## 5 Results  
As the goal of this paper is to improve the performance of the quality of solutions for the DGRP and improve the convergence rate (the number of generations) for finding the best solutions, verification by the results of experiments is needed to demonstrate the advantage of the proposed algorithm. In this section, the results of experiments obtained by applying the algorithm developed in this paper will be analyzed. Our analysis focuses on two algorithmic properties: performance and convergence rate. The evaluation process of the algorithms can be divided into five steps. The first step is to select the performance metrics for comparing different algorithms, the second step is to create instances for the DGRP, the third step is to set the parameters for different algorithms, the fourth step is to apply different algorithms to solve each instance of the DGRP and the fifth step is to calculate the performance metrics under consideration based on the results of experiments and compare all algorithms. For the first step, the performance metrics for comparing different algorithms include the average fitness function values, the average number of generations to find the best solutions and the average computation time to find the best solutions. For the second step, the locations of drivers and passengers are randomly generated based on a selected geographical area in Taichung City, which is located in the central part of Taiwan. The number of drivers and the number of passengers are increased gradually to generate instances of the DGRP with different size. For the third step, the parameters for PSO, NSDE, DE-1 and DE-3 are the same as the ones used in [13]. The parameters for SaNSDE-1-6 are specified later in this section. For the fourth step, we apply SaNSDE-1-6 ten times to solve each instance of the DGRP. As the results of applying PSO, NSDE, DE-1 and DE-3 to Case 1 through Case 10 are available in [13], we apply PSO, NSDE, DE-1 and DE-3 ten times to solve to Case 11 through Case 14. For the fifth step, we first calculate the average fitness function values, the average number of generations to find the best solutions and the average computation time to find the best solutions based on the results obtained. We then compare all algorithms based on the performance metrics \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Case** & **D** & **P** & **SaNSDE-1-6** & **DE-1** & **DE-3** & **NSDE** & **PSO** \\ \hline
1 & 3 & 10 & 9.6 & 16.6 & 19.8 & 15.6 & 64.6 \\
2 & 5 & 11 & 19.2 & 32.2 & 36.9 & 29.1 & 299.6 \\
3 & 5 & 12 & 29.4 & 39.7 & 47.6 & 43.3 & 394.5 \\
4 & 6 & 12 & 19.6 & 43.8 & 50.3 & 44.1 & 320.9 \\
5 & 7 & 13 & 16.7 & 31.8 & 44.1 & 37.3 & 304.1 \\
6 & 8 & 14 & 20 & 48.3 & 67.8 & 39.6 & 375.6 \\
7 & 9 & 15 & 60.8 & 101.4 & 135 & 70.7 & 553.6 \\
8 & 10 & 16 & 48.2 & 61.3 & 78.6 & 59.5 & 447.5 \\
9 & 11 & 17 & 53.9 & 59.7 & 65 & 64.2 & 580.7 \\
10 & 12 & 18 & 106.4 & 136.8 & 146.3 & 94.3 & 489.3 \\
11 & 20 & 20 & 191 & 436.5 & 817.1 & 542.5 & 21,314.5 \\
12 & 30 & 30 & 1392.5 & 5691.5 & 16,065.1 & 14,417.2 & 21,742.3 \\
13 & 40 & 40 & 18,439.777 & 15,185.8 & 27,574.4 & 27,260.1 & 22,734.2 \\
14 & 50 & 50 & 19,390.5 & 17,131.7 & 22,745.3 & 36,742.7 & 25,822.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average number of generations for discrete SaNSDE-1-6,DE-1, DE-3, NSDE and PSO algorithms with _NP_ = 30; _r\({}_{D}\)_ = _r\({}_{P}\)_ = 0.1.