To ensure the safe and stable operation of energy storage systems, accurately predicting the Remaining Useful Life (RUL) of lithium-ion batteries is crucial. This paper presents an integrated forecasting model that combines the Artificial Bee Colony (ABC) algorithm with a Long Short-Term Memory (LSTM) network enhanced by dropout techniques, which effectively improves the accuracy of RUL predictions for lithium-ion batteries. Initially, the dropout regularization method is utilized to effectively mitigate overfitting, thereby enhancing the generalization capability of the predictive model. Subsequently, an activation layer network structure is introduced to address capacity recovery and data noise issues, significantly enhancing the model's ability to handle complex nonlinear data. Then, the hyperparameters of the LSTM comprehensive forecasting model are optimized using the ABC algorithm to avoid local optima and improve the precision of RUL predictions. Finally, the predictive accuracy and robustness of the proposed model are verified using a public dataset from the NASA Research Center and the CALCE. The paper conducts an experimental analysis and verification of the predictive performance of various algorithms based on training data at 40% and 60% levels. It also compares with swarm optimization algorithms such as the Sparrow Search Algorithm and the Humpback Whale Optimization Algorithm. The experimental results demonstrate that the proposed ABC-LSTM integrated forecasting model can more accurately capture the global trends and local characteristics of lithium-ion battery capacity degradation. The root mean square error of the RUL prediction results at a 60% proportion is consistently kept within 1.02%, the mean absolute error is consistently maintained within 0.86%, and the fitting coefficient is above 97%.