融合教育心理学理论的分组教学优化算法

针对分组教学优化算法（group teaching optimization algorithm，GTOA）存在求解精度不高、易陷入局部最优的不足，提出了一种融入教育心理学理论的分组教学优化算法（educational psychology group teaching optimization algorithm，EPGTOA）。在杰出组学生的教师教学阶段融入支架式教学理论，教师在教学过程中帮助学生构建知识体系，更快地提高该组学生的学习能力，从而加强算法的局部搜索能力；在学生学习阶段融入建构主义发展观理论，学生逐渐形成自己独特的认知结构，吸收教师传授的知识，提高学习能力，从而增强算法的全局搜索能力。为验证EPGTOA的有效性，选取21个标准测试函数，将EPGTOA与GTOA和基于信息共享的分组教学优化算法、灰狼算法、蜉蝣算法、飞蛾扑火算法、教与学算法算法进行仿真实验，同时采用Wilcoxon检验和平均绝对误差对改进算法所得的数据进行统计分析，结果表明在5%的水平上是显著的。在算法稳定性、求解精度和收敛速度上，EPGTOA都比GTOA有所增强，尤其在求解高维问题上，改进算法有更好的性能。

Group teaching optimization algorithm integrating educational psychology theory

Aiming at the shortcomings of group teaching optimization algorithm(GTOA), such as low solution accuracy and poor local optimum, this paper proposed GTOA with educational psychology theory(educational psychology group teaching optimization algorithm, EPGTOA). In the teaching stage of the outstanding group students, the teacher integrated the scaffolded instructional theory to help the students construct the knowledge system in the teaching process, which could improve the learning ability of the outstanding group students more quickly and strengthen the local search ability of the algorithm. It integrated the development of constructivist theory into the students'' learning stage. Students gradually formed their unique cognitive structure, absorbed the knowledge imparted by the teacher to improve their learning ability, and thus enhanced the global search ability of the algorithm. This paper used 21 standard test functions to verify the effectiveness of the EPGTOA, and compared EPGTOA with GTOA algorithm, group teaching optimization algorithm with information share, grey wolf optimization, mayfly optimization algorithm, moth-flame optimization algorithm, and teaching-learning-based optimization. Meanwhile, it used Wilcoxon test and mean absolute error to analyze the data. The results show that EPGTOA is significant at the 5% level. EPGTOA is enhanced over GTOA algorithm in algorithm stability, solution accuracy and convergence speed. The improved algorithm has better performance, especially in solving high-dimensional problems.