A sequential-design metamodeling strategy for simulation optimization

This paper examines the feasibility and worthiness of a sequential simulation optimization strategy using nonparametric metamodeling. Incorporating notions advanced in the nonparametric statistics literature, the procedure starts with a uniform grid of points, and then adds points based on the solution of a mathematical programming problem involving quantiles of the squared second derivative of a thin-plate spline metamodel. Termination is reached based on two user-specified criteria. A feasibility study is conducted, generating 21,000 nonparametric metamodels to fit seven different, basic simulation surfaces. The appropriateness of metamodel fits is judged using recently published criteria. It is concluded that the nonparametric thin-plate spline sequential procedure faithfully reproduces the test case response surfaces and terminates reasonably. However, it is also seen that misleading results may be obtained in systems heavily constrained by budget, and that splines may do a poor job fitting plateaus due to their inherent predisposition to “create ripples.”