The use of correlated simulation experiments in response surface optimization

Response surface methodology (RSM) provides a useful framework for the optimization of stochastic simulation models. The sequential experimentation and model fitting procedures of RSM enable prediction of the response and location of the optimum operating conditions. In a simulation environment, the experimentation phase of RSM involves selecting the input variable levels for each simulation run and assigning pseudorandom number streams to the stochastic model components. Through an appropriate assignment of random number streams to simulation runs, correlation among the simulated responses can be induced, thereby affecting reductions in the variances of certain model coefficients. Three methods of correlation induction are considered in this research: (i) no correlation induction, achieved through the use of independent streams, (ii) positive correlation induction, achieved through the use of common streams, and (iii) a combination of positive and negative correlation induction, achieved through the use of the assignment rule blocking strategy.

The performance of the correlation induction strategies is evaluated in terms of two mean squared error design criteria; MSE of response and MSE of slope. The MSE of slope criteria is useful in the early stages of RSM, when the experimental objective is location of the region containing the optimum. The MSE of response criteria is useful in the latter stages of RSM, when the experimental objective is prediction of the optimum response. The correlation induction strategies are evaluated under two experimental situations; fitting a first order model while protecting against quadratic curvature in the response surface, and fitting a second order model while protecting against cubic curvature. In the case of fitting a first order model, two-level factorial designs are used to evaluate the correlation induction strategies, and in the second order case, four design classes are considered; central composite designs, Box-Behnken designs, three-level factorial designs, and small composite designs.

The findings of this research indicate that the assignment rule blocking strategy generally performs the best of the three strategies under both MSE criteria, and the performance of this strategy improves as the magnitudes of the induced correlations increase. The independent streams strategy is a poor choice when the design criteria is MSE of slope and the common streams strategy is a poor choice when the design criteria is MSE of response. The central composite and Box-Behnken designs were found to perform the best of the four second order design classes. The three-level factorial designs performed poorly under MSE of response criteria and the small composite designs performed poorly under the MSE of slope criteria.