# Improved GA-LNS Algorithm for Solving Vehicle Path Problems Considering Carbon Emissions
## 5 Analysis and Comparison of Experimental Findings
### Comparison of Initial Solutions Obtained by Different Algorithms  
Taking C101 as a case, this research aims to simulate and analyze the model. The initialization of the population in the genetic algorithm typically involves two commonly used methods: the random generation method (RGM) and the random traversal insertion method (RIM). The initial results obtained using the improved minimum cost nearest neighbor method are compared with those obtained by the RGM and the RIM, as shown in Table 2, where \(NV\) is the number of vehicles, \(TD\) is the distance travelled, \(D_{1}\) is the cost of travel, \(D_{2}\) is the carbon emission cost, and \(D\) is the total distribution cost.  
From the findings shown in Table 2, we can derive the following conclusions: 1. The initial solution generated by the INNC method accelerates the algorithm's convergence speed, enhances its search capabilities, and effectively guides it toward an improved solution space, thereby reducing randomness in the search process. The total cost of generating the initial solution using the INNC algorithm is significantly lower than that achieved by both the RGM and the RIM. Among the initial solutions generated by the INNC method, the distance traveled by the vehicle is significantly optimized, resulting in a corresponding reduction in travel costs and carbon emissions. 2. The total cost associated with the INNC method is reduced by 46.49% and 32.23% compared to the RGM and the RIM, respectively, with individual sub-costs also being optimized.  
In conclusion, employing the INNC method for population initialization results in superior initial solutions. These enhanced solutions are capable of converging more swiftly to the optimal outcome, which in turn decreases the number of generations needed, minimizes the consumption of computational resources, and ultimately leads to time and cost savings.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(f_{k}\) & 300 & \(p_{1}\) & 0.388 \\ \(c_{k}\) & 0.8 & \(NIND\) & 50 \\ \(\delta\) & 2.63 & \(MAXGEN\) & 300 \\ \(F_{e}\) & 0.16 & \(p_{c}\) & 0.8 \\ \(c_{m}\) & 0.76 & \(p_{m}\) & 0.2 \\ \(cap\) & 300 & GAP & 0.9 \\ \(P_{0}\) & 0.122 & \(r_{1}\) & 15 \\ \(r_{2}\) & 1 & \(w_{1}\) & 0.001 \\ \(w_{2}\) & & 0.005 & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Model parameters.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Relevant Indicators** & \(NV\) & \(TD\) & \(D_{1}\) & \(D_{2}\) & \(D\) \\ \hline \(R_{INNC}\) & 8 & 1269.21 & 1015.37 & 405.90 & 3821.27 \\ \(R_{RGM}\) & 13 & 2895.30 & 2316.24 & 925.94 & 7142.18 \\ \(R_{RIM}\) & 10 & 2356.12 & 1884.89 & 753.51 & 5638.40 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of initial solution results obtained by different algorithms.  
Additionally, they typically provide wider coverage of the solution space, which increases population diversity and enhances the algorithm's exploratory ability. Moreover, through the selection process, these high-quality solutions increase the probability of retention and reproduction, steering the entire population's evolution toward superior solutions.