In order to reduce the use of fossil fuels and meet the needs of different energy products, this paper proposes an integrated multi-generation system that can produce power, cooling, and freshwater. A mathematical model is established to analyze the system performance from the perspectives of energy, exergy and economics. Different machine learning algorithms are used to develop prediction models of the system performance. By comparing the predictive performance of different machine learning models, the optimal model is obtained to replace the thermodynamic model of the proposed system to accelerate the optimization process. The results show that the backpropagation neural network (BPNN) model demonstrates the highest predictive accuracy and the lowest relative error fluctuation. When comparing the multi-objective optimization results of the BPNN model with those of the thermodynamic model, it can be observed that the results achieved through both models are very close. Furthermore, the optimization time using the BPNN model is significantly shorter than the thermodynamic model. Finally, under the conditions of solar radiation intensity of 950 W/m2, heliostat field area of 1000 m2, and heat source temperature of 838.15 K, the total product output, thermal efficiency, exergy efficiency, and levelized cost of energy at the final optimal point obtained through BPNN model-based optimization are 2.486 MW, 26.16 %, 23.64 %, and 0.105 $/kWh, respectively. The net power output, cooling capacity, and freshwater flow rate are 2.006 MW, 131.06 kW, and 8.27 m3/h, respectively.