Robust parameter design optimization using Kriging, RBF and RBFNN with gradient-based and evolutionary optimization techniques

• Application of Kriging, RBF and RBFNN in robust parameter design.
• These models are superior the quadratic polynomial regression model.
• Kriging model is the most accurate model in comparison with the polynomial regression model.
• We introduced a new approach using multi-objective optimization instead of the mean squared error.

The dual response surface methodology is one of the most commonly used approaches in robust parameter design to simultaneously optimize the mean value and keep the variance minimum. The commonly used meta-model is the quadratic polynomial regression. For highly nonlinear input/output relationship, the accuracy of the fitted model is limited. Many researchers recommended to use more complicated surrogate models. In this study, three surrogate models will replace the second order polynomial regression, namely, ordinary Kriging, radial basis function approximation (RBF) and radial basis function artificial neural network (RBFNN). The results show that the three surrogate model present superior accuracy in comparison with the quadratic polynomial regression.The mean squared error (MSE) approach is widely used to link the mean and variance in one cost function. In this study, a new approach has been proposed using multi-objective optimization. The new approach has two main advantages over the classical method. First, the conflicting nature of the two objectives can be efficiently handled. Second, the decision maker will have a set of Pareto-front design points to select from.