Multiple Objective Latin Hypercube Designs for Computer Experiments

• Activity Number: 28 - Computation, Design, and Quality Assurance of Physical Science and Engineering Applications
• Type: Contributed
• Date/Time: Sunday, August 8, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Quality and Productivity Section
• Author(s): Damola Akinlana* and Lu Lu
• Companies: University of South Florida and University of South Florida
• Keywords: Space-filling designs; maximin distance; minimax distance; maximum projection; Pareto front approach; Gaussian process models

Abstract

Optimal Latin hypercube designs (LHD) based on optimizing a single criterion are commonly used space-filling designs for computer experiments. For instance, the maximin-LHD (MmLHD) and minimax-LHD (mMLHD) are popular to ensure a good spread and coverage, respectively, across the full input space while achieving uniform projections in each univariate dimension. The maximum projection-LHD (MaxProLHD) ensures space-filling across all possible subspaces. This paper proposes optimal LHDs to achieve robust and balanced performance across multiple objectives. Using the Pareto optimization approach, we employed the column-wise exchange simulated annealing algorithm and the nondominated sorting genetic algorithm to generate optimal LHDs that simultaneously optimize multiple space-filling characteristics, and the efficiency of these algorithms are compared. The methods are illustrated with examples of varied dimensions of input factors, and the generated optimal LHDs are evaluated based on their performance across simulations with different response surface models and compared with optimal designs from single criterion optimization. The nondominated sorting genetic algorithm proved to be more efficient for generating optimal LHDs with balanced performance across multiple distance metrics.