Construction of Uniform Designs over Continuous Domain in Computer Experiments

TL;DR

This paper introduces a novel method for constructing uniform designs over continuous domains in computer experiments, improving upon existing lattice-based designs by utilizing coordinate descent and threshold accepting algorithms.

Contribution

It proposes a new approach combining coordinate descent and threshold accepting to generate more uniform designs over continuous domains, enhancing design quality in computer experiments.

Findings

New UDs outperform existing designs in Kriging modeling.

The method achieves lower Centered L2-discrepancy values.

Designs show improved uniformity over continuous domains.

Abstract

The construction of uniform designs (UDs) has received much attention in computer experiments over the past decades, but most of the previous works obtain uniform designs over a U-type by lattice domain. Due to increasing demands for continuous factors, UDs over the continuous domain is in lack. Moreover, the uniformity can be further improved over a continuous domain. In this paper, we use coordinate descent methods with an initialization derived by threshold accepting (TA) algorithm to construct UDs over a continuous domain with Centered $L_2$-discrepancy. The new UDs perform better than the recorded ones in several computer experiments by the Kriging modeling.