**4. Experiments and Results Analysis**

In order to further test the performance of the algorithm, the algorithm was compared with the traditional NSGA-II. Experiments were carried out with three classical datasets (Solomon benchmark datasets r101, c101 and rc101 [42]) to test the performance of the algorithms. Customer influence, information dissemination and customer weight information were added to form the small-scale cases (c101\_25, r101\_25 and rc101\_25), the medium-scale cases (c101\_50, r101\_50 and rc101\_50) and the large-scale cases (c101\_100, r101\_100 and rc101\_100), which had 100 customers.

Table 2 shows the values for the model parameter settings. The values of the parameters were obtained from [5,40].


**Table 2.** Related parameters and values.

Table 3 represents the traffic congestion coefficients for different periods. The parameter values in both tables were from the study by Wang et al. [40]. All case tests were performed on an Intel(R) Core (TM) i5-7200U, 2.50 GHz, 4 GB RAM, Windows 10 (64-bit) computer, and the algorithms used in this paper were programmed on MATLAB R2019b.

**Table 3.** Traffic congestion factor.


#### *4.1. Model Solution*

There were six customer information points in Table 4. This study used customer point information to solve the CV-GVRP under the G-NSGA-II algorithm, and compared the obtained results with those under the uniparental genetic algorithm. Although the model and algorithm in this paper did not have an advantage in terms of time consumption, they performed better in reducing the total cost and increasing the customer value. The solution results are shown in Table 5.

**Table 4.** Point-related customer information.


**Table 5.** SAPGA and G-NSGA-II solution results.


### *4.2. Numerical Benchmark*

#### 4.2.1. Comparison between MOPSO, NSGA-II and G-NSGA-II

Using MOPSO, the conventional NSGA-II and G-NSGA-II to solve the nine cases, the parameter settings of the algorithms used in the experiments were as follows: Figures 8–10 show the r101\_100, r101\_50 and r101\_100 Pareto solution results. In this study, the algorithm parameters were set as per the study by Rabiee et al. [43]. The basic parameters of the experiment are shown in Table 6.

**Figure 8.** Solution results for r101\_100.

**Figure 9.** Solution results for r101\_50.

**Figure 10.** Solution results for r101\_25.


**Table 6.** Parameter settings of each algorithm.

The algorithm comparison continued using these nine examples, and the following three indicators were used to compare the performance of the algorithms:


For the first two indicators, the higher the value, the better the algorithm performance, while the lower the average ideal distance value, the better the algorithm performance [43]. The comparison results are shown in Table 7.



In Figure 11, the NPS of G-NSGA-II and NSGA-II was significantly greater than that of MOPSO. The first two were similar in terms of dispersion. However, the median NPS of G-NSGA-II was significantly higher than that of NSGA-II. Figure 12, showing the DM, shows the boxplot of G-NSGA-II, which outperformed the others in dispersion and median. The MID in Figure 13 shows that G-NSGA-II and NSGA-II performed significantly better than MOPSO, with G-NSGA-II having a slightly lower median. Based on the results as previously seen, G-NSGA-II performed better. In summary, the G-NSGA-II algorithm outperformed the traditional NSGA-II and MOPSO ones in terms of convergence and diversity. Its Pareto solutions were more uniformly distributed than those of the traditional NSGA-II. Therefore, it had better results in solving the problem.

**Figure 11.** NPS boxplot.

**Figure 12.** DM boxplot.

**Figure 13.** MID boxplot.

#### 4.2.2. Analysis of Carbon Trading Price Sensitivity

Through the analysis of different types of data, it was found that the total cost changed significantly under the influence of variable carbon trading prices, especially in the largescale examples. The change in price was not a single trend, which was why the carbon trading prices differed from the carbon tax policies. Under its influence, carbon emissions could increase or decrease, so the total cost also fluctuated. Due to firms gaining from selling carbon allowances, the cost could be reduced. Additionally, this behavior could incentivize firms to continue cutting carbon.

The total cost was lower than the situation with a fixed carbon trading price. The changes are shown in Figure 14. Furthermore, it indicated that a proper adjustment in carbon trading prices could motivate enterprises to adjust their distribution schemes. This could reduce the total cost and contribute to declining social carbon emissions from a macroperspective.

**Figure 14.** Graph of total cost versus *ω*ˆ .

4.2.3. Influence of Time-Dependent Network on Routing Strategy

In cases of different scales, the model in this paper had different improvements. For example, in the small-scale case, the total cost of the CV-GVRP was saved by 6.42%, and the customer value was increased by 15.43% on average. In the medium-scale case, the total cost of the CV-GVRP was saved by 5.4%, and the customer value was increased by 17.68% on average. In the large-scale case, the total cost of the CV-GVRP was saved by 3.75%, and the customer value was increased by 17.40% on average. The results of the comparison are shown in Table 8. The cost savings of the CV-GVRP were more significant in the small-scale cases, and the increase in customer value was more obvious in the medium-scale and largescale cases. The average increase in the total cost was 5.192%, and the average increase in customer value was 16.838%, which indicated that the CV-GVRP performed better than the model with a static road network in improving customer value. Considering traffic congestion could increase the delivery time and increase the total cost, but the CV-GVRP brought more customer value, which is conducive to the long-term development of the enterprise.


**Table 8.** Comparison of static road network and CV-GVRP results.

4.2.4. Influence of Customer Value on Routing Strategy

The GVRP is a model that does not consider the potential value of customers. It has the same constraints as the CV-GVRP. However, the objective function of the GVRP is customers' total cost and current value, which does not consider the impact of potential value on corporate reputation. Then, the G-NSGA-II was used to solve the GVRP for different cases. In the small-scale case of 25 customers, the total cost of CV-GVRP increased by 7%, the customer value increased by 14% and the satisfaction increased by 26% on average. In the medium-scale case of 50 customers, the total cost increased by 8%, the customer value increased by 14% and the satisfaction increased by 15% on average. In the large-scale case of 100 customers, the total cost increased by 3%, the customer value increased by 21% and the satisfaction increased by 13% on average. Overall, the average increase in the total cost was 3%, the average increase in customer value was 21% and the average increase in satisfaction was 13%. The increase in the total costs was most likely due to the increased delivery distance and time required to serve important customers. Additionally, the improvement in customer satisfaction brought more potential value to the enterprise and increased the total customer value. The results of the comparison are shown in Table 9.


**Table 9.** Comparison of GVRP and CV-GVRP results.
