A sequential optimal Latin hypercube design method using an efficient recursive permutation evolution algorithm

Abstract

Latin hypercube design (LHD) is one of the most frequently used sampling methods. However, most LHDs generate data samples in a manner that hinders computational efficiency and space-filling performance when high dimensions and large samples are involved. Therefore, a sequential recursive evolution Latin hypercube design (RELHD) is proposed in this article, which adopts a permutation inheritance algorithm to update and optimize the LHD. A recursive split algorithm is also proposed and used to enhance the computational efficiency by dividing the sample set into smaller subsets. Numerical experiments demonstrate that the space-filling quality of the RELHD compares well with the enhanced stochastic evolutionary algorithm (ESE) in complex problems with large samples and high dimensions, with RELHD having a significantly higher computational efficiency than ESE. Finally, the sequential approach of RELHD proves to be a more efficient strategy when dealing with sampling-based analysis problems.

KEYWORDS:

• Design of experiments
• optimal Latin hypercube design
• permutation information inheritance
• sequential evolution
• recursive algorithm

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 52005502]; Research Project of National University of Defense Technology [project number ZK19-11]; Science and Technology Innovation Program of Hunan Province [grant number 2020RC2035].