Heavy-duty vehicles are commonly used transport equipment in modern industrial systems. To achieve autonomous transportation, taking into account the multi-axle steering characteristics of such vehicles, a path tracking controller based on Linear Quadratic Regulator (LQR) is designed for the first and second steering axles. Furthermore, predictive controller is introduced to emulate the potential behavior of human drivers. As the effectiveness of the LQR is greatly influenced by its parameter settings, and tuning them is difficult, a genetic algorithm improved by fuzzy correlation entropy is proposed for parameter optimization. Finally, the Simulink-Trucksim co-simulation platform is used for heavy-duty vehicle operation in stacking yards as the experimental scenario for simulation verification. The results demonstrate that the optimization method proposed in this paper is able to pick more suitable parameters for the controller, thereby improving the vehicle’s trajectory tracking accuracy and stability.