# Improved GA-LNS Algorithm for Solving Vehicle Path Problems Considering Carbon Emissions
## 5 Analysis and Comparison of Experimental Findings
### Comparative Analysis of the Calculation Results of Different Optimization Algorithms  
To evaluate the algorithm's performance, the sets of C201, R104, and RC204 cases from the Solomon database are used as test data. The enhanced genetic algorithm presented in this paper is employed to conduct five random simulation experiments, comparing its performance with that of conventional genetic algorithms (GA) and particle swarm optimization (PSO). The optimal results obtained from these five simulation experiments are averaged, and the findings are presented in Table 3, where \(D_{\text{best}}\) represents the optimal value and \(D_{\text{ave}}\) represents the average optimal value. As shown in Table 3, the solution results of the GA-LNS algorithm designed in this paper outperform the traditional GA and the PSO. This demonstrates that the GA-LNS algorithm exhibits greater efficiency and accuracy in addressing the vehicle routing problem with time windows (VRPTW), yielding optimal solutions with enhanced robustness. Specifically, the optimal solution's performance reaches an optimization degree of 38.03%, with an average optimization degree of 35.48%, when compared to the traditional genetic algorithm. In comparison to the particle swarm algorithm, these figures are 29.71% and 26.01%, respectively. These results indicate that the GA-LNS algorithm not only performs better but also provides superior stability across multiple simulation experiments. This enhanced stability suggests that the GA-LNS algorithm is capable of delivering better solutions that meet more stringent performance requirements, thereby improving user satisfaction in real-world applications and contributing to the long-term competitive advantage of enterprises. With the country's emphasis on green logistics, the GA-LNS algorithm provides a practical application program for relevant enterprises. The results can assist decision-makers in formulating more scientifically grounded logistics policies and enable enterprises to implement energy-saving and emission-reduction measures in practice, thereby contributing to the country's environmental policies and sustainable development strategies. Furthermore, the successful application of the GA-LNS algorithm not only underscores the importance of technological innovation but also encourages companies to adopt similar intelligent optimization techniques more frequently in the future, thereby promoting the green transformation of the entire logistics industry. This transformation converts research findings into practical applications, further advancing a harmonious balance between economic development and environmental protection within China's logistics sector. To better illustrate the results of the GA-LNS algorithm's solutions for the C201, R104, and RC104 arithmetic sets, Figure 4 displays the optimal distribution roadmaps obtained from the simulations for each set. It is evident that the algorithm demonstrates the clearest distribution roadmap for C201, attributed to the centralized distribution of the customer base in the C-type test set, which features a more uniform distance between nodes and a reduction in route crossings and overlaps. This allows the algorithm to identify the optimal solution more efficiently, thereby enhancing overall distribution efficiency. Conversely, the optimal distribution roadmap for R104 appears the most chaotic, primarily due to the random distribution of the customer base in the R104 test set and the low permitted vehicle load, which fails to accommodate the needs of multiple customers. This situation necessi