# Improved GA-LNS Algorithm for Solving Vehicle Path Problems Considering Carbon Emissions
## 7 Conclusions  
In this paper, the time window, vehicle load, and carbon emission factors are comprehensively considered to construct a low-carbon logistics and distribution path model that accounts for the time window. Given that the genetic algorithm is contingent upon the initial solution, it is prone to suffering from the local optimum problem. First, the INNC method was employed to initialize the population; subsequently, a large-scale neighborhood search algorithm was incorporated, and an improved genetic algorithm was developed for the simulation and resolution of the constructed model, which led to the following conclusions:  
1. Compared with the RGM and RIM, the initialized population of the INNC method has higher-quality initial solutions, which enhances the search performance of the algorithm and facilitates the evolution of the entire population towards better solutions. 2. In comparison to traditional GA and PSO techniques, the results of the GA-LNS algorithm are optimal in each set of examples. This finding suggests that the proposed algorithm demonstrates superior efficiency and accuracy in addressing the VRPTW problem and is capable of identifying optimal solutions more effectively while exhibiting enhanced robustness. 3. Based on the analysis of the results obtained from various optimization objectives, we conclude that the total cost associated with the objective of minimizing the total cost is lower than that associated with the objectives of minimizing both driving costs and carbon emissions. This finding indicates that the model developed in this study effectively accounts for both the driving costs and carbon emissions of the vehicle while balancing the trade-offs among the different objectives to achieve the goal of minimizing the overall logistics distribution cost. It is worth mentioning that considering the ideas of [PERSON] et al. [40; 41] in the field of VRP, the application of this work can be further extended, especially for multi-criteria optimization and neighborhood operator selection, in order to improve the adaptability and efficiency of local search algorithms. However, the aforementioned results reveal several limitations inherent in the model's realistic assumptions: (1) speed varies significantly within urban environments, influenced by factors such as traffic congestion, signal timings, and road conditions, all of which affect vehicle speeds; (2) vehicles typically fail to achieve maximum load capacities due to actual traffic demands, road constraints, and parking conditions; (3) the assumption of a singular vehicle model inadequately represents the diversity of vehicle performance; (4) the analysis of carbon emissions exclusively considered carbon dioxide emissions, neglecting the impacts of other pollutants, including particulate matter and nitrogen oxides. Considering these limitations, future research should focus on the following areas: first, investigating joint scheduling models for multiple vehicles to accommodate a wider range of transportation needs; and second, integrating machine learning techniques to update and optimize distribution paths in real time, thereby enhancing the model's adaptability and accuracy. Additionally, attention will be directed towards developing a more complex cost structure that encompasses potential environmental and social costs, thereby enhancing the model's sustainability analysis capabilities. Finally, the iGREEN model from the literature [42] will be used to assess the pollutants emitted by vehicles in order to provide a more comprehensive environmental impact analysis. It is anticipated that these subsequent studies will offer a more detailed theoretical foundation and practical guidance for advancing low-carbon logistics practices. Conceptualization, F.C. and S.J. ; methodology, S.J. ; software, S.J. ; validation, F.C. and S.J. ; formal analysis, F.C. ; investigation, S.J. ; resources, S.J. ; data curation, S.J. ; writing--original draft preparation, S.J. ; writing--review and editing, F.C. and S.J. ; visualization, S.J.