Hybrid approximation algorithm with Kriging and quadratic polynomial‐based approach for approximate optimization

This paper describes a new hybrid algorithm that uses a Kriging and quadratic polynomial‐based approach for approximate optimization. The Kriging method is used for generating a global approximation model, and the polynomial‐based approximation method is used for generating a local approximation model. The Kriging system is only used to construct a polynomial‐based locally approximate model by estimating some function values and Hessian components of an estimated surface. The number of Kriging estimations can be reduced in comparison with direct Kriging‐based optimization, and a local optimum solution on an approximated surface can be clearly estimated without use of an optimization procedure based on a local appropriate quadratic polynomial model. Numerical examples of engineering optimization using the proposed method illustrate validity and effectiveness of the proposed method. Copyright © 2006 John Wiley & Sons, Ltd.