Petri nets were used to simulate intersection traffic, and an effective vehicle scheduling optimization algorithm was subsequently proposed. In response to the potential vehicle deadlock phenomenon, a deadlock detection and recovery method was developed to enhance the safety and reliability of traffic flow. An improved genetic algorithm was employed to generate the training and testing datasets for a BP neural network. Meanwhile, an attention mechanism module and Bayesian optimization technique were integrated into the BP model, resulting in a high-performance adaptive neural network. This neural network was then applied to solve the deadlock-free vehicle scheduling optimization problem of unsignalized intersections. In the experimental validation, the proposed algorithm was compared with not only traditional intelligent optimization algorithms such as the improved genetic algorithm, particle swarm optimization, and the sparrow search algorithm, but also the Transformer model and the multi-agent reinforcement learning algorithm. Results show that the adaptive neural network achieves both high efficiency and superior performance in solving the deadlock-free vehicle scheduling optimization problem of unsignalized intersections.