Increasing air pollutants significantly affect the proportion of diffuse (R-d) to global (R-s) solar radiation. This study proposed three new hybrid support vector machines (SVM) with particle swarm optimization algorithm (SVM-PSO), bat algorithm (SVM-BAT) and whale optimization algorithm (SVM-WOA) for predicting daily R-d in air-polluted regions. These models were further compared to standalone SVM, multivariate adaptive regression spline (MARS) and extreme gradient boosting (XGBoost) models. The results showed that models with suspended particulate matter with aerodynamic diameter smaller than 2.5 mu m and 10 mu m (PM2.5 and PM10) and ozone (O-3) produced more accurate daily R-d estimates than those without air pollution parameters, with average relative decreases in root mean square deviation (RMSD) of 11.1%, 10.0% and 10.4% for sunshine duration-based, R-s-based and combined models, respectively. SVM showed better accuracy than XGBoost and MARS. However, compared to SVM, SVM-BAT further enhanced the prediction accuracy and convergence rate in daily R-d modeling, followed by SVM-WOA and SVM-PSO, with relative decreases in RMSD of 2.9%-5.6%, 1.9%-4.9% and 1.1%-3.3%, respectively. The results highlighted the significance of incorporating air pollutants for more accurate estimation of daily R-d in air-polluted regions. Heuristic algorithms, especially BAT, are highly recommended for improving performance of standalone machine learning models. (c) 2019 Elsevier Ltd. All rights reserved.