## 3 Ga-Gwo Hybrid Algorithm
### SA Algorithm
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**GA-GWO Hybrid Algorithm Pseudocode**} \\ \hline Input: N (population size), maxGen (maximum number of & \\ evolutionary generations) & & \\ \hline \multicolumn{3}{c}{Output: Population (final evolved population)} \\ \hline
1 & model \(\leftarrow\) initModel Of Problem (0; & Initialisation problems \\
2 & alntial, aFinal \(\leftarrow\) 2, 0; & Initialise alntial, aFinal \\
3 & n, D \(\leftarrow\) 1, 2; & Initialise Hill coefficient n, threshold D \\
4 & p\({}_{\text{o}}\), p\({}_{\text{m}0}\)\(\leftarrow\) 0.6, 0.02; & Initialise crossover, mutation probability \\
5 & D \(\leftarrow\) Decision variable dimensions; & D is an integer \\
6 & pop \(\leftarrow\) Initial Population By Piecewise (N, D); & Piecewise Chaos Mapping Initial Grey Wolf Population \\
7 & pop\(\leftarrow\) repair Operation (pop, model); & population restoration \\
8 & popFitness \(\leftarrow\) get Population Fitness (pop, model); & Calculating population fitness \\
9 & Best Individualest \(\leftarrow\) maxGen \(\times\) D-dimensional all-0 matrices; & The set of optimal individuals per generation \\
10 & Best Fitness Set \(\leftarrow\) 1 \(\times\) maxGen-dimensional all-0 vector; & Highest fitness set per generation \\
11 & for t \(\leftarrow\) 1: maxGen & \\
12 & V\({}_{\text{ap}}\), V\({}_{\text{down}}\) \(\leftarrow\) get V\({}_{\text{ap}}\) and V\({}_{\text{down}}\) (t, D, n, 0); & hormone renewal \\
13 & p\({}_{\text{C}}\) \(\leftarrow\) \(\text{P}\)\(\leftarrow\) \(\text{P}\)\(\times\) V\({}_{\text{ap}}\); & Hormone Renewal Cross Probability \\
14 & P\({}_{\text{m}}\) \(\leftarrow\) \(\text{P}\)\(\leftarrow\) \(\text{P}\)\(\times\) V\({}_{\text{ap}}\); & Hormone Renewal Mutation Probability \\
15 & newPop \(\leftarrow\) selection Operation (pop, popFitness); & Selection of operation \\
16 & newPop \(\leftarrow\) crossover Operation (newPop, P\({}_{\text{c}}\)); & crossover operation \\
17 & newPop \(\leftarrow\) mutation Operation (newPop, P\({}_{\text{m}}\)); & variant operation \\
18 & newPopFit \(\leftarrow\) repair Operation (newPop, model); & population restoration \\
19 & newPopFitness \(\leftarrow\) get Population Fitness (newPop); & Adaptation of new populations \\
20 & pop, popFitness \(\leftarrow\) elite Strategy (pop, newPop, popFitness, & Merger of child and parent populations, selection (elite strategy) \\  & newPopFitness; & Merger of child and parent populations, selection (elite strategy) \\
21 & a \(\leftarrow\) updateA (alntial, aFinal, t, maxGeneration); & Updating the convergence factor a \\
22 & alphaWolf, betaWolf, deltaWolf \(\leftarrow\) get eliteWolf (pop, popFitness); & Obtain the first 3 elite woves \\
23 & newPop \(\leftarrow\) evolve Population GWO (alphaWolf, betaWolf, & Updating wolf packs based on step size Euclidean distance \\  & deltaWolf, pop, a, t, maxGen); & proportional weights \\
24 & newPopFitness \(\leftarrow\) repair Operation (newPop, model); & population restoration \\
25 & newPopFitness \(\leftarrow\) get Population Fitness (newPop); & Adaptation of new populations \\
26 & pop, popFitness \(\leftarrow\) elite Strategy (pop, newPop, popFitness, & Merger of child and parent populations, selection (elite strategy) \\  & newPopFitness); & Updating the current optimal \\
27 & Best Individual Set, best Fitness Set; & Return to the Final Evolutionary Population \\
28 & return Population; & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: GA-GWO hybrid algorithm pseudocode. changes in the internal energy, and k is [PERSON]'s constant. The Metropolis criterion is the following equation:  
\[p=\left\{ \begin{matrix}\frac{1}{e^{\frac{E(X_{new})-E(X_{old})}{T}}}&;&if\ E(X_{ new})=E(X_{old})\\ \frac{E(X_{new})-E(X_{old})}{T}&;&if\ E(X_{new})>E(X_{old})\end{matrix} \right. \tag{32}\]  
Components of the simulated annealing algorithm  
1. Search space: Also known as the state space, it consists of all feasible solutions to the problem; each state in the space corresponds to a feasible solution. 2.