We show how combinatorial optimisation algorithms can be applied to the problem of identifying c-optimal experimental designs when there may be correlation between and within experimental units and evaluate the performance of relevant algorithms. We assume the data generating process is a generalised linear mixed model and show that the c-optimal design criterion is a monotone supermodular function amenable to a set of simple minimisation algorithms. We evaluate the performance of three relevant algorithms: the local search, the greedy search, and the reverse greedy search. We show that the local and reverse greedy searches provide comparable performance with the worst design outputs having variance $<10\%$ greater than the best design, across a range of covariance structures. We show that these algorithms perform as well or better than multiplicative methods that generate weights to place on experimental units. We extend these algorithms to identifying moole-robust c-optimal designs.
翻译:我们展示了组合式优化算法如何适用于在实验单位之间和内部可能存在关联时确定C-最佳实验设计的问题,并评估了相关算法的性能。我们假设数据生成过程是一个一般的线性混合模型,并表明C-最佳设计标准是一种单一的超模式功能,适合一套简单的最小化算法。我们评估了三种相关算法的性能:本地搜索、贪婪搜索和逆向贪婪搜索。我们显示,本地和逆向贪婪搜索在一系列共变结构中提供了最差的设计产出的类似性能,其差值为<10美元,高于最佳设计。我们显示,这些算法的性能优于产生重量的倍增法或优于产生重量的倍增法,用于实验单位。我们将这些算法扩展到确定 Moole-robust c-optimal 设计。