An enhanced multi-strategy educational competition optimizer for numerical optimization

This study proposes an Enhanced Multi-Strategy Educational Competition Optimizer (EMSECO) to address the inherent limitations of the standard Educational Competition Optimizer, specifically its imbalanced exploration-exploitation dynamics, insufficient diversity preservation, and suboptimal convergence behavior. Three synergistic mechanisms are integrated. Firstly, an undergraduate education stage is embedded within the original cyclical framework, leveraging differential vector guidance to augment spatial coverage and sustain diversity. Secondly, a graduate education stage is introduced as an external intensification module, utilizing elite individual and elite subpopulation guidance to strengthen local exploitation. Thirdly, a random walk restart strategy is incorporated to perturb stagnated individuals, thereby suppressing premature convergence. Comparative experiments against AE, MRFO, SAO, EOSMA, ALSHADE, and EPSCA across multiple dimensionalities demonstrate that EMSECO achieves superior performance, attaining average Friedman rankings of 1.2, 1.4, 1.7, and 2.0 for 10-, 30-, 50-, and 100-dimensional CEC 2017 test functions, respectively. Practical applicability is further validated through seven real-world engineering problems. In summary, the proposed EMSECO algorithm exhibits enhanced global exploration capacity, improved local exploitation efficiency, and superior convergence stability.