## 5 Performance Evaluation and Comparison

Table 1: Parameter settings in the simulations. many similar individuals in each population is ascribable. Therefore, the GA approach is more likely to approach a local optimum than is the DPSO approach. As the size of the problem increased, the GA saved the better results from the previous generation and passed them to the next generation through an evolutionary process. By contrast, under the DPSO approach, the better results in each generation did not always have the chance to improve the outcomes of each particle. Consequently, the GA approach is more likely to approach the global optimum through the evolutionary process. Figure 7 displays the effect of the number of sensor spots on the quality of solutions generated by the greedy algorithms, the GA, and the DPSO algorithm. The fitness values obtained by the greedy algorithms were approximately 2.2% worse than were those obtained by the evolutionary algorithms. Regardless of the number of sensor spots, the GA had better fitness values than the DPSO algorithm (a difference of 0.14% to 0.43%). In short, the GA outperformed the DPSO algorithm according to the fitness function. Moreover, the GA approach was more likely to approach the global optimum than was the DPSO approach through evolutionary generation. Figure 5: Total traveled distance under the greedy algorithms, genetic algorithm (GA), and discrete particle swarm optimization (DPSO) algorithm. Figure 6: Differences in the total traveled distance under the greedy algorithms, GA, and DPSO algorithm. Figure 8 illustrates the effect of the number of evolutionary generations on the fitness function under the GA and DPSO schemes when \(n=60\), \(m=5\), and \(I_{c}=100\). With respect to the fitness values, the GA approach outperformed the DPSO approach after 15 generations and achieved solutions that were 0.3% better. We continued the preceding experiment, extending the number of iterations from 100 to 1000 to investigate the performance of the proposed GA and DPSO approaches. Figure 9 presents the experimental results obtained when \(n=60\), \(m=5\), and \(I_{c}=1000\). As the number of iterations increased, the fitness improved correspondingly, and after 300 generations, the GA had approached a convergent solution. Notably, the DPSO algorithm obtained a near-convergent solution after 150 generations. Figure 10 presents the effect of the number of sensor spots on the average running time required by the greedy algorithms, the GA, and the DPSO algorithm. The running time required by the greedy algorithms was less than 50 milliseconds, which is much less than that required by the meta-heuristic algorithms. Regardless of the number of sensor spots, the GA required considerably (approximately 4.8-10 times) more running time than did the DPSO algorithm. In short, the DPSO algorithm outperformed the GA with regard to average running time; therefore, the DPSO approach was more efficient in approaching the global optimum through evolutionary generation than was the GA approach. Figure 8: Fitness values of the GA and DPSO algorithm in 100 generations when \(n=60\) and \(m=5\). Figure 7: Fitness values of the greedy algorithms, GA, and DPSO algorithm. In the simulations, we further compared the performance of the GA and the DPSO algorithm (in terms of the average traveled distance, the average difference in the distance traveled, and average fitness values) by considering 40 distinct, randomly generated scenarios. Table 2 displays the average traveled distance of the 50 trajectories generated under a population size of 100 when \(n=40\) and \(m=5\). To compare our implementation of the GA and the DPSO algorithm, we conducted a \(t\)-test [51] of the cost distribution of the trajectories obtained by each algorithm. In Table 2, the \(p\)-value obtained in the \(t\)-test represents the probability that the difference between the two averages is due to chance. In other words, when the \(p\)-value obtained is \(<\)0.05, the two averages differ significantly, and the probability that this difference is not due to chance is 95%.