An efficient optimum Latin hypercube sampling technique based on sequencing optimisation using simulated annealing

Abstract

This paper proposes a new optimal Latin hypercube sampling method (OLHS) for design of a computer experiment. The new method is based on solving sequencing and continuous optimisation using simulated annealing. There are two sets of design variables used in the optimisation process: sequencing and real number variables. The special mutation operator is developed to deal with such design variables. The performance of the proposed numerical strategy is tested and compared with three established OLHS methods, namely genetic algorithm (GA), enhanced stochastic evolutionary algorithm (ESEA) and successive local enumeration (SLE). Based on 30 test problems with various design dimensions and numbers of sampling points, the proposed method gives the best results. The method can generate an optimum set of sampling points within reasonable computing time; therefore, it can be considered as a powerful tool for design of computer experiments.

Global sensitivity analysis using a Gaussian Radial Basis Function metamodel

“…To enhance the space filling and orthogonal performance, various approach have been developed [37,[39][40][41], including the Optimal Criteria and Optimal Algorithms. The widely used…”

Surrogate Assisted Teaching Learning Based Optimisation for Process Design of a Non-circular Drawing Sequence

“…Finally, the actual objective function of the optimal result obtained will be calculated. In this study, polynomial regression model (PR), radial basis function model (RBF) and Kriging model (KG) were used as surrogate models while the optimal Latin hyper cube sampling technique proposed in [11] was used to generate sampling points. Sixty two sampling points for 31 total number of design variables were generated and used for constructing the surrogate models.…”

Modified Algorithms for Fast Construction of Optimal Latin-Hypercube Design

“…Husslage et al [28] made a comparison of simulated annealing (SA), ESE and PermGA algorithms and the results showed that the ESE algorithm found better results than SA and PermGA algorithms for almost all of the cases. Moreover, the performance of ESE algorithm for establishment of OLHD with high space-filling quality was further validated in literatures [14], [22], [23] and [25] through comparing with SOBSA, GA, SLE, SLHD, LSGA and a novel extension algorithms. The results revealed that the ESE algorithm is a significantly efficient and robust algorithm for optimizations of LHDs within 10 dimensions.…”

“…Hence, the balance between time costs and optimality of solution in the global optimization of LHD interests and challenges researchers. Thus, many outstanding efforts for improving efficiency in construction of LHDs with high space-filling quality were made, which include enhancement of enhanced stochastic evolutionary (EESE) algorithm (Chantarawong et al [11]), successive local enumeration (SLE) algorithm (Zhu et al [12]), particle swarm optimization (PSO) algorithm (Chen et al [13]), sequencing optimization based on simulated annealing (SOBSA) algorithm (Pholdee, and S. Bureera [14]), a new DOE framework based on PermGA (Kianifar et al [15]), PermGA based on chromosome-length-expansion (CLE) scheme (Mahmoudi and Zimmermann [16]), slice latin-hypercube design (SLHD) (Ba et al [17]), maximum projection design (Joseph et al [18] and [19]), sequential-successive local enumeration (S-SLE) algorithm (Long et al [20]), inflate, expand and stack (IES) algorithm (GuiBan et al [21]), an efficient method for constructing space-filling and nearorthogonality Sequential LHD (Wu,et al [22]), a novel extension algorithm (Li et al [23]), maximin distance latin squares and related latin-hypercube design based on Costas arrays and the Welch, Gilbert and Golomb methods (Xiao and Xu [24]) and local search-based genetic algorithm (LSGA) (Shang et al [25]). Additionally, in publications, we noticed a quite efficient algorithm, the latin-hypercube via translational propagation (TPLHD), was developed by Grosso et al [26] to faster construct a near high-quality design.…”