一种基于进化算法的概化理论最佳样本量估计新方法：兼与三种传统方法比较

概化理论在心理与教育测量领域应用较广。如何使测量程序在预算限制的情况下达到较优的可靠性是研究者需要考虑的重要问题, 这个问题可以转换为最佳样本量估计的问题。提出了一种基于进化算法的估计概化理论下最佳样本量的新方法——约束进化算法, 并采用模拟研究的方法比较了微分优化法、拉格朗日法、柯西不等式法等三种传统方法与约束进化算法的优劣。结果表明：在两侧面交叉设计、两侧面嵌套设计和三侧面交叉设计中都证明了约束进化算法更具优越性, 建议研究者在今后的研究中优先使用。

A new method for estimating the optimal sample size in generalizability theory based on evolutionary algorithm: Comparisons with three traditional methods

Generalizability Theory (GT) is widely applied in psychological measurement and evaluation. A larger generalizability coefficient often indicates a higher reliability the test may have. Generalizability coefficients can be improved by increasing sample sizes. However, the size of a sample would be subject to budget constraints. Therefore, it is important to examine how to effectively determine the size of a sample considering the budget constraints. The existing literature has been largely limited to traditional methods, such as the differential optimization method, the Lagrange method and the Cauchy Schwartz inequality method.