The transient search algorithm (TSO) is a new physics-based metaheuristic algorithm that simulates the transient behavior of switching circuits, such as inductors and capacitors, but the algorithm suffers from slow convergence and has a poor ability to circumvent local optima when solving high-dimensional complex problems. To address these drawbacks, an improved transient search algorithm (ITSO) is proposed. Three strategies are introduced to the TSO. First, a chaotic opposition learning strategy is used to generate high-quality initial populations; second, an adaptive inertia weighting strategy is used to improve the exploration ability, exploitation ability, and convergence speed; finally, a neighborhood dimensional learning strategy is used to maintain population diversity with each iteration of merit seeking. The Friedman test and Wilcoxon’s rank sum test were also used by comparing the experiments with recently popular algorithms on 18 benchmark test functions of various types. Statistical results, nonparametric sign tests, and convergence curves all indicate that ITSO develops, explores, and converges significantly better than other popular algorithms, and is a promising intelligent optimization algorithm for applications.

Due to the limited number of air quality monitoring stations, the data collected are limited. Using supervised learning for air quality fine-grained analysis, that is used to predict the air quality index (AQI) of the locations without air quality monitoring stations, may lead to overfitting in that the models have superior performance on the training set but perform poorly on the validation and testing set. In order to avoid this problem in supervised learning, the most effective solution is to increase the amount of data, but in this study, this is not realistic. Fortunately, semi-supervised learning can obtain knowledge from unlabeled samples, thus solving the problem caused by insufficient training samples. Therefore, a co-training semi-supervised learning method combining the K-nearest neighbors (KNN) algorithm and deep neural network (DNN) is proposed, named KNN-DNN, which makes full use of unlabeled samples to improve the model performance for fine-grained air quality analysis. Temperature, humidity, the concentrations of pollutants and source type are used as input variables, and the KNN algorithm and DNN model are used as learners. For each learner, the labeled data are used as the initial training set to model the relationship between the input variables and the AQI. In the iterative process, by labeling the unlabeled samples, a pseudo-sample with the highest confidence is selected to expand the training set. The proposed model is evaluated on a real dataset collected by monitoring stations from 1 February to 30 April 2018 over a region between 118° E–118°53′ E and 39°45′ N–39°89′ N. Practical application shows that the proposed model has a significant effect on the fine-grained analysis of air quality. The coefficient of determination between the predicted value and the true value is 0.97, which is better than other models.