Second-order nearly orthogonal Latin hypercubes for exploring stochastic simulations

Abstract

This paper presents new Latin hypercube designs with minimal correlations between all main, quadratic, and two-way interaction effects for a full second-order model. These new designs facilitate exploratory analysis of stochastic simulation models in which there is considerable a priori uncertainty about the forms of the responses. We focus on understanding the underlying complexities of simulated systems by exploring the input variables’ effects on the behavior of simulation responses. These new designs allow us to determine the driving factors, detect interactions between input variables, identify points of diminishing or increasing rates of return, and find thresholds or change points in localized areas. Our proposed designs enable analysts to fit many diverse metamodels to multiple outputs with a single set of runs. Creating these designs is computationally intensive; therefore, several have been cataloged and made available online to experimenters.

Keywords:

• simulation
• design of experiments
• genetic algorithms
• Latin hypercube
• nearly orthogonal designs
• space-filling designs

Acknowledgements

The authors would like to thank our colleagues at the Naval Postgraduate School for their insightful comments. In addition, the authors are grateful to the referees, whose feedback improved the content and clarity of this paper. The research was made possible by a grant from the Office of Naval Research (N0001412WX20823).