We review the use of combinatorial optimisation algorithms to identify approximate c-optimal experimental designs when the assumed data generating process is a generalised linear mixed model and there is correlation both between and within experimental conditions. We show how the optimisation problem can be posed as a supermodular function minimisation problem for which algorithms have theoretical guarantees on their solutions. We compare the performance of four variants of these algorithms for a set of example design problems and also against multiplicative methods in the case where experimental conditions are uncorrelated. We show that a local search starting from either a random design or the output of a greedy algorithm provides good performance with the worst outputs having variance $<10\%$ larger than the best output, and frequently better than $<1\%$. We extend the algorithms to robust optimality and Bayesian c-optimality problems.

翻译：我们审查了组合优化算法的使用情况,以确定假设的生成数据过程是一种通用线性混合模型,而且试验条件之间和试验条件之内都存在相互关系时,如何使用组合优化算法来确定大约的C-最佳实验设计。我们展示了如何将优化问题作为一个超模式功能最小化问题提出来,而算法对于其解决办法具有理论保证。我们比较了这些算法的四种变种在一系列示例设计问题方面的性能,以及在实验条件不相干的情况下,与多倍复制的方法的性能。我们显示,从随机设计或贪婪算法的输出开始的本地搜索能够提供良好的性能,而最差的结果是大于最佳产出的<10美元,往往优于1美元。我们将这些算法的性能扩大到稳健的最佳性和巴耶斯式的c-opyality问题。