## 3 Utilized Meta-Heuristic Algorithms
### Standard Genetic Algorithm
```
Population size = N;  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  % Selection and Crossover for\(i=1:N\)do  Choose individual \(i\) via ST if\(p_{i}\leq p_{c}\)then  i attends Crossover  Randomly choose a partner for individual \(i\) via ST  Mate them else  i is saved for the next generation endif endfor % Mutation for\(j=1:N\)do  Randomly choose individual \(j\) if\(p_{j}\leq p_{m}\)then  j attends Mutation  Changes the genetic structures of \(j\) else  j passes Mutation step endif endfor  Combine the new individuals and the current population members  Evaluate the fitness value of each individual \(count=count+1\) endwhile
```  
**Algorithm 2** Standard Genetic Algorithm  
Population size = N;  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  % Selection and Crossover for\(i=1:N\)do  Choose individual \(i\) via ST if\(p_{i}\leq p_{c}\)then  i attends Crossover  Randomly choose a partner for individual \(i\) via ST  Mate them else  i is saved for the next generation endif endfor  % Mutation for\(j=1:N\)do  Randomly choose individual \(j\) if\(p_{j}\leq p_{m}\)then  j attends Mutation  Changes the genetic structures of \(j\) else  j passes Mutation step endif endfor  Combine the new individuals and the current population members  Evaluate the fitness value of each individual \(count=count+1\) endwhile ```
**Algorithm 3** Standard Genetic Algorithm  
Population size = N;  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  % Selection and Crossover for\(i=1:N\)do  Choose individual \(i\) via ST if\(p_{i}\leq p_{c}\)then  i attends Crossover  Randomly choose a partner for individual \(i\) via ST  Mate them  else  i is saved for the next generation endif endfor  % Mutation for\(j=1:N\)do  Randomly choose individual \(j\) if\(p_{j}\leq p_{m}\)then  j attends Mutation  Changes the genetic structures of \(j\) else  j passes Mutation step endif endfor  Combine the new individuals and the current population members  Evaluate the fitness value of each individual \(count=count+1\) endwhile
```

**Algorithm 4** Standard Genetic Algorithm

Population size = N;  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  % Selection and Crossover for\(i=1:N\)do  Choose individual \(i\) via ST if\(p_{i}\leq p_{c}\)then  i attends Crossover  Randomly choose a partner for individual \(i\) via ST  Mate them  else  i is saved for the next generation endif endfor  % Mutation for\(j=1:N\)do  Randomly choose individual \(j\) if\(p_{j}\leq p_{m}\)then  j attends Mutation  Changes the genetic structures of \(j\) else  j passes Mutation step endif endfor  Combine the new individuals and the current population members  Evaluate the fitness value of each individual \(count=count+1\) endwhile ```
**Algorithm 5** Standard Genetic Algorithm

Population size = N;  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  % Selection and Crossover for\(i=1:N\)do  Choose individual \(i\) via ST if\(p_{i}\leq p_{c}\)then  i attends Crossover  Randomly choose a partner for individual \(i\) via ST  Mate them  else  i is saved for the next generation endif endfor  % Mutation for\(j=1:N\)do  Randomly choose individual \(j\) if\(p_{j}\leq p_{m}\)then  j attends Mutation  Changes the genetic structures of \(j\) else  j passes Mutation step endif endfor  Combine the new individuals and the current population members  Evaluate the fitness value of each individual \(count=count+1\) endwhile
```  
**Algorithm 6** Standard Genetic Algorithm  
Population size = N;  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  % Selection and Crossover for\(i=1:N\)do  Choose individual \(i\) via ST if\(p_{i}\leq p_{c}\)then  i attends Crossover  Randomly choose a partner for individual \(i\) via ST  Mate them  else  i is saved for the next generation endif endfor  % Mutation for\(j=1:N\)do  Randomly choose individual \(j\) if\(p_{j}\leq p_{m}\)then  j attends Mutation  Changes the genetic structures of \(j\) else  j passes Mutation step endif endfor  Combine the new individuals and the current population members  Evaluate the fitness value of each individual \(count=count+1\) endwhile ```
