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

TL;DR

This paper develops a novel methodology for creating maximin distance designs that effectively incorporate mixed variable types, enhancing the design of computer experiments with continuous, ordinal, and binary inputs.

Contribution

It introduces the first general approach and three algorithms for maximin distance designs accommodating mixed variable types, with theoretical support and improved performance.

Findings

Algorithms achieve greater separation distances than existing methods.

Methods are computationally efficient and scalable.

Designs offer flexible configurations for mixed-variable experiments.

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.