# GBUO: \"The Good, the Bad, and the Ugly\" Optimizer
## 2 \"The Good, the Bad, and the Ugly\" Optimizer (GBUO)
Optimization algorithms utilize 20 independent runs for each objective function, where each run employs 1000 iterations to generate and report the results. ### Results

In this section, simulation and implementation of optimization algorithms on standard objective functions are presented. A set of seven objective functions \(F_{1}\) to \(F_{7}\) is introduced as \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Parameter** & **Value** \\ \hline GA & & Real coded \\  & Selection & Roulette wheel (Proportionate) \\  & Crossover & Whole arithmetic (Probability = 0.8, \\  & Mutation & \(\alpha=[-0.5,\,1.5]\)) \\ PSO & & \\  & Topology & Fully connected \\  & Cognitive and social constant & \((C_{1},C_{2})\) 2, 2 \\  & Inertia weight & Linear reduction from 0.9 to 0.1 \\  & Velocity limit & 10\% of dimension range \\ \hline GSA & & \(\text{Alpha},G_{0},R_{num},R_{power}\) & \(20,100,2,1\) \\ \hline TLBO & & \(T_{F}\): teaching factor & \(T_{F}\) = round \([(1+rand)]\) \\  & random number & _rand_ is a random number between \([0-1]\). \\ GWO & & \\  & Convergence parameter (\(a\)) & \(a\): Linear reduction from 2 to 0. \\ \hline WOA & & \\  & Convergence parameter (\(a\)) & \(a\): Linear reduction from 2 to 0. \\  & \(r\) is a random vector in \([0-1]\). & \\  & \(l\) is a random number in \([-1,1]\). & \\ SHO & & \\  & Control parameter (\(h\)) & \([5,\,0]\). \\  & \(M\) constant & \([0.5,\,1]\). \\ \hline MPA & & \\  & Constant number & \(P\)=0.5 \\  & Random vector & \(R\) is a vector of uniform random numbers in \([0-1]\). \\  & Fish Aggregating Devices (\(FADs\)) & _FADs_=0.2 \\  & Binary vector & \(U\)= 0 or 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter values for the comparative algorithms. unimodal objective functions. Six objective functions \(F_{8}\) to \(F_{13}\) are considered multimodal objective functions. Finally, a set of ten objective functions \(F_{14}\) to \(F_{23}\) is introduced as fixed-dimension multimodal objective functions. The optimization of the unimodal objective functions using GBUO and the mentioned eight optimization algorithms are presented in Table 3. According to the results in this table, GBUO and SHO are the best optimizers for \(F_{1}\) to \(F_{4}\) functions. After these two algorithms, TLBO is the third best optimizer for \(F_{1}\) to \(F_{4}\) functions. GBUO is also the best optimizer for \(F_{5}\) to \(F_{7}\) functions. Moreover, Table 4 presents the results for implementing the proposed optimizer compared with the eight optimization algorithms considered in this study for multimodal objective functions. According to this table, GBUO, SHO, MPA are the best optimizers for \(F_{9}\) and \(F_{11}\) objective functions. GBUO in \(F_{10}\) function has the best performance among algorithms. After the proposed algorithm, GWO is the second and SHO is the third best optimizers for \(F_{10}\). GA for \(F_{8}\), TLBO for \(F_{12}\), and GSA for \(F_{13}\) are the best optimizers. GBUO is the second-best optimizer on \(F_{8}\), \(F_{12}\), and \(F_{13}\). The results of applying the proposed optimizer and the eight other optimization algorithms on the third type objective functions are presented in Table 5. Based on the results in this table, GBUO provides the best performance in all \(F_{14}\) to \(F_{23}\) objective functions.