Swarm intelligence and evolutionary algorithms are widely applied in industrial scheduling, mobile edge computing, etc due to their strong robustness and fast optimization speed. However, some real-world industrial optimization problems involve numerous decision variables, known as high-dimensional problems. Current algorithms often require considerable computational resources to evaluate objective function values because of high-dimensional decision spaces. Moreover, they are also prone to be trapped in local optima. To solve the above problems, this work proposes an improved algorithm named Surrogate-assisted Multi-class Collaborative Teaching and learning optimizer (SMCT). A multi-class collaborative teaching and learning optimizer is proposed as a base optimizer to improve exploration and exploitation abilities. Furthermore, an autoencoder-assisted radial basis function is proposed as the surrogate model to replace true function evaluations, thereby saving computational resources and balancing the complexity and accuracy in fitting true models. Finally, experimental results demonstrate that SMCT surpasses its existing peers in both search accuracy and convergence speed across eight high-dimensional benchmark functions.