## 4 Experimental Results
### Experiment on the Effect of the Improved PSO Algorithm
#### 4.3.2 Comparison with Other Swarm Intelligence Algorithms  
The proposed algorithm was compared with other classical swarm intelligence algorithms, including the Artificial Bee Colony (ABC) Algorithm [43], Firefly Algorithm (FA) [44], Grey Wolf Optimizer (GWO) [45], and Whale Optimization Algorithm (WOA) [46].  
The evaluation shown in Figure 11 is used for different swarm intelligence algorithms. For an algorithm, R rounds of experiments are performed, where the maximum number of iterations for each experiment is T, and bf is the maximum fitness function value obtained with T iterations. The global best fitness values (last column) for each round of experiments can be analyzed by calculating their mean, variance, and other statistical metrics, as well as by plotting box-and-line plots. In this paper, a larger mean value, a fitness closer to \(1\) after the same number of iterations, and a higher combinatorial coverage of pairwise tests suggest the better performance for the corresponding algorithm. The mean value in each column is the mean value of the fitness at the current number of iterations in the R-round experiments, and the average convergence curve of the algorithm can be plotted. The convergence process of each tested algorithm can thus be analyzed.  
In this section, the number of experimental rounds was set to 20, the number of populations in all populations was set to 100, and the maximum number of iterations (T) was set to 2000. The parameters of each algorithm were as follows: 1 In the ABC algorithm, the numbers of both the employed foragers bees and following bees were 50, and the following bees were generated via the roulette algorithm. If a nectar source was exploited 75 times, it was discarded and the hired bees corresponding to it became scout bees and a new nectar source was generated; 2 The step coefficient \(\alpha=1\), the maximum attraction \(\beta 0=0.8\), and the light absorption intensity coefficient \(\gamma=2\) were set in the FA; 3 There were no parameters that needed to be set in the GWO and WOA algorithms. 4 The parameterization of the method in this paper was the same as in Section 4.3.1. Experiments were performed with input variables (\(k\)) of 5 and 10.  
Figure 12 shows the average convergence curves for all the algorithms for the case \(K=5\). The fitness functions of all the algorithms eventually converged quickly to 1, indicating that all the algorithms achieved 100% combinatorial coverage of the pairwise tests in 20 rounds of experiments. \(k=5\) is the relatively simple case. (All algorithms can reach the desired goal within 20 iterations, and for the sake of a more concise figure, only the first 20 iterations were plotted when making the graph).  
Figure 11: The evaluation of different swarm intelligence algorithms.  
As can be seen from Figures 13 and 14, the improved PSO in this paper can have a very fast convergence rate in the early part of the iteration and can find the final objective smoothly. This fact suggests that the proposed approach is less likely to fall into a local optimal solution.  
Figure 12: Average convergence curves for all algorithms for the case \(K=5\).  
Figure 13: Average convergence curves for all algorithms for the case \(K=10\).