# Low-Carbon Logistics Distribution Vehicle Routing Optimization Based on INNC-GA
## 1 Introduction  
The rise of e-commerce and the global economy has highlighted the critical role of logistics and distribution in urban settings. However, the operation of vehicles in logistics not only contributes to traffic congestion in cities but also leads to significant carbon emissions, posing a serious threat to the environment. Currently, vehicle exhaust emissions are a major contributor to greenhouse gases on a global scale. Addressing the urgent need to reduce energy consumption and carbon emissions in logistics is paramount. The issue of green vehicle routing, aimed at minimizing energy consumption and carbon emissions, has emerged as a prominent topic in this domain. Domestic and international research on vehicle routing optimization problems predominantly centers around three key aspects: vehicle routing problems with time windows [1; 2; 3], vehicle routing problems involving capacity constraints [4; 5; 6; 7], and dynamic vehicle routing problems [8; 9; 10]. However, there is a lack of comprehensive studies that simultaneously address time window constraints, vehicle load constraints, and speed constraints in vehicle routing problems. As environmental concerns gain more attention, the inclusion of carbon emissions in vehicle routing problems, known as green vehicle routing problems, is emerging as a popular research area. [PERSON] et al. [11] conducted a comprehensive analysis of the social, economic, and environmental impacts, proposing an optimization model that minimizes total costs, including fixed vehicle costs, fuel costs, carbon emissions costs, and penalty costs. They utilized particle swarm optimization and taboo search algorithms to find a balanced solution that considers economic, social, and environmental factors. [PERSON] et al. [12] and [PERSON] et al. [13] developed heterogeneous vehicle routing models that incorporate carbon emissions costs and multi-vehicle type routing models aimed at minimizing total distribution costs while maximizing customer satisfaction. Their use of improved hybrid genetic algorithms and simulated annealing algorithmsyielded valuable insights for optimizing the distribution of fresh agricultural products. [PERSON] et al. [14] and [PERSON] et al. [15] focused on constructing garbage vehicle routing optimization models within a low-carbon environmental protection framework, offering solutions to the challenges of the efficient collection and low-carbon transport of urban household waste. [PERSON] et al. [16] established a dynamic vehicle routing optimization model and applied an enhanced traditional Dijkstra algorithm to solve it, demonstrating the practical significance of a dynamic vehicle routing model that accounts for carbon emissions. Their research not only provides important research results for and insights into the fields of green logistics and environmental protection but also offers innovations in theories and methods. It plays a positive role in various aspects of operational management and service quality for logistics enterprises, providing important references and guidance for businesses in the development of green logistics and environmental protection. The current methods for solving vehicle routing problems mainly consist of exact algorithms and heuristic algorithms. Exact algorithms, such as branch and bound and dynamic programming, are typically used for small-scale problems to find the optimal solution. On the other hand, heuristic algorithms, including genetic algorithms, ant colony algorithms, taboo search algorithms, and simulated annealing algorithms, are more suitable for large-scale problems as they can quickly find near-optimal solutions. For instance, [PERSON] et al. [17] developed an improved multi-objective genetic algorithm based on Pareto optimality for a logistics distribution routing model with low-carbon and stochastic demand. [PERSON] et al.