# Enhanced Ant Colony Algorithm Based on Islands for Mobile Robot Path Planning
## 6 Simulation and Analysis
### Comparison with Other Algorithms
#### 6.2.3 Environment with 40 \(\times\) 40 Grids and 50 \(\times\) 50 Grids  
To further verify the performance of the proposed algorithm in more complex environments, two additional experimental scenarios were selected: 40 \(\times\) 40 and 50 \(\times\) 50 grid environments. In these scenarios, the start positions were assigned sequence numbers 1 and 2451, and the goal positions were 1600 and 50, respectively. To ensure the objectivity of the evaluation and to minimize the influence of random factors, each simulation experiment was repeated 20 times. Four algorithms--ACO, IACO, MAACO (Modified Adaptive Ant Colony Optimization Algorithm) [42], and EACI--were compared in terms of optimal path, convergence curve, and number of lost ants. In the 40 \(\times\) 40 grid environment, the optimal paths generated by each algorithm are shown in Figure 25, the convergence curves of the optimal paths are presented in Figure 26, and the number of lost ants for each algorithm is illustrated in Figure 27. In the 50 \(\times\) 50 grid environment, the corresponding results are shown in Figures 28-30. Additionally, the average values of relevant parameters were calculated, with the detailed statistical results provided in Table 3. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Item**} & **Average** & **Average of** & **Optimal** & **Standard** & **Mean Value of** & **Total Corner** \\  & **Iterative** & **Path Length** & **Rout Length** & **Deviation** & **Lost Ants** & **Angle (\({}^{\circ}\))** \\ \hline ACO & 77.10 & 45.89 & 45.36 & 1.6564 & 3112.40 & 675 \\ IACO & 21.90 & 45.22 & 44.53 & 0.5409 & 415.30 & 810 \\ CMEACO & 11.7 & 44.70 & 44.53 & 0.2043 & 237.70 & 630 \\ EACI & 1.4 & 44.53 & 44.53 & 0 & 27.5 & 765 \\ \hline \end{tabular}
\end{table} 
Table 2: Summary of the relevant data generated by the four simulation algorithms in the 30 \(\times\) 30 grid environment. Figure 26: Convergence curve of the optimal path for the four algorithms in the \(40\times 40\) grid environment. Figure 25: Optimal path planning results of the four algorithms in the \(40\times 40\) grid environment. Figure 28: Optimal path planning results of the four algorithms in the \(50\times 50\) grid environment. Figure 27: Number of lost ants generated by the four algorithms in the \(40\times 40\) grid environment. As shown in Figures 25 and 28, all algorithms were able to successfully plan effective paths from the start point to the goal point in both the 40 \(\times\) 40 and 50 \(\times\) 50 grid \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Map**} & \multirow{2}{*}{**Item**} & \multicolumn{2}{c}{**Average**} & \multicolumn{2}{c}{**Average of**} & \multicolumn{1}{c}{**Optimal**} & \multirow{2}{*}{**Standard**} & \multicolumn{1}{c}{**Mean Value**} & \multicolumn{1}{c}{**Total**} \\  & & **Iterative** & **Path** & **Route** & **Length** & **Deviation** & **of Lost** & **Corner** \\  & & **Times** & **Length** & **Length** & **Length** & **Ants** & **Angle (\({}^{\circ}\))** \\ \hline \multirow{4}{*}{\(40\times 40\)} & ACO & 100 & 65.34 & 63.94 & 2.1236 & 3993.8 & 900 \\  & IACO & 26.1 & 61.94 & 61.84 & 0.6412 & 694.5 & 765 \\  & MAACO & 15.7 & 60.24 & 59.84 & 0.3615 & 189.3 & 585 \\  & EACI & 6.2 & 60.21 & 59.25 & 0.2335 & 47.6 & 585 \\ \hline \multirow{4}{*}{\(50\times 50\)} & ACO & 100 & 84.64 & 81.59 & 2.5233 & 3988.7 & 630 \\  & IACO & 27.3 & 76.43 & 74.81 & 0.7122 & 879.2 & 900 \\ \cline{1-1}  & MAACO & 17.6 & 75.23 & 74.57 & 0.3813 & 394.4 & 540 \\ \cline{1-1}  & EACI & 7.1 & 74.54 & 72.81 & 0.2704 & 99.2 & 585 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of the relevant data generated by the four simulation algorithms in the 40 \(\times\) 40 and 50 \(\times\) 50 grid environments. Figure 30: Number of lost ants generated by the four algorithms in the 50 \(\times\) 50 grid environment. Figure 29: Convergence curve of the optimal path for the four algorithms in the 50 \(\times\) 50 grid environment. maps.