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：我们展示了如何将组合优化算法应用于在实验单元间和单元内可能存在相关性时识别c-最优实验设计的问题，并评估了相关算法的性能。我们假设数据生成过程为广义线性混合模型，并证明c-最优设计准则是一个单调超模函数，适用于一组简单的极小化算法。我们评估了三种相关算法的性能：局部搜索、贪心搜索和反向贪心搜索。结果表明，局部搜索和反向贪心搜索的性能相当，在一系列协方差结构下，其最差设计输出的方差比最佳设计高出不到10%。我们证明这些算法的表现与生成实验单元权重的乘法方法相当或更优。我们将这些算法扩展到识别模型鲁棒的c-最优设计。