Automatic update of Gaussian and multiquadric shape parameter for sequential metamodels based optimization

Several metamodeling techniques and strategies have been developed in recent decades for assisting the global optimization process of costly functions. These have been applied in two ways mainly: through the construction of a unique metamodel that is used as the objective function inside the optimization algorithm; or through the sequential metamodel, construction used to assist the domain exploration and exploitation during the optimization process. The multiquadric and Gaussian radial basis functions contain a shape parameter, which affects the metamodel accuracy and the convergence of the metamodels based optimization algorithms. The use of a simple and efficient algorithm to automatically adjust the shape parameter inside these algorithms is proposed in the present article to increase the robustness of sequential metamodel assisted optimization algorithms. The technique is applied in the context of a specific algorithm of such kind for which the shape parameter adjustment was not apparently investigated yet. Comparative numerical results for benchmark functions and a real engineering problem about blade cascade design optimization are presented and discussed. The results attest that the proposed technique can produce optimization process accelerations comparable to those obtained using fixed shape parameters previously optimized.