Student Psychological Optimization Algorithm Based on Teaching and Learning for Global Optimization Problems and Optimal Scheduling Problems

To overcome the limitations of the standard Student Psychology-Based Optimization (SPBO) algorithm, such as strategy homogeneity, insufficient elite-guided diversity, and inefficient evolution of low-quality individuals, this paper proposes a Hierarchical Teaching–Learning Enhanced Student Psychology-Based Optimization (HTL-SPBO) algorithm. The proposed method introduces a fitness-based three-layer teaching mechanism to realize differentiated learning behaviors for individuals with different evolutionary states. In addition, a multi-elite mentor pool strategy is employed to generalize elite guidance and alleviate premature convergence, while an elite-neighborhood-guided restart mechanism is designed to improve the evolutionary efficiency of poorly performing individuals. The effectiveness of HTL-SPBO is comprehensively evaluated on the CEC2017 and CEC2022 benchmark test suites under multiple dimensional settings. Experimental results demonstrate that HTL-SPBO achieves superior performance in terms of convergence accuracy, convergence speed, and robustness when compared with several State-of-the-Art optimization algorithms. The convergence behavior shows that the proposed algorithm is capable of rapid early-stage exploration followed by stable and accurate exploitation in later iterations. Furthermore, HTL-SPBO is applied to an optimal scheduling problem for a grid-connected microgrid to verify its practical applicability. The results indicate that HTL-SPBO attains the lowest average operating cost while maintaining small performance variance across multiple independent runs, highlighting its effectiveness and stability in solving complex engineering optimization problems. Overall, the proposed HTL-SPBO provides a robust and efficient optimization framework and exhibits strong potential for application in large-scale and real-world optimization scenarios.