# Enhanced Ant Colony Algorithm Based on Islands for Mobile Robot Path Planning
## 6 Simulation and Analysis
### Comparison with Other Algorithms
#### 6.2.1 Environment with \(20\times 20\) Grids  
In a simple environment, the start and end positions are assigned sequence numbers 1 and 400, respectively. The initial pheromone distribution of EACI is illustrated in Figure 15, while Figure 16 presents the pheromone distribution across different iterations. To ensure a more objective evaluation of the algorithm and to minimize the impact of random factors, each simulation experiment was conducted 20 times. The comparative simulation results of the four algorithms--ACO, IACO, CMEACO, and EACI--are illustrated in Figure 17, where each algorithm generated an optimal path. Figure 18 presents the convergence curves of the optimal paths for the four algorithms, while Figure 19 depicts the number of lost ants produced by each algorithm. Furthermore, the average values of relevant parameters were calculated, with the detailed statistical results summarized in Table 1.  
Figure 14: Experimental results showing variations with different adaptive coefficients. Figure 16: Pheromone distribution in the EACI algorithm at different iterations in the 20 \(\times\) 20 grid environment: (**a**) after 1 iteration, (**b**) after 5 iterations, (**c**) after 15 iterations, and (**d**) after 30 iterations. Figure 15: Initial pheromone distribution of the EACI algorithm in the 20 \(\times\) 20 grid environment. Figure 17: Optimal path planning results of the four algorithms in the 20 \(\times\) 20 grid environment. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Item**} & \multicolumn{2}{c}{**Average**} & \multirow{2}{*}{**Average of**} & \multirow{2}{*}{**Optimal**} & \multirow{2}{*}{**Standard**} & \multirow{2}{*}{**Mean Value of**} & \multirow{2}{*}{**Total Corner**} \\  & **Iterative** & & & & & \\
**Times** & & & & & & \\ \hline ACO & 40.5 & 30.97 & 30.97 & 0 & 1246.0 & 675 \\ IACO & 10.5 & 30.97 & 30.97 & - & 172.3 & 675 \\ CMEACO & 6.4 & 30.97 & 30.97 & 0 & 165.10 & 585 \\ EACI & 1 & 30.97 & 30.97 & 0 & 9.85 & 675 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the relevant data generated by the four simulation algorithms in the 20 \(\times\) 20 grid environment. Figure 18: Convergence curve of the optimal path for the four algorithms in the 20 \(\times\) 20 grid environment. As presented in Figures 15 and 16, it is obvious that the pheromone quickly concentrates on the optimal path as the number of iterative times grows. As illustrated in Figure 16a, a large amount of pheromones was distributed near the optimal path after the first iteration, clearly indicating that EACI is capable of identifying the optimal route from the very beginning. Figure 16b depicts that, after the fifth iteration, the pheromones were entirely concentrated on the optimal path, with only minimal changes in subsequent iterations, thereby validating the extremely fast convergence speed of EACI. As presented in Figure 17, all four algorithms successfully captured the path from the starting to the ending points. The convergence curves of the optimal path for these algorithms are shown in Figure 18, while Table 1 provides a summary of the experimental results. Among the four algorithms, EACI demonstrated the fastest convergence speed. However, its total turning angle was 675\({}^{\circ}\), which was identical to that of the ACO and IACO but slightly larger than CMEACO. As depicted in Figure 19, as the number of iterations increased, the occurrence of deadlock ants decreased for all algorithms. Notably, EACI produced the fewest deadlock ants and exhibited the most rapid decline in their numbers, further highlighting its efficiency in path optimization. Table 1 shows that all algorithms successfully identified the shortest path, with a length of 30.97. The most notable observation was that EACI resulted in the least average number of deadlock ants and the lowest average number of iterations among the four algorithms, with values of 9.85 (9.85 \(<\) 165.10 \(<\) 172.3 \(<\) 1246.0) and 1 (1 \(<\) 6.4 \(<\) 10.5 \(<\) 40.5), respectively, which are provided in the table.