空氣品質對於人體健康有強烈的關係，如心血管疾病、慢性疾病。
當我們能事先知道空氣品質好壞，我們可以做出相對應的措施。
傳統上有許多統計模型可以進行預測，如自回歸整數移動平均(ARIMA)。
但是空氣品質是屬於高波動性的時間序列，傳統的統計方法無法更準確預測未來走向。
近幾年來，在機器學習中循環式神經網路(Recurrent Neural Network, RNN)在時間序列預測及自然語言處理中皆有出色的表現。
RNN模型使用反向傳摸算法(Back-propagation, BP)，訓練權重及偏誤，進而使成本函數(Cost function)越來越小。
而常見的BP算法中最常見的優化器為隨機梯度下降(Stochastic Gradient Decent, SGD)，也有Adam這種基於SGD下再加上動量(Momentum)的概念來改進算法。
近年來，使用啟發式演算法來改善BP算法的研究慢慢出現，而他們的融合幫助BP演算法跳離區域最佳解。

此論文提出新的混合式演算法(SGD hybrid Repository and Mutation Improved Simplified Particle Swarm Optimization, RMiSPSO-SGD)
此演算法利用粒子群演算法(Particle Swarm Optimization , PSO)早期搜尋能力及改良式簡化群演算法(Improved Simplified Swarm Optimization, ISSO)的高度隨機搜尋避免訓練晚期陷入區域最佳解。
進行兩個成本函數的評估，研究顯示RMiSPSO-SGD有統計上顯著的優於其他算法，證實本研究確實可以解決SGD的缺點並使表現更好。\\
\textbf{關鍵詞:}空氣品質指標、機器學習、循環式神經網路、啟發式演算法

Air quality has a strong relationship with human health, such as cardiovascular diseases.
When we can know in advance whether air quality is good or bad, we can make corresponding measures.
Air quality is a highly volatile time series, and statistical methods, such as autoregressive integer moving average, cannot predict more accurately.
Fortunately, Recurrent Neural Network(RNN) has high performance in time series prediction and natural language processing in recent years.
The RNN model uses Back-propagation(BP) to train weights and biases which makes Cost function smaller and smaller.
The most common optimizer is Stochastic Gradient Decent(SGD), and there is also Adam based on SGD and the concept of Momentum to improve the algorithm.
In recent years, research on using heuristic algorithms to improve BP algorithms has gradually emerged, and it has helped it jump away from local optimum.

This paper proposed a new hybrid algorithm SGD hybrid Repository and Mutation Improved Simplified Particle Swarm Optimization.
This algorithm used the early search ability of Particle Swarm Optimization and the highly randomized search of Improved Simplified Swarm Optimization to avoid falling into the regional optimal solution.
After evaluating the two cost functions, the research shows that RMiSPSO-SGD is statistically significantly greater than other algorithms, and we confirm that this study can solve the shortcomings of SGD and make it perform better.\\
\textbf{Keywords:} AQI, Machining learning, RNN, Heuristic algorithms

[1] S. Feng, D. Gao, F. Liao, F. Zhou, and X. Wang. The health effects of ambi- ent pm2.5 and potential mechanisms. Ecotoxicology and Environmental Safety, 128:67–74, 2016.
[2] A B.Chelani and S.Devotta. Air quality forecasting using a hybrid autoregressive and nonlinear model. Atmospheric Environment, 40:1774–1780, 2006.
[3] A A. Ariyo, A O. Adewumi, and C K. Ayo. Stock price prediction using the arima model. In 2014 UKSim-AMSS 16th International Conference on Computer Modelling and Simulation, 2014.
[4] T Young, D Hazarika, S Poria, and E Cambria. Recent trends in deep learning based natural language processing [review article]. IEEE Computational Intelli- gence Magazine, 13:55 – 75, 2018.
