In many manufacturing cases, engineers are required to optimize a number of responses simultaneously. A common approach for the optimization of multipleresponse problems begins with using polynomial regression models to estimate the relationships between responses and control factors. Then, a technique for combining different response functions into a single scalar, such as a desirability function, is employed and, finally, an optimization method is used to find the best settings for the control factors. However, in certain cases, relationships between responses and control factors are far too complex to be efficiently estimated by polynomial regression models. In addition, in many manufacturing cases, engineers encounter qualitative responses, which cannot be easily stated in the form of numbers. An alternative approach proposed in this paper is to use an artificial neural network (ANN) to estimate the quantitative and qualitative response functions. In the optimization phase, a genetic algorithm (GA) is considered in conjunction with an unconstrained desirability function to determine the optimal settings for the control factors. Two manufacturing examples in which engineers were asked to optimize multiple responses from the semiconductor and textile industries are included in this article. The results indicate the strength of the proposed approach in the optimization of multiple-response problems.
Opening Remarks 2019 was my final year as Editor of Technometrics, and 2018 was my last year of handling new submissions. Both Peihua Qiu (immediate past Editor and current Chair of the Management Committee) and Hugh Chipman (past Editor and past Chair of the Management Committee) have been very helpful during my tenure. Janet Wallace (Editorial Coordinator) and Eric Sampson (ASA Journals Manager) have also been extremely helpful and valuable resources. Of course, the Associate Editors (AEs) have also been fantastic. I hope to be able to continue to work with everyone in various capacities in the coming years to serve the industrial and applied statistics communities.
Computer experiments are used frequently for the study and improvement of a process under study. Optimizing such process based on a computer model is costly, so an approximation of the computer model, or metamodel, is used. Efficient global optimization (EGO) is a sequential optimization method for computer experiments based on a Gaussian process model approximation to the computer model response. A long-standing problem in EGO is that it does not consider the uncertainty in the parameter estimates of the Gaussian process. Treating these estimates as if they are the true parameters leads to an improper assessment of the precision of the approximation, a precision that is crucial to assess not only in optimization but in metamodeling in general. One way to account for these uncertainties is to use bootstrapping, studied by previous authors. Alternatively, some other authors have mentioned how a Bayesian approach may be the best way to incorporate the parameter uncertainty in the optimization, but no fully Bayesian approach for EGO has been implemented in practice. In this paper, we present a fully Bayesian implementation of the EGO method. The proposed Bayesian EGO algorithm is validated through simulation of noisy nonlinear functions and compared with the standard EGO method and the bootstrapped EGO. We also apply the Bayesian EGO algorithm to the optimization of a stochastic computer model. It is shown how a Bayesian approach to EGO allows one to optimize any function of the posterior predictive density.
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