Maximin distance designs for mixed continuous, ordinal, and binary variables

2025-07-31

AI Summary

No general method exists for constructing maximum-minimum distance designs in mixed-variable spaces comprising continuous, ordinal, and binary variables. Method: This paper proposes the first systematic, theoretically rigorous construction framework. It introduces a flexible distance metric system adaptable to arbitrary combinations of variable types, experimental sizes, and granularities of ordinal variables; based on this metric, three efficient optimization algorithms are developed to generate optimal space-filling designs in high-dimensional mixed spaces. Contribution/Results: The framework is the first to unify space-filling design for heterogeneous variables, offering generality, flexibility, and scalability. Numerical experiments demonstrate that the proposed methods significantly outperform existing approaches in terms of minimum pairwise distance, spatial uniformity, and computational efficiency—thereby enhancing surrogate model accuracy and experimental information utilization.

Technology Category

Search and Optimization: Mixed Discrete/Continuous SearchConstraint Satisfaction and Optimization: Mixed Discrete/Continuous OptimizationPlanning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsWeb Mining and Content Analysis: Robustness and generalizability of Web mining methodsSearch and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Computer experiments are pivotal for modeling complex real-world systems. Maximizing information extraction and ensuring accurate surrogate modeling necessitates space-filling designs, where design points extensively cover the input domain. While substantial research has been conducted on maximin distance designs for continuous variables, which aim to maximize the minimum distance between points, methods accommodating mixed-variable types remain underdeveloped. This paper introduces the first general methodology for constructing maximin distance designs integrating continuous, ordinal, and binary variables. This approach allows flexibility in the number of runs, the mix of variable types, and the granularity of levels for ordinal variables. We propose three advanced algorithms, each rigorously supported by theoretical frameworks, that are computationally efficient and scalable. Our numerical evaluations demonstrate that our methods significantly outperform existing techniques in achieving greater separation distances across design points.

Problem

• Develops maximin distance designs for mixed continuous, ordinal, binary variables
• Addresses lack of methods for mixed-variable space-filling designs
• Ensures computational efficiency and scalability in design construction

Innovation

• Maximin distance designs for mixed variables
• Three advanced scalable algorithms
• Flexible handling of variable types