Modified Algorithms for Fast Construction of Optimal Latin-Hypercube Design

Abstract

As accuracy of optimization can not be guaranteed without high-quality samples, the distribution of a finite number of evaluation points where experiments should be conducted in design space is an important issue, particularly when the experiment to obtain sample is expensive. To utilize limited number of evaluation points to represent the design space, optimal latin-hypercube design (OLHD), with considerable space-filling quality, is widely used as a methodology in design of experiments (DOE). However, OLHD generation requires significant time. This study focuses on further improvement of efficiency in generation of OLHD in terms of both time and latin-hypercube design (LHD) optimization. Two modified algorithms, namely the modified enhanced stochastic evolutionary (MESE) and translational propagation modified enhanced stochastic evolutionary (TPMESE) algorithms, based on existing algorithms, are proposed. The MESE algorithm is modified from the enhanced stochastic evolutionary (ESE) algorithm by using a new update method for “temperature,” while the TPMESE algorithm optimizes the LHD via translational propagation (TPLHD) instead of optimizing a random LHD like the MESE algorithm does. Their performance is evaluated by comparison with several famous heuristic algorithms and each original algorithm using optimization tests of LHDs with various sizes. For all cases, proposed algorithms show better performance of convergence than other heuristic algorithms participated in our comparison. For large and medium LHDs, the MESE algorithm faster converges to a solution with the same level as original algorithm (ESE). For large LHDs, the TPMESE algorithm is the most time efficient algorithm in obtaining near-optimal or sufficient near-optimal designs.

Keywords

• Optimal latin-hypercube design
• design of experiments
• evolutionary algorithm
• translational propagation