Shale gas reserves represent a significant source of natural gas, but unlocking their full potential depends on effective hydraulic fracturing. This research investigates the application of machine learning (ML) techniques to predict fracability index (FI), offering a faster and more cost-effective alternative to traditional experimental methods. Focusing on the Upper Ordovician Wufeng to Lower Silurian Longmaxi Formation in the Weiyuan shale gas field, Sichuan Basin, China, this study employed deep neural networks that integrate two metaheuristic algorithms—genetic algorithm (GA) and particle swarm optimization (PSO)—with the back-propagation technique. These combined algorithms—termed GABPNN and PSOBPNN—were utilized to predict the FI. Model performance was assessed using three metrics: R2, RMSE, and MAE. The GABPNN achieved R2, RMSE, and MAE of 0.97531, 0.024754, and 0.0042875, respectively, while the PSOBPNN yielded values of 0.97494, 0.024938, and 0.0048962, respectively. Notably, when predicting FI values for the test well, the PSOBPNN model attained a R2 of 0.99848, and the GABPNN model achieved a R2 of 0.9993, indicating exceptional predictive accuracy. Both models demonstrated nearly perfect prediction accuracy for FI in the testing dataset, underscored by their high R2 values. Importantly, the GABPNN model exhibited superior capability in mitigating overfitting, a common challenge in ML applications. Overall, the GABPNN and PSOBPNN models offer effective alternatives for assessing the fracability of shale gas reservoirs. By facilitating the identification of sweet spots for fracturing, these ML-based approaches have the potential to optimize operations in shale gas reservoirs.