# Improved Trimming Ant Colony Optimization Algorithm for Mobile Robot Path Planning
## 5 Experimental Simulation and Results
### Algorithm Performance Testing
\begin{table}
\begin{tabular}{c c c c c} \hline
**Map Scale** & **Path Endpoint Index** & **Number of Ants** & **Pheromone Evaporation Rate \((\rho)\)** & **Pheromone Intensity \((Q)\)** \\ \hline \(10\times 10\) & 100 & 50 & 0.5 & 10 \\ \(20\times 20\) & 400 & 50 & 0.5 & 10 \\ \(30\times 30\) & 625 & 50 & 0.5 & 10 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameter settings for grid maps of different scales. ation, and best value--are presented in Table 3. IACO is introduced solely to validate the effectiveness of the path pruning improvement strategy in ITACO. Since the experimental results of IACO and ITACO on the standard test set are similar, the results of IACO are not included in Table 3.  
From Table 3, which shows the results for the unimodal function tests, ITACO performs the best for function F1, with both the average and best values close to the theoretical optimum, demonstrating strong convergence ability and search precision. AMACA performs significantly worse than ITACO but slightly better than ACO and AOA. Both AOA and ACO perform poorly and almost fail to converge effectively. For F3, ITACO's average and best values are again close to the theoretical optimum, indicating good global search capability. AOA and AMACA follow closely and also perform well. ACO shows the worst performance, suggesting that it easily falls into local optima and lacks fine search capability. In the multimodal function tests, ITACO achieves the lowest average values across nearly all functions and exhibits low standard deviations, indicating strong overall convergence ability and excellent robustness. For functions F4, F5, F6, and F9, the best results are close to the theoretical optimum, highlighting ITACO's optimization efficiency. ACO, on the other hand, generally produces average values over 10 times higher than the optimum for most functions, especially on F6 and F7, suggesting slow convergence and poor search quality. Although ACO occasionally achieves good best values on some functions (e.g., F4 and F9), its performance is unstable. AOA generally performs between ITACO and ACO in terms of average performance and standard deviation. On some functions (like F5 and F9), AOA achieves best values close to ITACO, but the average values remain high, indicating slow or unstable convergence. AMACA outperforms AOA on some functions (e.g., F5 and F7), but it shows significant fluctuations on more complex functions like F6 and F7. Overall, it performs slightly better than ACO and AOA but still falls behind ITACO. In the hybrid function tests, ITACO achieves the lowest average values and the best results closest to the theoretical optimum among all the algorithms, indicating that it excels not only in overall search quality but also in local search ability. AMACA achieves good best results on F13 and F18 but is slightly inferior on most other functions. In addition, ITACO  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Function**} & **ITACO** & **ACO** & **AOA** & **AMACA** \\  & **(Mean, Std, Best)** & **(Mean, Std, Best)** & **(Mean, Std, Best)** & **(Mean, Std, Best)** \\ \hline F1 & \(1.42\times 103,549\times 104,441\times 102\) & \(7.96\times 104,787\times  
consistently shows the smallest standard deviations across most functions, demonstrating high stability. AOA sometimes finds good best results, but its average performance is unstable with large standard deviations. AMACA achieves outstanding best values on some functions (e.g., F18), but its overall performance is slightly weaker than ITACO, especially in terms of stability. Across all metrics (average, best, and stability), ACO is clearly outperformed by the other algorithms, with average values generally far from the theoretical optimum, indicating poor convergence accuracy and limited search capability.