[5] Z Che, S Purushotham, K Cho, D Sontag, and Y Liu. Recurrent neural networks for multivariate time series with missing values. CoRR, abs/1606.01865, 2016.
[6] S Hochreiter and J Schmidhuber. Long short-term memory. Neural Computation, 9:1735–1780, 1997.
[7] J Chung, C Gulcehre, K Cho, and Y Bengio. Empirical evaluation of gated recur- rentneural networks on sequence modeling. CoRR, abs/1412.3555, 2014.
[8] W Yeh. A two-stage discrete particle swarm optimization for the problem of mul- tiple multi-level redundancy allocation in series systems. Expert Systems with Applications, 36:9192–9200, 2009.
[9] Air quality index. https://airtw.epa.gov.tw/CHT/Information/Standard/ AirQualityIndicator.aspx. Accessed: October 29, 2019.
[10] KKohara,TIshikawa,YFukuhara,andYNakamura.Stockpricepredictionusing prior knowledge and neural networks. Intelligent systems in accounting,finance and management, 6:11–22, 1997.
[11] S. Bordignon, C. Gaetan, and F. Lisi. Nonlinear models for ground-level ozone forecasting. Statistical Methods and Applications, 11:117–146, 2002.
[12] Chen L.-J. and Islam S. Biswas P. Nonlinear dynamics of hourly ozone concentra- tions: Nonparametric short term prediction. Atmospheric Environment, 32, 1998.
[13] Y Vibha and | N Satyendra. Forecasting of pm10 using autoregressive models and exponential smoothing technique. Asian Journal of Water, Environment and Pollution, 14, 2017.
[14] G Özel Kadilar and C Kadilar. Assessing air quality in aksaray with time series analysis. In AIP Conference Proceedings, 2017.
[15] S Abdullah, M Ismail, and S Yuen Fong. Multiple linear regression (mlr) models for long term pm10 concentration forecasting during different monsoon seasons. ournal of Sustainability Science and Management, 12, 2017.
[16] P.J.G Nieto, F.S Lasheras, E.García-Gonzalo, and F.J.de Cos Juez. Pm10 con- centration forecasting in the metropolitan area of oviedo (northern spain) using models based on svm, mlp, varma and arima: A case study. Science of The Total Environment, 621:753–761, 2018.
[17] A B.Chelani and S.Devotta. Air quality forecasting using a hybrid autoregressive and nonlinear model. Atmospheric Environment, 40, 2006.
[18] J JuanCarbajal-Hernández, L P.Sánchez-Fernández, J A.Carrasco-Ochoa, and J Fco.Martínez-Trinidad. Assessment and prediction of air quality using fuzzy logic and autoregressive models. Atmospheric Environment, 60, 2012.
[19] L A.Díaz-Robles, J C.Ortega, Joshu S.Fu, Gregory D.Reed, Judith C.Chow, John G.Watson, and Juan A.Moncada-Herrera. A hybrid arima and artificial neural networks model to forecast particulate matter in urban areas: The case of temuco, chile. Atmospheric Environment, 42, 2008.
[20] A.S.Luna, M.L.L.Paredes, G.C.G.de Oliveira, and S.M.Corrêa. Prediction of ozone concentration in tropospheric levels using artificial neural networks and sup- port vector machine at rio de janeiro, brazil. Atmospheric Environment, 98:98–104, 2014.
[21] H Li, J Wang, R Li, and H Lu. Novel analysis–forecast system based on multi-objective optimization for air quality index. Journal of Cleaner Production, 208:1365–1383, 2019.
[22] P.Allen D. Recursive neural network model for analysis and forecast of pm10 and pm2.5. Atmospheric Pollution Research, 8:652–659, 2017.
[23] K Srinivasa Rao, G. Lavanya Devi, and N. Ramesh. Air quality prediction in visakhapatnam with lstm based recurrent neural networks. International Journal of Intelligent Systems and Applications, 11:18–24, 2019.
