# Enhanced Teaching-Learning-Based Optimization Algorithm for the Mobile Robot Path Planning Problem
## 5 Experimental Studies
### Results of multimodal functions  
In Table 4, the simulation results of all tested multimodal functions are collected. The resulting best, worst, median, average, and SD values of each algorithm were computed by virtue of independent runs. The best values are emphasized in bold, and the following comments can be provided:  
* ETLBO obtained the optimum of functions F13 and F16 in all 50 independent runs; the resulting SD values were zero;
* For functions F15 and F19, ETLBO obtained near-optimal solutions and performed better than all compared algorithms. Regarding function F19, the result provided by ETLBO was a close approximation to the optimum and the corresponding SD value was very close to zero;
* The six algorithms all performed very well for function 14, and no significant difference was found regarding stability;
* For functions 18 and 20, TLBO(S) and DE yielded the best solution performances of all compared algorithms, respectively. Despite the fact that ETLBO failed to obtain the best solution performance, its metrics were acceptable in a relative manner since those values were located in an acceptable range;
* For function 17, ETLBO failed to obtain a good solution in 50 independent runs. The resulting metrics of ETLBO were higher when compared to the simulation results obtained by the compared algorithms, to a certain extent. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Function** & **Statistic** & **ETLBO** & **TLBO** & **TLBO(S)** & **PSO** & **DE** & **GA** \\ \hline \multirow{4}{*}{F13} & Best & \(\mathbf{0.00\times 10^{00}}\) & \(8.10\times 10^{-05}\) & \(2.58\times 10^{-04}\) & \(3.53\times 10^{-15}\) & \(1.91\times 10^{-04}\) & \(\mathbf{0.00\times 10^{00}}\) \\  & Worst & \(\mathbf{0.00\times 10^{00}}\) & \(5.01\times 10^{-02}\) & \(5.46\times 10^{-02}\) & \(2.22\times 10^{-03}\) & \(2.35\times 10^{-02}\) & \(2.40\times 10^{-05}\) \\  & Median & \(\mathbf{0.00\times 10^{00}}\) & \(8.70\times 10^{-03}\) & \(6.52\times 10^{-03}\) & \(1.27\times 10^{-06}\) & \(3.67\times 10^{-03}\) & \(\mathbf{0.00\times 10^{00}}\) \\  & Average & \(\mathbf{0.00\times 10^{00}}\) & \(1.16\times 10^{-02}\) & \(1.37\times 10^{-02}\) & \(1.11\times 10^{-04}\) & \(5.68\times 10^{-03}\) & \(1.45\times 10^{-06}\) \\  & SD & \(\mathbf{0.00\times 10^{00}}\) & \(1.05\times 10^{-02}\) & \(1.30\times 10^{-02}\) & \(3.62\times 10^{-04}\) & \(5.50\times 10^{-03}\) & \(4.87\times 10^{-06}\) \\ \hline \multirow{4}{*}{F14} & Best & \(\mathbf{3.98\times 10^{-01}}\) & \(\mathbf{3.98\times 10^{-01}}\) & \(\mathbf{3.98\times 10^{-01}}\) & \(\mathbf{3.98\times 10^{-01}}\) & \(\mathbf{3.98\times 10^{-01}}\) & \(\mathbf{3.98\times 10^{-01}}\) \\  & Worst & \(\mathbf{3.98\times 10^{-01}}\) & \(\mathbf{3.98\times 10^{-01}}\) & \(\mathbf{3.98\times 10^{-01}}\) & \(\mathbf{3.98\times 10^{-01}}\) & \(\mathbf{3.98\times 10^{-01}}\) & \(\mathbf{3.98\times 10^{-01}}\) \\  & Average & \(\mathbf{3.98\times 10^{-01}}\) & \(\mathbf{3.98\times 10^{-01}}\) & \(\mathbf{3.98\times 10^{-01}}\) & \(\mathbf{3.98\times 10^{-01}}\) & \(\mathbf{3.98\times 10^{-01}}\) & \(\mathbf{3.98\times 10^{-01}}\) \\  & SD & \(\mathbf{4.84\times 10^{-08}}\) & \(9.98\times 10^{-09}\) & \(4.02\times 10^{-07}\) & \(8.54\times 10^{-07}\) & \(\mathbf{3.34\times 10^{-01}}\) & \(8.46\times 10^{-08}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation results of multimodal functions.