Update strategies for kriging models for use in variable fidelity optimization

Many optimization methods for simulation-based design rely on the sequential use of metamodels to reduce the associated computational burden. In particular, kriging models are frequently used in variable fidelity optimization. Nevertheless, such methods may become computationally inefficient when solving problems with large numbers of design variables and/or sampled data points due to the expensive process of optimizing the kriging model parameters each iteration. One solution to this problem would be to replace the kriging models with traditional Taylor series response surface models. Kriging models, however, have been shown to provide good approximations of computer simulations that incorporate larger amounts of data, resulting in better global accuracy. In this paper two metamodel update management schemes (MUMS) are proposed to reduce the cost of using kriging models sequentially by updating the kriging model parameters only when they produce a poor approximation. The two schemes differ in how they determine when the parameters should be updated. The first method uses ratios of likelihood values (L-MUMS), which are computed based on the model parameters and the data points used to construct the kriging model. The second scheme uses the trust region ratio (TR-MUMS), which is a ratio that compares the approximation to the true model. Two demonstration problems are used to evaluate the proposed methods: an internal combustion engine sizing problem and a control-augmented structural design problem. The results indicate that the L-MUMS approach does not perform well. The TR-MUMS approach, however, was found to be very effective; on the demonstration problems, it reduced the number of likelihood evaluations by three orders of magnitude compared to using a global optimizer to find the kriging parameters every iteration. It was also found that in trust region-based methods, the kriging model parameters need not be updated using a global optimizer-local methods perform just as well in terms of providing a good approximation without effecting the overall convergence rate, which, in turn, results in a faster execution time.