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PM 2.5 forecasting has always been difficult. Neural networks are widely used in the forecasting of PM 2.5 , however, the accuracy is not satisfactory due to uncertainty. In order to solve this problem, a new PM 2.5 forecasting system based on data preprocessing, combined neural network, and the unconstrained weighting method based on an improved multi-objective optimization algorithm is proposed. A new chaotic map is introduced to our model to improve the traditional population initialization. In addition, a new unconstrained weighting method was proposed, and a combination of MAPE value (prediction accuracy) and STD value (prediction stability) were set as the objective functions. The predicted results of each neural network were judged by statistical index and a dynamic weight was given to different neural networks to achieve the optimal prediction result. We demonstrated the superiority, accuracy and generalization ability of our proposed model through experiments on the PM 2.5 data of four cities around the Bohai Economic Belt in China: Beijing, Tianjin, Dalian, and Yantai. • VMD method is robust to the sampling and noise which can effectively avoid the mode aliasing. • The combination of ANN, RNN, CNN is adopted, which greatly improves the prediction ability of the model. • The unconstrained weighting algorithm is used to obtain the optimal weight of different neural networks. • A new chaotic mapping is proposed, which can effectively improve the global search ability. • The combination of point prediction and interval prediction can provide more effective information. [ABSTRACT FROM AUTHOR]