Metamodel-based Optimization of Stochastic Computer Models for Engineering Design under Uncertain Objective Function

Stochastic computer models are prevailingly used to help the design engineer to understand and optimize analytically intractable systems. A frequently encountered, but often ignored problem is that the objective function representing system performance may contain some uncertain parameters. Due to lack of computationally efficient tools, rational procedures for dealing with the problem such as finding multiple Pareto-optimal solutions or conducting sensitivity analysis on the uncertain parameters require the stochastic computer model to be optimized many times, which would incur extensive computational burden. In this work, we provide a computationally efficient metamodel-based solution to capture this uncertainty. This solution first constructs a Cartesian product design over the space of both design variables and uncertain parameters. Thereafter, a radial basis function metamodel is used to provide a smooth prediction surface of the objective value over the space of both design variables and uncertain parameters. Based on the Cartesian product design structure, a fast fitting algorithm is also derived for fitting the metamodel. To illustrate the effectiveness of the developed tools in solving practical problems, they are applied to seek a robust optimal solution to a drug delivery system with uncertain desirability function parameters based on a criterion that we propose.