改进教育竞争优化器，提升复杂优化问题求解能力

The educational competition optimizer is a recently introduced metaheuristic algorithm inspired by human behavior, originating from the dynamics of educational competition within society. Nonetheless, ECO faces constraints due to an imbalance between exploitation and exploration, rendering it susceptible to local optima and demonstrating restricted effectiveness in addressing complex optimization problems. To address these limitations, this study presents an enhanced educational competition optimizer (IECO-MCO) utilizing multi-covariance learning operators. In IECO, three distinct covariance learning operators are introduced to improve the performance of ECO. Each operator effectively balances exploitation and exploration while preventing premature convergence of the population. The effectiveness of IECO is assessed through benchmark functions derived from the CEC 2017 and CEC 2022 test suites, and its performance is compared with various basic and improved algorithms across different categories. The results demonstrate that IECO-MCO surpasses the basic ECO and other competing algorithms in convergence speed, stability, and the capability to avoid local optima. Furthermore, statistical analyses, including the Friedman test, Kruskal-Wallis test, and Wilcoxon rank-sum test, are conducted to validate the superiority of IECO-MCO over the compared algorithms. Compared with the basic algorithm (improved algorithm), IECO-MCO achieved an average ranking of 2.213 (2.488) on the CE2017 and CEC2022 test suites. Additionally, the practical applicability of the proposed IECO-MCO algorithm is verified by solving constrained optimization problems. The experimental outcomes demonstrate the superior performance of IECO-MCO in tackling intricate optimization problems, underscoring its robustness and practical effectiveness in real-world scenarios.