Radial basis functions with a priori bias as surrogate models:A comparative study

Radial basis functions are augmented with a posteriori bias in order to perform robustly when used as metamodels. Recently, it has been proposed that the bias can simply be set a priori by using the normal equation, i.e., the bias becomes the corresponding regression model. In this study, we demonstrate the performance of the suggested approach (RBFpri) with four other well-known metamodeling methods; Kriging, support vector regression, neural network and multivariate adaptive regression. The performance of the five methods is investigated by a comparative study, using 19 mathematical test functions, with five different degrees of dimensionality and sampling size for each function. The performance is evaluated by root mean squared error representing the accuracy, rank error representing the suitability of metamodels when coupled with evolutionary optimization algorithms, training time representing the efficiency and variation of root mean squared error representing the robustness. Furthermore, a rigorous statistical analysis of performance metrics is performed. The results show that the proposed radial basis function with a priori bias achieved the best performance in most of the experiments in terms of all three metrics. When considering the statistical analysis results, the proposed approach again behaved the best, while Kriging was relatively as accurate and support vector regression was almost as fast as RBFpri. The proposed RBF is proven to be the most suitable method in predicting the ranking among pairs of solutions utilized in evolutionary algorithms. Finally, the comparison study is carried out on a real-world engineering optimization problem.