Thin-Plate Spline RBF surrogate model for global optimization algorithms

Improving performance and reducing costs are major challenges in many engineering design problems. The processes or accurate models are usually time-consuming and computationally expensive; therefore, the objective function requires a large number of evaluations. This paper considers surrogate modeling to approximate the expensive function and to ensure the quality of results in a reduced CPU time for mono-objective optimization. The Basic idea of surrogate models, also known as a meta-model, is to build a model from a sampled data, then, the outputs of other design data can be predicted by the approximated model instead of using the heavy one. Once the surrogate model is built, an optimization method is used to look for new design points until convergence. In this work, we propose a surrogate-based optimization algorithm using backtracking search algorithm optimization, and the thin spline basis function to build the surrogate model. During the construction of the surrogate, a minimization problem of error is carried out by updating the position of the node that produces the maximum error. Experiments are carried out on many test functions.