Neural Networks for Solving the Vehicle Routing Problem

The article addresses the vehicle routing problem, which belongs to the class of NP-hard combinatorial optimization problems and holds significant practical importance in the field of transport logistics. A detailed review of modern machine learning methods, particularly neural networks, used to solve the vehicle routing problem is presented. Deep neural networks, recurrent architectures, graph neural networks, and transformer models are analysed, revealing their specific features and operational mechanisms in the context of route construction for vehicle fleets. Special attention is given to the training methods of neural models, among which reinforcement learning, supervised learning, and hybrid approaches that combine the advantages of neural and classical optimization algorithms are distinguished. The main achievements in this field are described, including the development of models capable of generating solutions within milliseconds after training completion, demonstrating efficiency compared to classical heuristic methods such as greedy algorithms, ant colony methods, and genetic algorithms. At the same time, the limitations of modern neural approaches are highlighted, particularly their insufficient generalization capability when applied to other problem classes or significantly larger graph sizes, which necessitates the use of architectural modifications, meta-learning methods, and model adaptation techniques. The prospects for the development of neural network-based vehicle routing methods are analysed, including the creation of universal models for various variants of the routing problem, the development of hybrid systems that combine the speed of neural networks with the guaranteed solution quality of classical algorithms, as well as the integration of multi-objective goals, such as minimisation of delivery time, fuel consumption, CO₂ emissions, and delay risks. A comparative analysis of the advantages and disadvantages of neural and traditional methods is provided, emphasising that in the near future, the most effective solutions will be hybrid approaches. It is concluded that neural networks play a significant role in enhancing the flexibility, speed, and adaptability of transport logistics systems, ensuring their potential for widespread practical implementation.