The quantum particle swarm optimization algorithm is a global convergence guarantee algorithm. Its searching performance is better than the original particle swarm optimization algorithm (PSO), but the control parameters are less and easy to fall into local optimum. The paper proposed teamwork evolutionary strategy for balance global search and local search. This algorithm is based on a novel learning strategy consisting of cross-sequential quadratic programming and Gaussian chaotic mutation operators. The former performs the local search on the sample and the interlaced operation on the parent individual while the descendants of the latter generated by Gaussian chaotic mutation may produce new regions in the search space. Experiments performed on multimodal test and composite functions with or without coordinate rotation demonstrated that the population information could be utilized by the TEQPSO algorithm more effectively compared with the eight QSOs and PSOs variants. This improves the algorithm performance, significantly.

Since air pollution is an important factor hindering China’s economic development, China has passed a series of bills to control air pollution. However, we still lack an understanding of the status of environmental efficiency in regard to air pollution, especially PM2.5 (diameter of fine particulate matter less than 2.5 μm) pollution. Using panel data on ten major Chinese city groups from 2004 to 2016, we first estimate the environmental efficiency of PM2.5 by epsilon-based measure (EBM) meta-frontier model. The results show that there are large differences in PM2.5 environmental efficiency between cities and city groups. The cities with the highest environmental efficiency are the most economically developed cities and the city group with the highest environmental efficiency is mainly the eastern city group. Then, we use the meta-frontier Malmquist EBM model to measure the meta-frontier Malmquist total factor productivity index (MMPI) in each city group. The results indicate that, overall, China’s environmental total factor productivity declined by 3.68% and 3.49% when considering or not the influence of outside sources, respectively. Finally, we decompose the MMPI into four indexes, namely, the efficiency change (EC) index, the best practice gap change (BPC) index, the pure technological catch-up (PTCU) index, and the frontier catch-up (FCU) index. We find that the trend of the MMPI is consistent with those of the BPC and PTCU indexes, which indicates that the innovation effect of the BPC and PTCU indexes are the main driving forces for productivity growth. The EC and FCU effect are the main forces hindering productivity growth.

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