**1. Introduction**

Pollution describes the appearance and retention of the regular circulation of material, fine particles, biomaterial, and energy, or a deterioration technique or atmospheric change, which also has or may have significantly negative effects on human beings or the natural environment. Air pollutants are exhaust gases, particulate matter compounds, solid particulate matter, and other substances that emanate into the air, threatening the health of the community and damaging the environment. Air pollutants can be classified into smog and soot, pollution from contaminated air, greenhouse gas emissions, pollen, and mold.

PM refers to particulate matter, also known as particulate emissions. PM comprises aggregated rigid particles and atmospheric fluid droplets. Some are large enough or visible enough to be seen with the naked eye, and others are so small that they can only be seen with electron microscopes. PM10 and PM2.5 are some classes of these particulate

**Citation:** Caraka, R.E.; Yasin, H.; Chen, R.-C.; Goldameir, N.E.; Supatmanto, B.D.; Toharudin, T.; Basyuni, M.; Gio, P.U.; Pardamean, B. Evolving Hybrid Cascade Neural Network Genetic Algorithm Space–Time Forecasting. *Symmetry* **2021**, *13*, 1158. https://doi.org/ 10.3390/sym13071158

Academic Editor: José Carlos R. Alcantud

Received: 7 May 2021 Accepted: 24 June 2021 Published: 28 June 2021

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pollutants [1–4]. Let us consider a hair: the mean diameter of a single human hair is approximately 70 micrometers. This is roughly 28 times the diameter of PM2.5. The diameter of particulate matter in PM10 is 10 micrometers or below. Similarly, PM2.5 is normally particles of diameter 2.5 micrometers or below. Both PM10 and PM2.5 are inhalable. We can thus imagine how tiny 2.5 and 10 micrometers are.

PM can be made up of various chemicals, including sulfur dioxide (SO2) and nitrogen oxides, originating in PM (NOx) [5–7]. All this can be found as a product of building materials, farms, explosions, power stations, industry, and vehicles. PM is seriously damaging, as described above, as it may be opaque and small enough to be inhaled into the lungs or even into the circulation. Therefore, PM contamination affects the cardiovascular system and can cause fatal illnesses such as cardiovascular diseases, erratic heartbeat, and worsening asthma [8–10].

The estimation of future air pollution is an important task because it can be used to manage risk. The Artificial Neural Network (ANN) is the most frequently used among many data-driven applications and is a modern method and an effective paradigm for predicting and forecasting variables in the managemen<sup>t</sup> of contamination risk due to intrinsic contaminant source uncertainties using quality data [11,12]. ANNs were inspired by the human brain's biochemical neural networks. McCulloch and Pitts in (1943) [13] initially developed a mathematically dependent model and referred to it as a threshold logic computing model for neural networks [14–19].

The neurons are important in the neural network's operating condition, they are very connected and share signals with one another, whether it is a neuron or node. Every layer consists of one or more simple elements called neurons. As the input data are transferred to the input layer, they bind with the weight and are nonlinearized by the activation function; the process of being sent to the next neuron is replicated before the final outcome is achieved. Each new neuron consists of one weight and one activation function [20,21]. The connectivity of neurons is handled by utilizing established inputs and outputs and is seen in an organized way in the ANN. The training phase is represented as a trial-and-error process to select the number of neurons [22,23]. The intensity of these interconnections is adapted to the known pattern using an error convergence technique. In this article, a cascade neural network procedure based on the genetic algorithm is developed for space–time forecasting data. This article is organized as follows: In Section 2, we review the training using the cascade neural network and employ a genetic algorithm. The performance is examined in Section 3 via simulation studies and analysis of four benchmark real datasets of air pollution data. Finally, Section 4 presents our conclusions.
