Polynomial Response Surface based on basis function selection by multitask optimization and ensemble modeling

Abstract Polynomial Regression Surface (PRS) is a commonly used surrogate model for its simplicity, good interpretability, and computational efficiency. The performance of PRS largely dependent on basis functions. With limited samples, how to correctly select functions remains challenging problem. To improve prediction accuracy, modeling approach based multitask optimization ensemble (PRS-MOEM) proposed rational function selection with robustness. First, the training set partitioned into multiple subsets by cross validation method, each subset sub-model independently constructed optimization. effectively solve these tasks, an improved evolutionary algorithm transfer migration developed, which can enhance efficiency robustness useful information exchange between similar tasks. Second, novel method integrate sub-models final model. significance scored according error estimation occurrence frequency in all sub-models. Then are ranked selected bias-corrected Akaike’s criterion. PRS-MOEM mitigate negative influence from large error, alleviate uncertain impact resulting randomness subsets. Thus accuracy be enhanced. Seven numerical examples engineering problem utilized test verify effectiveness PRS-MOEM.