## 4 Numerical Experiments and Results  
### Example and Parameter Setting  
#### 4.1.1 Example Setting  
In this study, two types of examples are designed for the experiments and analyses. Among them, the adapted standard example of the basic MCVRP is used to analyze the solution quality and solution timeliness of the two-stage VNS-TA algorithm. The simulation  
Figure 2: Changes in the tolerance coefficients of the two strategies. (**a**) The change in the tolerance coefficient for Strategy 1. (**b**) The change in the tolerance coefficient for Strategy 2.  
example of the MCVRP considering traffic congestion under the mixed carbon policy is used to analyze the effects of cost saving and energy conservation and emission reduction of the two-stage VNS-TA algorithm. Firstly, with reference to the literature [29], 7 international standard examples of CVRP are adapted into 14 MCVRP examples. Based on the vrpnc2-S2 example, numerical experiments are used to analyze the effectiveness of the two-stage VNS-TA algorithm in solving the basic MCVRP. The two-stage VNS-TA algorithm is used to calculate 14 adapted standard examples to obtain results. The results obtained are compared with those of the IPSO [32] and IVNS [42] to verify the optimization ability of our algorithm. Secondly, with reference to the relevant literature and based on the vrpnc1-S2 example, a simulation example vrpnc1-S2' of the MCVRP considering traffic congestion under the mixed carbon policy is designed. This example is used to simulate a real situation. Consider a multi-compartment vehicle distribution system in which customers demand two different categories of products with split-compartment loading and distribution requirements. The distribution center uses two-compartment vehicles. In addition, this distribution center area suffers from traffic congestion and is subject to the mixed carbon policy. Sensitivity analyses of different scenarios are used to analyze the optimization effect, cost saving effect and energy conservation and emission reduction effect. It should be noted that the design of the simulation example refers to relevant research literature and reports. Simulation examples are not real cases. Although, in a real situation, traffic congestion and multi-variety product distribution are more complex, and the formulation of the mixed carbon policy also needs to consider various aspects, this paper simplifies these problems. Among them, in the simulation example, only the distribution of two categories of products is considered, the traffic congestion scenarios are simplified into three and the mixed carbon policy scenarios are simplified into five. The simulation example is set as follows. The coordinates of the customer, the demand of the customer and the capacity of the vehicle are adapted by referring to the literature [29]. The unit of distance is km. The unit of product demand is kg. The unit of maximum load for each compartment and the entire vehicle is also in kg. The free-flow travel speed of the vehicle in the uncongested road section is 80 km/h [48]. The parameters of the BPR function are 0.15 and 4 [20]. The cost of vehicle dispatch is 150 CNY/vehicle [21]. The vehicle use cost and labor cost after dispatching vehicles are 5 CNY/hour and 10 CNY/hour, respectively [21]. The fuel cost is 7.9 CNY/L [48]. The predefined parameters and load correction factor of the vehicles [21] are \(\{0,110,0,0,0,0.000375,8702\}\) and \(\{1.27,0.0614,0,0.0011,0.00235,0,0,1.33\}\). The carbon emission coefficient is 2.32 kg CO\({}_{2}\)/L [21]. Referring to China's carbon trading website and relevant reports from several countries, we set the carbon tax price at 0.06 CNY/kg and the carbon trading price at 0.05 CNY/kg. The simulation scenarios are set as follows. On the one hand, it is assumed that there are three traffic congestion scenarios, namely, the no congestion scenario, normal congestion scenario and very congested scenario. The coefficient matrix of the congestion degree for the three scenarios is generated [20].