With the expansion of power grids, the increasing peak-valley load difference threatens grid security, a challenge addressed by time-of-use pricing which incentivizes load shifting. Since central air-conditioning systems account for over 60% of building energy use, optimizing them for efficiency and cost under time-of-use pricing is crucial. This study presents an integrated optimization framework that coordinates photovoltaic generation, battery storage, and grid power. The approach develops a BES-LSTM forecasting model by using the Bald Eagle Search (BES) algorithm to tune Long Short-Term Memory (LSTM) network parameters for accurate cooling-load prediction. A central air-conditioning water-system energy-minimization model is then formulated and solved with an improved BES algorithm that incorporates adaptive opposition-based learning, logistic chaotic mapping, and Lévy flight. Finally, a daily schedule is optimized by partitioning time according to time-of-use price intervals and treating generation output, battery charge/discharge, and grid draw as decision variables. Simulations demonstrate that the framework reduces the central air-conditioning water system’s total energy consumption by an average of 28.7% and lowers energy costs under time-of-use pricing by 22.38%, achieving both significant energy savings and economic benefits.