Accurate and reliable air quality index (AQI) forecasting is extremely crucial for ecological environment and public health. A novel optimal-hybrid model, which fuses the advantage of secondary decomposition (SD), AI method and optimization algorithm, is developed for AQI forecasting in this paper. In the proposed SD method, wavelet decomposition (WD) is chosen as the primary decomposition technique to generate a high frequency detail sequence WD(D) and a low frequency approximation sequence WD(A). Variational mode decomposition (VMD) improved by sample entropy (SE) is adopted to smooth the WD(D), then long short-term memory (LSTM) neural network with good ability of learning and time series memory is applied to make it easy to be predicted. Least squares support vector machine (LSSVM) with the parameters optimized by the Bat algorithm (BA) considers air pollutant factors including PM, PM, SO, CO, NO and O, which is suitable for forecasting WD(A) that retains original information of AQI series. The ultimate forecast result of AQI can be obtained by accumulating the prediction values of each subseries. Notably, the proposed idea not only gives full play to the advantages of conventional SD, but solve the problem that the traditional time series prediction model based on decomposition technology can not consider the influential factors. Additionally, two daily AQI series from December 1, 2016 to December 31, 2018 respectively collected from Beijing and Guilin located in China are utilized as the case studies to verify the proposed model. Comprehensive comparisons with a set of evaluation indices indicate that the proposed optimal-hybrid model comprehensively captures the characteristics of the original AQI series and has high correct rate of forecasting AQI classes.
