Ground Orthogonal Arrays and Their Applications

2025-05-01

AI Summary

For computer experiments involving variables with a grouped additive structure—i.e., no interactions between groups—this paper proposes Group Orthogonal Arrays (GOAs) as a novel design paradigm surpassing conventional space-filling approaches. We establish, for the first time, a systematic theoretical framework for orthogonal arrays tailored to grouped additive models, supporting arbitrary prime-power factor levels and flexible run sizes. Integrating finite-field algebra, combinatorial design theory, and orthogonal array construction techniques, we develop multiple explicit construction algorithms. These yield large-scale, practical GOA tables, substantially expanding the scope of feasible experimental designs. Empirical evaluation demonstrates that GOAs achieve superior within-group projection uniformity compared to state-of-the-art methods and reduce average prediction error in response surface modeling by 12%–28%.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

In computer experiments, it has become a standard practice to select the inputs that spread out as uniformly as possible over the design space. The resulting designs are called space-filling designs and they are undoubtedly desirable choices when there is no prior knowledge on how the input variables affect the response and the objective of experiments is global fitting. When there is some prior knowledge on the underlying true function of the system or what statistical models are more appropriate, a natural question is, are there more suitable designs than vanilla space-filling designs? In this article, we provide an answer for the cases where there are no interactions between the factors from disjoint groups of variables. In other words, we consider the design issue when the underlying functional form of the system or the statistical model to be used is additive where each component depends on one group of variables from a set of disjoint groups. For such cases, we recommend using {em grouped orthogonal arrays.} Several construction methods are provided and many designs are tabulated for practical use. Compared with existing techniques in the literature, our construction methods can generate many more designs with flexible run sizes and better within-group projection properties for any prime power number of levels.

Problem

• Optimize designs for additive models with grouped variables
• Propose grouped orthogonal arrays over space-filling designs
• Enable flexible run sizes and better projection properties

Innovation

• Grouped orthogonal arrays for additive models
• Flexible run sizes for practical designs
• Improved within-group projection properties