The rapid industrial development in the human society has brought about the air pollution, which seriously affects human health. PM2.5 concentration is one of the main factors causing the air pollution. To accurately predict PM2.5 microns, we propose a dendritic neuron model (DNM) trained by an improved state-of-matter heuristic algorithm (DSMS) based on STL-LOESS, namely DS-DNM. Firstly, DS-DNM adopts STL-LOESS for the data preprocessing to obtain three characteristic quantities from original data: seasonal, trend, and residual components. Then, DNM trained by DSMS predicts the residual values. Finally, three sets of feature quantities are summed to obtain the predicted values. In the performance test experiments, five real-world PM2.5 concentration data are used to test DS-DNM. On the other hand, four training algorithms and seven prediction models were selected for comparison to verify the rationality of the training algorithms and the accuracy of the prediction models, respectively. The experimental results show that DS-DNM has the more competitive performance in PM2.5 concentration prediction problem.

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The famous McCulloch–Pitts neuron model has been criticized for being overly simplistic in the long term. At the same time, the dendritic neuron model (DNM) has been shown to be effective in prediction problems, and it accounts for the nonlinear information-processing capacity of synapses and dendrites. Furthermore, since the classical error back-propagation (BP) algorithm typically experiences problems caused by the overabundance of saddle points and local minima traps, an efficient learning approach for DNMs remains desirable but difficult to implement. In addition to BP, the mainstream DNM-optimization methods include meta-heuristic algorithms (MHAs). However, over the decades, MHAs have developed a large number of different algorithms. How to screen suitable MHAs for optimizing DNMs has become a hot and challenging area of research. In this study, we classify MHAs into different clusters with different population interaction networks (PINs). The performance of DNMs optimized by different clusters of MHAs is tested in the financial time-series-forecasting task. According to the experimental results, the DNM optimized by MHAs with power-law-distributed PINs outperforms the DNM trained based on the BP algorithm.

Complex systems provide an opportunity to analyze the essence of phenomena by studying their intricate connections. The networks formed by these connections, known as complex networks, embody the underlying principles governing the system’s behavior. While complex networks have been previously applied in the field of evolutionary computation, prior studies have been limited in their ability to reach conclusive conclusions. Based on our investigations, we are against the notion that there is a direct link between the complex network structure of an algorithm and its performance, and we demonstrate this experimentally. In this paper, we address these limitations by analyzing the dynamic complex network structures of five algorithms across three different problems. By incorporating mathematical distributions utilized in prior research, we not only generate novel insights but also refine and challenge previous conclusions. Specifically, we introduce the biased Poisson distribution to describe the algorithm’s exploration capability and the biased power-law distribution to represent its exploitation potential during the convergence process. Our aim is to redirect research on the interplay between complex networks and evolutionary computation towards dynamic network structures, elucidating the essence of exploitation and exploration in the black-box optimization process of evolutionary algorithms via dynamic complex networks.