A novel ensemble of metamodels using improved stepwise metamodel selection and two-layer pointwise ensemble

Abstract

Although an independent metamodel may be used to accurately describe certain response relationships, it can be challenging to find suitable metamodels for various problems. The ensembled metamodel, in contrast, is a more universal method. The key to enhancing the performance of the ensembled metamodel is determining how to select the optimal set of metamodels to be ensembled (MBEs) and how to ensemble them to obtain a better fit. However, existing methods face challenges in exploring the fitting ability of individual metamodels within a pre-set sample set, often requiring prior knowledge or additional sample sets for assistance to get optimal MBEs, and they struggle to fully utilize the fitting ability of individual metamodels at each sample point. To address these challenges, this paper proposes a novel ensemble of metamodels using improved stepwise metamodel selection and two-layer pointwise ensemble (OSF-TLPE) through research in three aspects: model selection, weight calculation, and residual compensation. Firstly, the Leave-P-Out Prediction (LPOP) proposed in this paper reconstructs the response of the metamodel to the problem, which reduces the complexity of model selection. Then, considering the redundancy of the metamodel during ensemble, the Out-of-Bag Estimation (OOBE) based Stepwise Fit (OSF) eliminates redundancy as feature selection, which is a globally optimal method for metamodel selection. The two-layer pointwise ensemble of metamodels (TLPE), which consists of weight metamodels (WMs) and a residual metamodel (RM) provide a more robust ensemble strategy by assigning weights point by point and compensating for residuals. Finally, the performances of OSF and TLPE are evaluated on 12 benchmark functions using 6 and 13 typical metamodels, respectively. A performance comparison was also conducted on an aircraft final assembly line performance prediction problem. The results demonstrate that OSF-TLPE can deliver more flexible and reliable performances compared to common ensemble methods.