**Algorithm 7** Standard Genetic Algorithm  
Population size = N;  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  % Selection and Crossover for\(i=1:N\)do  Choose individual \(i\) via ST if\(p_{i}\leq p_{c}\)then  i attends Crossover  Randomly choose a partner for individual \(i\) via ST  Mate them  else  i is saved for the next generation endif endfor  % Mutation for\(j=1:N\)do  Randomly choose individual \(j\) if\(p_{j}\leq p_{m}\)then  j attends Mutation  Changes the genetic structures of \(j\) else  j passes Mutation step endif endfor  Combine the new individuals and the current population members  Evaluate the fitness value of each individual \(count=count+1\) endwhile
```

**Algorithm 8** Standard Genetic Algorithm

Population size = N;  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  % Selection and Crossover for\(i=1:N\)do  Choose individual \(i\) via ST if\(p_{i}\leq p_{c}\)then  i attends Crossover  Randomly choose a partner for individual \(i\) via ST  Mate them  else  i is saved for the next generation endif endfor  % Mutation for\(j=1:N\)do  Randomly choose individual \(j\) if\(p_{j}\leq p_{m}\)then  j attends Mutation  Changes the genetic structures of \(j\) else  j passes Mutation step endif endfor  Combine the new individuals and the current population members  Evaluate the fitness value of each individual \(count=count+1\) endwhile ```
**Algorithm 8** Standard Genetic Algorithm

Population size = N;  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  % Selection and Crossover for\(i=1:N\)do  Choose individual \(i\) via ST if\(p_{i}\leq p_{c}\)then  i attends Crossover  Randomly choose a partner for individual \(i\) via ST  Mate them  Randomly choose a partner for individual \(i\) via ST  Mate them  else  i is saved for the next generation endif endfor  % Mutation for\(j=1:N\)do  Randomly choose individual \(j\) if\(p_{j}\leq p_{m}\)then  j attends Mutation  Changes the genetic structures of \(j\) endif  end for  Combine the new individuals and the current population members  Evaluate the fitness value of each individual \(count=count+1\) endwhile
```  
**Algorithm 9** Standard Genetic Algorithm  
Population size = N;  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  % Selection and Crossover for\(i=1:N\)do  Choose individual \(i\) via ST if\(p_{i}\leq p_{c}\)then  i attends Crossover  Randomly choose a partner for individual \(i\) via ST  Mate them  end if \(p_{i}\leq p_{c}\)then  i attends Crossover  Randomly choose a partner for individual \(i\) via ST  Mate them  end if  end for  % Mutation for\(j=1:N\)do  Randomly choose individual \(j\) if\(p_{j}\leq p_{m}\)then  i attends Mutation  Changes the genetic structures of \(j\) endif  end for  Combine the new individuals and the current population members  Evaluate the fitness value of each individual \(count=count+1\) endwhile ```
**Algorithm 9** Standard Genetic Algorithm  
Population size = N;  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  % Selection and Crossover for\(i=1:N\)do  Choose individual \(i\) via ST if\(p_{i}\leq p_{c}\)then  i attends Crossover  Randomly choose a partner for individual \(i\) via ST  Mate them  end if  i attends Crossover  Randomly choose a partner for individual \(i\) via ST  Mate them  else  i is saved for the next generation endif endfor  % Mutation for\(j=1:N\)do  Randomly choose individual \(j\) if\(p_{j}\leq p_{m}\)then  i attends Mutation  Changes the genetic structures of \(j\) endif  end for  Combine the new individuals and the current population members  Evaluate the fitness value of each individual \(count=count+1\) endwhile
```

**Algorithm 9** Standard Genetic Algorithm

Population size = N;  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  % Selection and Crossover for\(i=1:N\)do  Choose individual \(i\) via ST if\(p_{i}\leq p_{c}\)then  i attends Crossover  Randomly choose a partner for individual \(i\) via ST  Mate them  end if  i attends Crossover  Randomly choose a partner for individual \(i\) via ST  Mate them  end if  i attends Crossover  Randomly choose a partner for individual \(i\) via ST  Mate them  end if  i attends Mutation  end for  % Mutation for\(j=1:N\)do  Randomly choose individual \(j\) if\(p_{j}\leq p_{m}\)then  i attends Mutation  end for  % Mutation for\(j=1:N\)do  Randomly choose individual \(

### Differential Evolution

Another widely recognized EA employed in optimization problems is the DE algorithm [6], which is a population-based stochastic algorithm.