# Enhanced Ant Colony Algorithm Based on Islands for Mobile Robot Path Planning
## 6 Simulation and Analysis  
### Determination of Parameter Optimization Combination  
In this study, to determine the optimal combination of parameters, numerous simulation experiments were conducted using both empirical and experimental methods [30]. The experiments were conducted on a laptop equipped with a 12 th Gen Intel(r) Core(tm) i7-12700H processor (2.30 GHz) and 16 GB of RAM using MATLAB R2021b as the simulation platform. A group of parameters was established for the simulation experiments, where, in each experiment, only one of the parameters was varied, while the others remained constant. Each experiment was run ten times with the same parameters to minimize the impact of random variations, and the average of all the results was calculated. The advantages and disadvantages of different parameter combinations were analyzed, including the number of iterations, the length of the global optimal route, and the quantity of deadlock ants encountered during the algorithm's execution. Since parameters \(\alpha\) and \(\beta\) have been extensively studied, this study primarily focuses on optimizing parameters \(\varepsilon\), \(\lambda\), \(\kappa\), and \(N\). In a certain map, the parameters are set as follows: \(m=50\), \(Nc_{max}=100\), \(\alpha=1.1\), \(\beta=7\), \(Q=100\), \(\kappa=0.9\), \(N=6\), and \(\lambda=3\). The number of iterations, global optimal route length, and the amount of deadlock ants are monitored for each set of parameters, including \(\varepsilon=0.1\), \(\varepsilon=0.2\), \(\varepsilon=0.3\), \(\cdots\), and \(\varepsilon=1.0\). The detailed simulation results of the EACI are shown in Figure 11.  
From Figure 11, as the angle coefficient increases, the optimal path length changes very slightly, but both the number of lost ants and iterations increase gradually. When the parameters are set to \(\varepsilon\in[0.1,0.7]\), the EACI algorithm demonstrates good performance in all the three aspects mentioned above. Under the condition of the same grid map, the setting parameters are as follows: \(m=50\), \(Nc_{max}=100\), \(\alpha=1.1\), \(\beta=7\), \(Q=100\), \(\kappa=0.9\), \(N=6\), and \(\varepsilon=0.5\). When the parameters were varied as \(\lambda=1\), \(\lambda=10\), \(\lambda=20\), \(\cdots\), and \(\lambda=100\), the experimental simulation results of the EACI were recorded, as presented in Figure 12.  
By analyzing Figure 12, it can be observed that, regardless of the pheromone expansion coefficient \(\lambda\), the EACI algorithm showed minimal variations in the optimal route, iterative times, and the quantity of deadlock ants. This observation suggests that \(\lambda\) does not significantly affect the path planning performance of the EACI algorithm. Figure 11: Experimental findings showing variations across different angle coefficients. In the same environment, experiments were conducted with the varying parameters \(N=2\), \(N=3\), \(\cdots\), and \(N=12\), while the remaining parameters were set as \(m=50\), \(Nc_{max}=100\), \(\alpha=1.1\), \(\beta=7\), \(Q=100\), \(\kappa=0.9\), \(\lambda=3\), and \(\varepsilon=0.5\). The simulation results were plotted as a curve, as presented in Figure 13.  
By analyzing Figure 13, it is clear that the optimal route path length remains relatively stable as the number of islands increases, while iterative times and deadlock ants gradually decrease, with iterative times fluctuating between 1 and 10. Additionally, the figure shows that adding more islands does not necessarily improve performance; beyond a certain point, the algorithm's efficiency no longer improves. In this experiment, the EACI demonstrated good performance when \(N\in[6,12]\). The parameters for the same environment were set as follows: \(m=50\), \(Nc_{max}=100\), \(\alpha=1.1\), \(\beta=7\), \(Q=100\), \(\lambda=3\), \(N=12\)\(\varepsilon=0.5\), \(\kappa=0.3\), \(\kappa=0.4\), \(\cdots\), and \(\kappa=1.3\). The results of the experiment are presented in Figure 14.  
Figure 12: Experimental results showing variations with different pheromone expansion coefficients.