Multivariate Gaussian Process Interpolators with Varying-Parameter Covariance: An Application to Pareto Front Estimation

• Activity Number: 416
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Po-Hsu Chen*+ and Thomas J. Santner and Angela Dean
• Companies: Ohio State University and Ohio State University and University of Southampton
• Keywords: Computer experiments ; Kriging ; Nonseparable model ; Pareto optimization

Abstract

Gaussian process (GP) models provide rapidly-computable, interpolating emulators of the output from simulator codes. This research develops a multivariate GP model with a nonseparable, smoothly changing, covariance structure for flexible modeling of between-output dependencies. GP models with varying covariance structure have the potential to better predict multivariate output with nonconstant associations over their entire input space. As an application, this "dependence model" is used to estimate the Pareto Front of a set of expensive simulator codes whose outputs are to be minimized simultaneously. In addition, the model is used to select new points sequentially in the updated Pareto set. The expected maximin improvement function of Svenson (2011) is used to guide the choices of new points. The proposed Pareto methodology is illustrated with analytic examples from the multi-objective optimization literature. Using the Hypervolume Indicator for optimization, the accuracy of the estimated Pareto Front from this dependence model is compared with that from an independence-based GP emulator.

Svenson, J. (2011), Ph.D. Dissertation, The Ohio State University.