## 5 Comparison of Results
### Experiments and Results for the Benchmark Control Problem  
Thirty experiments were performed with the proposed OFDE and OFHS methods applied to mobile robot controller. The parameters used for the experiment with the OFDE method are shown in Table 10 and for the OFHS method are shown in Table 11.  
The results obtained by optimizing the parameters of the mobile robot controller, with the OFDE and OFHS methods are presented in Tables 15 and 16, respectively. The noise applied to this controller is 0.5 (Gaussian random number). The execution times of each algorithm are also shown. We can summarize that, in both optimized algorithms, with our proposal, the improvement on average is observed, and in the same way, we can observe that the best result obtained is by using our new proposal. The comparison between the optimized method with noise and without noise also shows that our proposal improves on problems with uncertainty, and this is observed for both algorithms. Figures 11 and 12 represent the best simulations obtained with each of the methods; for Figure 11, the OFDE method with the best paths without noise and noise are illustrated, and Figure 12 illustrates the OFHS method with the best paths without noise and with noise. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **HS without Noise FLC** & **HS with Noise FLC** & **FHS without Noise FLC** & **GFHS without Noise FLC** & **GFHS with Noise FLC** \\ \hline Minimum & \(4.72\times 10^{-2}\) & \(8.02\times 10^{-2}\) & \(9.80\times 10^{-3}\) & \(9.00\times 10^{-4}\) & \(8.90\times 10^{-3}\) & \(2.00\times 10^{-4}\) \\ Maximum & \(2.89\times 10^{1}\) & \(9.81\times 10^{-1}\) & \(2.04\times 10^{0}\) & \(1.14\times 10^{0}\) & \(2.18\times 10^{+0}\) & \(1.26\times 10^{0}\) \\ Average & \(1.50\times 10^{0}\) & \(3.66\times 10^{-1}\) & \(3.77\times 10^{-1}\) & \(3.26\times 10^{-1}\) & \(3.39\times 10^{-1}\) & \(2.37\times 10^{-1}\) \\ Std. & \(5.28\times 10^{0}\) & \(3.00\times 10^{-1}\) & \(4.73\times 10^{-1}\) & \(3.22\times 10^{-1}\) & \(4.61\times 10^{-1}\) & \(3.07\times 10^{-1}\) \\ Execution time & \(2529.2\) s & \(3027.8\) s & \(3789.4\) s & \(4295.4\) s & \(8239.3\) s & \(9765.9\) s \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Results of the OFHS method applied to benchmark controller. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Function** & **Differential Evolution Algorithm** & **Harmony Search Algorithm** & \multicolumn{2}{c}{**Z-Test**} \\ \hline  & Average & Std & Average & Std & Z Value & Evidence \\ \hline Sum Square & \(4.12\times 10^{-6}\) & \(1.93\times 10^{-5}\) & \(4.45\times 10^{-4}\) & \(2.44\times 10^{-3}\) & \(-0.9896\) & Not significant \\ \hline Rosenbrock & \(8.20\times 10^{-8}\) & \(1.20\times 10^{-7}\) & \(1.63\times 10^{-2}\) & \(7.44\times 10^{-3}\) & \(-11.9998\) & Significant \\ \hline Sphere & \(8.49\times 10^{-24}\) & \(4.65\times 10^{-23}\) & \(7.63\times 10^{-4}\) & \(3.63\times 10^{-4}\) & \(-11.5127\) & Significant \\ \hline [PERSON] & \(9.67\times 10^{1}\) & \(1.74\times 10^{1}\) & \(4.91\times 10^{-4}\) & \(1.08\times 10^{-4}\) & \(30.4394\) & Not significant \\ \hline Schwefel & \(1.52\times 10^{3}\) & \(1.75\times 10^{3}\) & \(1.57\times 10^{-2}\) & \(3.24\times 10^{-2}\) & \(4.7573\) & Not significant \\ \hline [PERSON] & \(7.07\times 10^{0}\) & \(6.33\times 10^{0}\) & \(4.76\times 10^{-13}\) & \(5.63\times 10^{-13}\) & \(6.1175\) & Not significant \\ \hline [PERSON] & \(6.95\times 10^{-6}\) & \(3.37\times 10^{-5}\) & \(6.65\times 10^{-14}\) & \(7.77\times 10^{-14}\) & \(1.1296\) & Not significant \\ \hline [PERSON] & \(6.34\times 10^{-4}\) & \(1.66\times 10^{-3}\) & \(2.64\times 10^{-3}\) & \(9.10\times 10^{-4}\) & \(-5.8040\) & Significant \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Results for the statistical test.