A0193
Title: Systematic construction methods for uniform designs
Authors: Yongdao Zhou - Nankai University (China) [presenting]
Abstract: Quasi-Monte Carlo (QMC) methods replace random numbers in Monte Carlo methods with deterministic low-discrepancy sequences. They solve many difficult analyses, including the approximate calculation of multiple definite integrals. As a QMC method, uniform design aims to distribute points evenly on a restricted domain. Such a point set has low discrepancy and has enjoyed increasing popularity in applications. However, most designs obtained by numerical optimization algorithms in the literature are just nearly uniform. Thus, there is significant room for improvement. The existing work on uniform designs is firstly reviewed, and their structure is characterized. Then, deterministic construction methods are theoretically proposed, which break through a common limitation of setting the number of levels to be prime or prime power. Moreover, a structural optimization method is provided to search nearly uniform designs under more general parameters for practical use. Numerical experiments show that the performance and runtime of the proposed algorithm are far superior to existing ones.
