A1200
Title: Uniform position designs for order-of-addition experiments
Authors: Yao Xiao - Zhongnan University of Economics and Law (China) [presenting]
Abstract: Order-of-addition (OofA) experiments are increasingly important in scientific studies. Their experimental domain involves permutations of component positions, forming the vertex set of a permutohedron with rich combinatorial-geometric structure that encodes both permutation symmetry and positional proximity. However, existing OofA design methods largely ignore this structure, leading to inefficient exploration of the underlying permutation space. A principled OofA design framework is developed that formalizes geometry-adapted uniformity on the permutohedron and formulates design construction as the selection of uniformly distributed vertices. This uniformity is quantified via a geometry-aware discrepancy based on reproducing kernel theory. The proposed discrepancy admits invariance properties, characterizes optimal uniformity, and satisfies a Koksma-Hlawka-type inequality linking discrepancy to integration error. A computable instance based on an absolute-distance kernel is derived, its connection to the maximin $L_1$-distance criterion is established, and both deterministic and stochastic methods for constructing OofA designs are presented. Empirical studies show that the resulting designs provide improved predictive accuracy and robustness, highlighting the value of explicitly incorporating geometric uniformity into OofA designs.
