Ensemble of meta-models based on local error measure using cross-validation

Many meta-models have been developed to approximate true responses. These meta-models are often used for optimization instead of computer simulations which require high computational cost. However, designers do not know which meta-model is the best one in advance because the accuracy of each meta-model becomes different from problem to problem. To address this difficulty, research on the ensemble of meta-models that combines stand-alone meta-models has recently been pursued with the expectation of improving the prediction accuracy. In this study, we propose a selection method of weight factors for the ensemble of meta-models based on v-nearest neighbors' cross-validation error (CV). The four stand-alone meta-models we employed in this study are polynomial regression, Kriging, radial basis function, and support vector regression. Each method is applied to five 1-D mathematical examples and ten 2-D mathematical examples. The prediction accuracy of each stand-alone meta-model and the existing ensemble of meta-models is compared. Ensemble of meta-models shows higher accuracy than the worst stand-alone model among the four stand-alone meta-models at all test examples (30 cases). In addition, the ensemble of meta-models shows the highest accuracy for the 5 test cases. Although it has lower accuracy than the best stand-alone meta-model, it has almost same RMSE values (less than 1.1) as the best stand-alone model in 16 out of 30 test cases. From the results, we can conclude that proposed method is effective and robust. Copyright �� 2009 by ASME