An Efficient Sequential Optimization Approach Based on the Multivariate Expected Improvement Criterion

An efficient sequential optimization approach for complex computer models was presented by Jones et al. (1998). After fitting a stochastic process model based on an initial space filling design, this model is sequentially refined by the expected improvement criterion. This criterion balances the need to search in areas in the design space where the prediction is optimal with the need to search where the model uncertainty is high. This approach can easily be extended to physical processes. Since in practice the overall quality of products of production processes is assessed by more than one response, a multivariate version of the expected improvement criterion is proposed based on desirability functions. This criterion is then used to optimize a metal spinning process.