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 q 2006 John Wiley & Sons, Ltd