Fuzzy Modeling in Response Surface Method for Complex Computer Model Based Design Optimization

Metamodel based optimization serves as an effective tool for carrying out multi-disciplinary and multi-objective design optimization using complex, "black box" computer modeling, analysis and simulation tools. The response surface based metamodeling method uses simple surrogate polynomial model to approximate the complex objective and constraint functions to reduce computation time, thus making prohibitive global optimization requiring extensive computation feasible. In this paper, another important issue in metamodeling, the uncertainty of the result data from the "black box" functions and their appropriate processing are addressed. The newly introduced fuzzy modeling method inherits the advantages of the well tested response surface method and removes a major fault assumption of the approach on sure result data, thus leading to better accuracy to the identified design optimum. The close form solution of the second order response surface model in fuzzy setting has been derived and demonstrated using a bench mark global design optimization problem