Nonparametric metamodeling for simulation optimization

Optimization of simulation model performance requires finding the values of the model's controllable inputs that optimize a chosen model response. Responses are usually stochastic in nature, and the cost of simulation model runs is high. The literature suggests the use of metamodels to synthesize the response surface using sample data. In particular, nonparametric regression is proposed as a useful tool in the global optimization of a response surface. As the general simulation optimization problem is very difficult and requires expertise from a number of fields, there is a growing consensus in the literature that a knowledge-based approach to solving simulation optimization problems is required. This dissertation examines the relative performance of the principal nonparametric techniques, spline and kernel smoothing, and subsequently addresses the issues involved in implementing the techniques in a knowledge-based simulation optimization system.

The dissertation consists of two parts. In the first part, a full factorial experiment is carried out to compare the performance of kernel and spline smoothing on a number of measures when modeling a varied set of surfaces using a range of small sample sizes. In the second part, nonparametric metamodeling techniques are placed in a taxonomy of stochastic search procedures for simulation optimization and a method for their implementation in a knowledge-based system is presented. A sequential design procedure is developed that allows spline smoothing to be used as a search technique. Throughout the dissertation, a two-input, single-response model is considered.

Results from the experiment show that spline smoothing is superior to constant-bandwidth kernel smoothing in fitting the response. Kernel smoothing is shown to be more accurate in placing optima in X-space for sample sizes up to 36. Inventory model examples are used to illustrate the results. The taxonomy implies that search procedures can be chosen initially using the parameters of the problem. A process that allows for selection of a search technique and its subsequent evaluation for further use or for substitution of another search technique is given. The success of a sequential design method for spline smooths in finding a global optimum is demonstrated using a bimodal response surface.