An Evolutionary Risk Adjusting Model Fusion Framework For Optimizing Models With Variable Fidelity
Mohammed A. El-Beltagy · 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference · 2004
We present a novel framework for fusing models of varying computational cost and fldelity for the purposes of optimization. Such model fusion results in a surrogate model that is used by an evolutionary optimizer. The fused model is built using Gaussian Processes regression. It has useful properties that allows it be adjusted in an adaptive fashion to mitigate the risk of the evolutionary optimizer chasing after false optima. We demonstrate the strength of the framework on an engineering design problem using a predetermined computational budget. Nomenclature CN Covariance Matrix of the input data „ Gaussian Process mean r Hyperparameter vector of length scales x Design variable vector xn Gaussian Process input vector D Training data set consisting of input/output pairs ·a=e The ratio in computational efiort between low and high fldelity models fa(x) Low fldelity, computationally cheap model fe(x) High fldelity, computationally expensive model ^N+1 Prediction mean pi Candidate design to be evaluated during optimization maxstdtol Maximum allowable tolerance on prediction uncertainty stdtol Currently allowable tolerance for model accuracy during the optimization ae 2N+1 Prediction variance ae(pi) Standard deviation on fusion model prediction accuracy for input pi µ1 Hyperparameter controlling overall vertical scale µ2 Hyperparameter controlling the bias of the correlation µ3 Hyperparameter setting the noise level bn Input to the model fusion Gaussian Processes model L Dimension of Gaussian Process input vector N Number of samples in the training data set na The number of fa(x) evaluations carried out during optimization Ne Maximum allowable equivalent number of fe(x) evaluations ne The number of fe(x) evaluations carried out during optimization Np Number of individuals in a population tn Gaussian Process output scalar