \([0,1]\) (randomly selected), and \(x_{i}(t)\) is the position of the ith individual at time t.

```
Number of particles in the swarm = N;  Assign random values to each particle in the swarm  Evaluate the fitness value of particles in the swarm  Specify \(p_{Best}\) and \(g_{Best}\) values \(count\gets 1\) while\(count\leq The\ number\ of\ iteration\)do for\(i=1:N\)do  Determine the velocity of particle i  Determine the position of particle i  Evaluate the fitness value of particle i, \(f_{i}\)  % For a minimization problem if\(f_{i}\leq p_{Best}\)then  Assign \(f_{i}\) as \(p_{Best}\) if\(p_{Best}\leq g_{Best}\)then  Assign \(p_{Best}\) as \(g_{Best}\) endif endfor  Determine the velocity of particle i  Determine the position of particle i \(count=count+1\) endwhile
```

**Algorithm 4** Particle Swarm Optimization

### Cuckoo Search

CS is a swarm-based optimization algorithm that was inspired from the behaviour of cuckoo birds [11]. In the CS algorithm, potential solutions are associated with cuckoo eggs.