An improved LHS approach for constrained design space based on successive local enumeration algorithm

Abstract

Surrogate models are commonly used to replace expensive simulations in engineering design and optimization by virtue of their low computational cost and high prediction accuracy. The design of experiments (DoE) plays an indispensable role in constructing surrogate models. However, most of existing DoEs are applied to regular design space such as rectangular or cube space, and not applied to constrained design space. An approach of Latin Hypercube Sampling (LHS) based on successive local enumeration (SLE) named SLE-LHS is such a kind of algorithm. In this paper, an improved SLE-LHS approach for constrained design space is proposed, named as SLE-CLHS approach. Compared with the existing LHS methods based on maximin algorithm, SLE-LHS algorithm employs global objective functions and a sequential local objective function aiming at maximizing the minimum distance between the sample points and the untried points. The proposed SLE-CLHS is an improved algorithm of SLE-LHS, which taking into account constraints between the sample variables and can be used in the constrained space. In the process of design, the points that do not satisfy the constrained condition are to be eliminated, then new points are generated in the constrained space and they will be updated until the optimal position has been attained. Two numerical examples are given in this paper, and the results of 2-D and 3-D sampling in constrained design space indicate that the SLE-CLHS approach performs well both in space-filling and in projection.