Enhanced Educational Optimization Algorithm Based on Student Psychology for Global Optimization Problems and Real Problems

To address the insufficient exploration ability, susceptibility to local optima, and limited convergence accuracy of the standard Student Psychology-Based Optimization (SPBO) algorithm in three-dimensional UAV trajectory planning, we propose an enhanced variant, Enhanced SPBO (ESPBO). ESPBO augments SPBO with three complementary strategies: (i) Time-Adaptive Scheduling, which uses normalized time (τ=t/T) to schedule global step-size shrinking, Gaussian fine-tuning, and Lévy flight intensity, enabling strong early exploration and fine late-stage exploitation; (ii) Mentor Pool Guidance, which selects a top-K mentor set and applies time-varying guidance weights to reduce misleading attraction and improve directional stability; and (iii) Directional Jump Exploration, which couples a differential vector with Lévy flights to strengthen basin-crossing while keeping the differential step bounded for robustness. Numerical experiments on CEC2017, CEC2020 and CEC2022 benchmark functions compare ESPBO with Grey Wolf Optimization (GWO), Whale Optimization Algorithm (WOA), Improved multi-strategy adaptive Grey Wolf Optimization (IAGWO), Dung Beetle Optimization (DBO), Snake Optimization (SO), Rime Optimization (RIME), and the original SPBO. We evaluate best path length, mean trajectory length, standard deviation, and convergence curves and assess statistical stability via Wilcoxon rank-sum tests (<i>p</i> = 0.05) and the Friedman test. ESPBO significantly outperforms the comparison algorithms in path-planning accuracy and convergence stability, ranking first on both test suites. Applied to 3D UAV trajectory planning in mountainous terrain with no-fly zones, ESPBO achieves an optimal path length of 199.8874 m, an average path length of 205.8179 m, and a standard deviation of 5.3440, surpassing all baselines; notably, ESPBO's average path length is even lower than the optimal path length of other algorithms. These results demonstrate that ESPBO provides an efficient and robust solution for UAV trajectory optimization in intricate environments and extends the application of swarm intelligence algorithms in autonomous navigation.