[24] R. J. Kuo, B Prasetyo, and B. S. Wibowo. Deep learning-based approach for air quality forecasting by using recurrent neural network with gaussian process in tai- wan. In 2019 IEEE 6th International Conference on Industrial Engineering and Applications (ICIEA), 2019.
[25] D Zang, J Ding, J Cheng, D Zhang, and K Tang. A hybrid learning algorithm for the optimization of convolutional neural network. In International Conference on Intelligent Computing, 2017.
[26] K Diederik P and B Jimmy. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.
[27] Sanjiv Kumar Sashank J. Reddi, Satyen Kale. On the convergence of adam and beyond. In ICLR 2018, 2018.
[28] A M.Ibrahim and N H.El-Amary. Particle swarm optimization trained recurrent neural network for voltage instability prediction. Journal of Electrical Systems and Information Technology, 5:216–228, 2018.
[29] J Kennedy and R Eberhart. Particle swarm optimization. volume 4, page 1942– 1948, 1995.
[30] B.Jana, S.Mitra, and S.Acharyy. Repository and mutation based particle swarm optimization (rmpso): A new pso variant applied to reconstruction of gene regu- latory network. Applied Soft Computing, 74:330–355, 2019.
[31] JGao,HSultan,JHu,andWWTung.Denoisingnonlineartimeseriesbyadaptive filtering and wavelet shrinkage: A comparison. IEEE Signal Processing Letters, 17:237 – 240, 2010.
[32] M.C.AKorbaRDjemili,HBourouba.Applicationofempiricalmodedecomposi- tion and artificial neural network for the classification of normal and epileptic eeg signals. Biocybernetics and Biomedical Engineering, 36:285–291, 2016.
[33] O Abedinia N Amjady. Short term wind power prediction based on improved kriging interpolation, empirical mode decomposition, and closed-loop forecasting engine. Sustainability, page 2104, 2017.
[34] D P.Allen. A frequency domain hampel filter for blind rejection of sinusoidal interference from electromyograms. Journal of Neuroscience Methods, 177:303– 310, 2009.
[35] R.K. Pearson. Outliers in process modeling and identification. IEEE Transactions on Control Systems Technology, 10:55 – 63, 2002.
[36] NE.Huang,ZShen,SR.Long,MC.Wu,HH.Shih,QZheng,N-CYen,CC Tung, and H H. Liu. The empirical mode decomposition and the hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the royal society a mathematical, physical and engineering sciences, 454, 1998.
[37] J.B Ali, N Fnaiech, L Saidi, B.Chebel-Morello, and F Fnaiech. Application of empirical mode decomposition and artificial neural network for automatic bearing fault diagnosis based on vibration signals. Applied Acoustics, 89:16–27, 2015.
[38] Y Lei, J Lin, Z He, and M J Zuob. A review on empirical mode decomposition in fault diagnosis of rotating machinery. Mechanical Systems and Signal Processing, 35:108–126, 2013.
[39] P.Flandrin,G.Rilling,andP.Goncalves.Empiricalmodedecompositionasafilter bank. IEEE Signal Processing Letters, 11:112–114, 2004.
[40] K Cho, B Merrienboer, C Gulcehre, D Bahdanau, F Bougares, H Schwenk, and Y Bengio. Learning phrase representations using rnn encoder-decoder for statisti- cal machine translation. In EMNLP 2014, 2014.
[41] R Józefowicz, W Zaremba, and I Sutskever. An empirical exploration of recurrent network architectures. In ICML 2015, 2015.
[42] Understanding lstm networks. https://colah.github.io/posts/ 2015-08-Understanding-LSTMs/. Accessed: April 27, 2020.
[43] A. RezaeeJordehi. Enhanced leader pso (elpso): A new pso variant for solving global optimisation problems. Applied Soft Computing, 26:401–417, 2015.
[44] W C Yeh. An improved simplified swarm optimization. Knowledge-Based Sys- tems, 82:60–69, 2015.