Advances in Uniform Experimental Designs: A Decade Selective Review of Algorithmic Search and Deterministic Construction Methods

Abstract

This paper presents a comprehensive and selective review of the last decade's progress in the construction of uniform experimental designs. Confronting the growing complexity of modern experiments—characterized by high-dimensional factor spaces and constrained resources—recent research has produced promising methods  tools for constructing efficient, cost-effective designs. The review is organized around three pivotal themes:

(1) enhanced stochastic search algorithms, including adjusted threshold accepting and permutation-projection methods, for constructing (nearly) uniform minimum aberration designs, supported by benchmarks  that reduce computational search;

(2) frameworks for constructing uniform fold-over designs in two-stage sequential experimentations, enabling the breaking of aliasing structures across symmetric and asymmetric designs; and

(3) deterministic construction algorithms—such as multiple doubling, tripling, and quadrupling, and their integration—for efficiently generating large-scale uniform designs with low, high, or mixed levels without exhaustive search.

Collectively, these advances offer researchers a robust, computationally efficient, and theoretically coherent toolkit for designing experiments across scientific and industrial domains, representing a substantial leap beyond conventional methodologies. A critical discussion and comparative analysis of the reviewed methods are also provided, along with practical recommendations for implementation.