AI 中文总结
研究高中数学学生学术资源分配的0-1二元组合优化问题，提出集成专门约束修复机制的遗传算法，经实验评估，该算法能快速收敛、求解质量高且稳定性强，证实元启发式方法对中等教育实时决策支持系统有用。
AI 中文摘要
在伊拉斯谟+KA220-SCH项目框架内，本文将高中数学学生的教材选择建模为受严格学习时间限制的0-1二元组合优化问题。鉴于该公式的NP难复杂性，随着资源目录规模扩大，精确求解方法在计算上变得难以处理。为应对这一挑战，我们提出一种集成专门约束修复机制的遗传算法，以有效搜索二元决策空间。通过10次独立运行的实验评估表明，该算法具有快速收敛、高求解质量和强算法稳定性。这些结果证实了元启发式方法在中等教育实时决策支持系统中的实际效用。
英文摘要
The optimal allocation of academic resources to individual students is essential for addressing learner diversity and fostering equitable educational outcomes. Within the framework of the Erasmus+ KA220-SCH project, this paper models the selection of educational materials for high school mathematics students as a 0--1 binary combinatorial optimization problem subject to strict study time constraints. Given the NP-hard complexity of the formulation, exact solution methods become computationally intractable as resource catalogs scale. To address this challenge, we propose a Genetic Algorithm integrated with a specialized constraint repair mechanism to effectively search the binary decision space. Experimental evaluation across 10 independent runs demonstrates fast convergence, high solution quality, and strong algorithmic stability across different base seeds. These results confirm the practical utility of metaheuristic approaches for real-time decision-support systems in secondary education.
Comments9 pages, 1 figure
