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The precise forecasting of daily solar radiation (DSR) is receiving prominent attention among thriving solar energy studies. In this study, three standalone models, including gene expression programing (GEP), multivariate adaptive regression splines (MARS), and self-adaptive MARS (SaMARS), were evaluated to forecast DSR. A SaMARS model was classified as MARS model when using the crow search algorithm (CSA). In addition, to overcome the limitations of the standalone models, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) was employed to enhance the accuracy of DSR forecasting. Therefore, three hybrid models including CEEMDAN-GEP, CEEMDAN-MARS, and CEEMDAN-SaMARS were proposed to forecast DSR in Busan and Incheon stations in South Korea. The performance of proposed models were evaluated and affirmed that the accuracy of the CEEMDAN-SaMARS model (NSE = 0.878–0.883) outperformed CEEMDAN-MARS (NSE = 0.819–0.818), CEEMDAN-GEP (NSE = 0.873–0.789), SaMARS (NSE = 0.846–0.769), MARS (NSE = 0.819–0.758), and GEP (NSE = 0.814–0.755) models at both stations. Therefore, it can be concluded that the optimized CEEMDAN-SaMARS model significantly enhanced the accuracy of DSR forecasting compared to that of standalone models.