# Enhanced Teaching-Learning-Based Optimization Algorithm for the Mobile Robot Path Planning Problem
## 5 Experimental Studies
### Statistical comparison  
Table 6 collects the simulation results obtained for all considered problem instances and algorithms. The resulting best, worst, and average objective values, as well as the corresponding deviations, were computed according to 50 independent runs. The best values among the three compared algorithms are emphasized in bold, and the following comments can be drawn according to these results. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multirow{2}{*}{**Algorithm**} & \multicolumn{2}{c}{**Best**} & \multicolumn{2}{c}{**Average**} & \multicolumn{2}{c}{**Worst**} \\ \cline{3-8}  & & **Length** & **Deviation (\%)** & **Length** & **Deviation (\%)** & **Length** & **Deviation (\%)** \\ \hline \multirow{3}{*}{\(20\times 20\)} & ACO(L) & 156.07 & 2.73\% & 160.16 & 5.42\% & 163.64 & 7.71\% \\  & ACO(G) & 154.85 & 1.93\% & 158.78 & 4.52\% & 161.92 & 6.58\% \\  & ETLBO & **151.92** & **0.00\%** & **156.64** & **3.10\%** & **160.71** & **5.78\%** \\ \hline \multirow{3}{*}{\(30\times 30\)} & ACO(L) & 232.63 & 3.13\% & 240.06 & 6.43\% & 245.56 & 8.87\% \\  & ACO(G) & 231.42 & 2.60\% & 238.56 & 5.76\% & 244.35 & 8.33\% \\  & ETLBO & **225.56** & **0.00\%** & **233.78** & **3.64\%** & **240.21** & **6.49\%** \\ \hline \multirow{3}{*}{\(40\times 40\)} & ACO(L) & 302.99 & 4.02\% & 313.52 & 7.64\% & 322.99 & 10.89\% \\  & ACO(G) & 301.27 & 3.43\% & 309.56 & 6.28\% & 318.85 & 9.47\% \\  & ETLBO & **291.27** & **0.00\%** & **303.87** & **4.33\%** & **312.49** & **7.28\%** \\ \hline \multirow{3}{*}{\(50\times 50\)} & ACO(L) & 400.42 & 5.73\% & 412.07 & 8.81\% & 421.13 & 11.20\% \\  & ACO(G) & 395.77 & 4.51\% & 409.77 & 8.20\% & 418.70 & 10.56\% \\ \cline{1-1}  & ETLBO & **378.70** & **0.00\%** & **398.27** & **5.17\%** & **410.42** & **8.37\%** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Simulation results for MRPP problems. Figure 9: Best solution information of instance \(50\times 50\). * In terms of the optimum, ETLBO was able to find the best solutions for all considered problem instances of different problem scales. However, ACO(L) and ACO(G) failed to obtain the best or near-optimal solutions especially for large-scale problem instances. In this regard, the values of the best deviation metric amounted to 5.73% (given by ACO(L)) and 4.51% (given by ACO(G));
* ETLBO yielded the best solution performance when it was applied to address different problem instances in terms of best-, worst-, and average-related metrics. ACO(G) performed second to ETLBO, while ACO(L) showed the weakest solution performance;
* The average metrics versus the problem size indicated that the increasing problem dimensionality raised the optimization difficulty. In this regard, the average deviations of ACO(L), ACO(G), and ETLBO for the 20 \(\times\) 20 instance were 5.42%, 4.52%, and 3.10%, respectively. For the large-scale instance with a 50 \(\times\) 50 size, the average deviations amounted to 8.81%, 8.20%, and 5.17%, respectively;
* Despite the diversity of problem instances, it is evident that all generated values from the proposed ETLBO were more acceptable when compared to the two other algorithms compared. To reveal the statistical significance of the simulation results, the Wilcoxon rank-sum test was utilized to independently compare the ETLBO with the ACO(L) and ACO(G). As stated in the previous subsection, the value of \(w_{A}\) fell in range [1275, 3775] when comparing ETLBO with another robot-path-planning algorithm. The minimal \(w_{A}\) occurred when ETLBO completely outperformed the compared algorithm in all 50 runs, while the maximal \(w_{A}\) was observed in the circumstance that ETLBO underperformed its rival in all executions. The \(w_{A}\) metric and the \(p\) values of the Wilcoxon rank-sum test associated with each compared algorithm were calculated and presented in Table 7, where mark \"\(\surd\)\" represents a win for ETLBO over its rival.