## 4 Experimental Simulations
### Analysis on Experimental Results  
Figure 7 shows work environment of a cleaning robot. The red nodes denote non-cleaned cells, which shall be traversed again by the robot. The two curves shown in Figure 8 present the optimal path length determined at the time of sampling by the dynamic Inver-Over evolutionary algorithm and the static algorithm respectively. As demonstrated in the figure, the results of both algorithms are the same at certain time points. At these time points, no cell is found occupied, with the dynamic algorithm degraded into the static algorithm.  
Figure 9 presents the optimal paths of both algorithms at 1 s, 75 s, 150 s and 200 s, respectively. The red path represents the results obtained from the dynamic algorithm, while the blue path indicates the results obtained from the static algorithm. At the time point (\(t\)) of 75 s, three cells are found occupied by dynamic obstacles under the environment. In order to address this problem with the dynamic algorithm, the globally planned old path is transformed into a new one by the Occupy operator, while the static algorithm is to restart. Though the optimal solution can be obtained from the static algorithm, it is time-consuming as compared to the dynamic algorithm.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline iterations & 1000 \\ pop\_size & 100 \\ \(k\) & 0.4 \\ \(p\) & 0.5 \\ \(f\) & 0.4 \\ \(m\) & 200 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experimental parameters.  
Figure 8: Curves on optimal path length determined by both algorithms.  
Figure 7: Non-cleaned cells.  
To illustrate the real-time performance of dynamic algorithm better, 10 sets of comparative experiments are performed with one cell occupied by the dynamic obstacle in the paper. The dynamic algorithm uses Occupy operator to calculate the results, while the static algorithm is to restart by inputting the cell position. The running time of both algorithms is shown in Figure 10. The results in Figure 10 indicate that the time required by the dynamic algorithm is far less than the static algorithm, proving the superiority of the dynamic algorithm in time.  
In this paper, the results at the time of sampling were determined by the static Inver-Over algorithm, and compared against the results obtained from the dynamic algorithm to analyze errors. Figure 11 is the curve of relative errors, while Figure 12 is the curve of absolute errors. As shown in Figure 12, relative error is below 7% in most cases. More detailed results are indicated in Table 2, which indicates that the mean absolute error is 1.4574 and the mean relative error is merely 2.2%. Considering that the environment remains unchanged under some circumstances, the data without any error are discounted and deleted when the mean error is calculated. These results demonstrate that the dynamic Inver-Over evolutionary algorithm proposed in this paper is conducive to monitoring the best path under dynamic environment and making rapid responses. In addition, this algorithm is validated to be effective on addressing the problems with re-entry path planning.  
Figure 10: Running time of both algorithms.  
Figure 9: Optimal paths of both algorithms.