Inverse distance weighting and radial basis function based surrogate model for high-dimensional expensive multi-objective optimization

Abstract

Radial basis function (RBF) models have attracted a lot of attention in assisting evolutionary algorithms for solving computationally expensive optimization problems. However, most RBFs cannot directly provide the uncertainty information of their predictions, making it difficult to adopt principled infill sampling criteria for model management. To overcome this limitation, an inverse distance weighting (IDW) and RBF based surrogate assisted evolutionary algorithm, named IR-SAEA, is proposed to address high-dimensional expensive multi-objective optimization problems. First, an RBF-IDW model is developed, which can provide both the predicted objective values and the uncertainty of the predictions. Moreover, a modified lower confidence bound infill criterion is proposed based on the RBF-IDW for the balance of exploration and exploitation. Extensive experiments have been conducted on widely used benchmark problems with up to 100 dimensions. The empirical results have validated that the proposed algorithm is able to achieve a competitive performance compared with state-of-the-art SAEAs.