Order-of-addition experiments arise when the response depends on the order in which a set of components is added. Since the number of possible orders increases factorially with the number of components, full permutation designs are rarely feasible except for small problems. This paper studies space-filling fractional designs for order-of-addition experiments based on the Kendall tau distance, a natural metric for comparing permutations through pairwise ordering disagreements. We consider the maximin Kendall tau distance criterion and related dispersion criteria, and establish their connections with statistical optimality under the pairwise ordering model and a Gaussian process model with the Mallows kernel. To construct such designs, we propose an efficient foldover simulated annealing algorithm, denoted by FSA-KD, based on swap moves in the permutation space, together with foldover and incremental updating strategies. Numerical studies show that the resulting FSA-KD designs have large minimum pairwise Kendall tau distances, denoted by k_min(D), and stable pairwise distance distributions, and perform well in surrogate modeling and permutation-based optimization tasks.

翻译：当响应变量取决于一组组分的添加顺序时，即产生序贯添加实验问题。由于可能顺序的数量随组分数量呈阶乘增长，除小规模问题外，全排列设计通常不可行。本文基于Kendall tau距离（一种通过成对排序不一致性比较排列的自然度量）研究序贯添加实验的空间填充部分因子设计。我们考虑极大极小Kendall tau距离准则及相关离散准则，并建立其与成对排序模型及含Mallows核的高斯过程模型下统计最优性之间的联系。为构造此类设计，我们提出一种高效的折迭模拟退火算法FSA-KD，该算法基于排列空间中的交换操作，结合折迭与增量更新策略。数值研究表明，所得FSA-KD设计具有较大的最小成对Kendall tau距离（记为k_min(D)）与稳定的成对距离分布，并在代理建模及基于排列的优化任务中表现优异。