Gaussian process based optimization algorithms with input uncertainty

Metamodels as cheap approximation models for expensive to evaluate functions have been commonly used in simulation optimization problems. Among various types of metamodels, the Gaussian Process (GP) model is popular for both deterministic and stochastic simulation optimization problems. However, input uncertainty is usually ignored in simulation optimization problems, and thus current GP-based optimization algorithms do not incorporate input uncertainty. This article aims to refine the current GP-based optimization algorithms to solve the stochastic simulation optimization problems when input uncertainty is considered. The comprehensive numerical results indicate that our refined algorithms with input uncertainty can find optimal designs more efficiently than the existing algorithms when input uncertainty is present.