The optimisation of transportation networks is of paramount importance in the context of logistics systems. In the face of changing demand and environmental conditions, the dynamic optimisation of these networks represents a crucial means of improving logistics efficiency and reducing operating costs. This study proposes a dynamic optimisation model of a logistics and transportation network based on a Long Short-Term Memory (LSTM) neural network. Building on the existing model, our scheme combines LSTM networks, attention mechanisms, and reinforcement learning to capture time-dependent and dynamic behaviour in the network, thereby improving the ability to predict future demand and transportation delays. A hybrid architectural approach has been introduced to enhance the adaptability of LSTM networks in terms of adjusting routing decisions and network configurations in real time. Furthermore, the model is optimised through a multi-objective optimisation framework that balances travel time, cost, and congestion. The experimental results demonstrate that the proposed model exhibits superior performance compared to the traditional optimization method in dynamic routing tasks across a range of logistics scenarios.