## 4 Case Study
### Sensitivity Analysis  
To evaluate the structural robustness of the generalized minimum cost model and identify key sensitivity parameters, this study designs a univariate perturbation test. The proportion of electric vehicle traffic in the total traffic flow is taken as the core control variable, and the remaining parameters are fixed. Systematic deviations are applied in the range of [\(-60\%\),\(+60\%\)] with a step size of \(\pm 20\%\). The model is run after each disturbance and the second-order response output is recorded. One is the generalized minimum cost dynamics, and the other is the spatial distribution variation in the charging station location decisions. By observing the fluctuation pattern of the output value with the disturbance of the proportion of electric vehicles in the total traffic flow, accurately analyzing the impact strength and critical failure threshold of the input parameter on the planning scheme, and providing uncertainty resistance basis for core decision-making, the final result is the floating situation shown in Figures 10 and 11. Figure 8: Site selection and capacity comparison diagram. Figure 9: Comparison of actual and algorithmic charging station site selection and capacity determination. Figure 11: Changes in charging station site selection under different proportion. (**A**) Spatial allocation of charging infrastructure under 100% EV traffic penetration scenario. (**B**) Spatial allocation of charging infrastructure under 80% EV traffic penetration scenario. (**C**) Spatial allocation of charging infrastructure under 60% EV traffic penetration scenario. (**D**) Spatial allocation of charging infrastructure under 40% EV traffic penetration scenario. Figure 10: The variation in generalized minimum cost under different proportions. By conducting a sensitivity analysis on the proportion of electric vehicle traffic flow in the total traffic flow using the generalized minimum total cost model, the dual impact of traffic volume changes on algorithm performance and charging network planning decisions was revealed. Firstly, in terms of computational efficiency, as the proportion of electric vehicle traffic in the total traffic gradually decreases, the decrease in traffic significantly improves the convergence speed of the three algorithms, manifested as a systematic reduction in the number of iterations required to reach the termination condition. Secondly, when the proportion of traffic flow decreases to about 60%, the objective function values obtained by the GA and PSO tend to be consistent. This indicates that in low traffic load scenarios, the model structure may be simplified, significantly improving the accuracy and stability of these two types of algorithms, enabling them to approach the global optimal solution more reliably. On the other hand, at the level of charging infrastructure planning, analysis has found that its strategy exhibits significant traffic dependence and key node stability. Under the condition that the proportion of electric vehicle traffic in the total traffic flow reaches 80%, the optimal location of charging stations and the configuration of charging pile capacity show robustness and are not affected by traffic volume fluctuations. When the proportion of electric vehicle traffic in the total traffic flow reaches 60%, the economic efficiency is weakened due to the level of traffic flow and the characteristics of driving distance, which triggers spatial decision restructuring. Location B has been excluded from the site construction plan and replaced by location E, which has higher demand potential, reflecting the sensitivity of planning to the spatial distribution of demand. When the proportion of electric vehicle traffic in the total traffic reaches 40%, the probability of user charging behavior significantly decreases in some areas, resulting in a concentration of network planning towards a few core nodes exhibiting network shrinkage characteristics.