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International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749


Application of Modified Grey Forecasting Model to Predict the Municipal Solid Waste Generation using MLP and MLE

Application of Modified Grey Forecasting Model to Predict the Municipal Solid Waste Generation using MLP and MLE

Mohd Anjum
Department of Computer Engineering, Aligarh Muslim University, Aligarh, Uttar Pradesh, India.

Sana Shahab
Department of Business & Administration, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia.

Mohammad Sarosh Umar
Department of Computer Engineering, Aligarh Muslim University, Aligarh, Uttar Pradesh, India.

DOI https://doi.org/10.33889/IJMEMS.2021.6.5.077

Received on April 04, 2021
  ;
Accepted on August 05, 2021

Abstract

Grey forecasting theory is an approach to build a prediction model with limited data to produce better forecasting results. This forecasting theory has an elementary model, represented as the GM(1,1) model , characterized by the first-order differential equation of one variable. It has the potential for accurate and reliable forecasting without any statistical assumption. The research proposes a methodology to derive the modified GM(1,1) model with improved forecasting precision. The residual series is forecasted by the GM(1,1) model to modify the actual forecasted values. The study primarily addresses two fundamental issues: sign prediction of forecasted residual and the procedure for formulating the grey model. Accurate sign prediction is very complex, especially when the model lacks in data. The signs of forecasted residuals are determined using a multilayer perceptron to overcome this drawback. Generally, the elementary model is formulated conventionally, containing the parameters that cannot be calculated straightforward. Therefore, maximum likelihood estimation is incorporated in the modified model to resolve this drawback. Three statistical indicators, relative residual, posterior variance test, and absolute degree of grey indices, are evaluated to determine the model fitness and validation. Finally, an empirical study is performed using actual municipal solid waste generation data in Saudi Arabia, and forecasting accuracies are compared with the linear regression and original GM(1,1). The MAPEs of all models are rigorously examined and compared, and then it is obtained that the forecasting precision of GM(1,1) model , modified GM(1,1) model, and linear regression is 15.97%, 8.90%, and 27.90%, respectively. The experimental outcomes substantiate that the modified grey model is a more suitable forecasting approach than the other compared models.

Keywords- GM(1,1) model, Linear regression, Multilayer perceptron, Maximum likelihood estimation, Forecasting.

Citation

Anjum, M., Shahab, S., & Umar, M. S (2021). Application of Modified Grey Forecasting Model to Predict the Municipal Solid Waste Generation using MLP and MLE. International Journal of Mathematical, Engineering and Management Sciences, 6(5), 1276-1296. https://doi.org/10.33889/IJMEMS.2021.6.5.077.

Conflict of Interest

The authors confirm that there is no conflict of interest to declare for this publication.

Acknowledgements

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. The authors would like to thank the editor and anonymous reviewers for their comments that help improve the quality of this work.

References

Araiza-Aguilar, J.A., Rojas-Valencia, M.N., & Aguilar-Vera, R.A. (2020). Forecast generation model of municipal solid waste using multiple linear regression. Global Journal of Environmental Science and Management, 6(1), 1-14. DOI: https://doi.org/10.22034/gjesm.2020.01.01.

Balochian, S., & Baloochian, H. (2020). Improving grey prediction model and its application in predicting the number of users of a public road transportation system. Journal of Intelligent Systems, 30(1), 104-114. DOI: https://doi.org/10.1515/jisys-2019-0082.

Duman, G.M., Kongar, E., & Gupta, S.M. (2019). Estimation of electronic waste using optimized multivariate grey models. Waste Management, 95, 241-249. DOI: https://doi.org/10.1016/j.wasman.2019.06.023.

Elsheikh, A.H., Sharshir, S.W., Abd Elaziz, M., Kabeel, A.E., Guilan, W., & Haiou, Z. (2019). Modeling of solar energy systems using artificial neural network: a comprehensive review. Solar Energy, 180, 622-639. DOI: https://doi.org/10.1016/j.solener.2019.01.037.

General Authority for Statistics. (2018). Per capita daily waste collection In Saudi Arabia during the period 2010-2018. https://www.stats.gov.sa/sites/default/files/Per capita waste generation 2018 EN.pdf.

Heidari, A.A., Faris, H., Aljarah, I., & Mirjalili, S. (2019). An efficient hybrid multilayer perceptron neural network with grasshopper optimization. Soft Computing, 23(17), 7941-7958. DOI: https://doi.org/10.1007/s00500-018-3424-2.

Hsu, C.C., & Chen, C.Y. (2003). Applications of improved grey prediction model for power demand forecasting. Energy Conversion and Management, 44(14), 2241-2249. DOI: https://doi.org/10.1016/S0196-8904(02)00248-0.

Hsu, L.C., & Wang, C.H. (2007). Forecasting the output of integrated circuit industry using a grey model improved by the bayesian analysis. Technological Forecasting and Social Change, 74(6), 843-853. DOI: https://doi.org/10.1016/j.techfore.2006.02.005.

Hu, Y.C. (2020). Constructing grey prediction models using grey relational analysis and neural networks for magnesium material demand forecasting. Applied Soft Computing, 93. DOI: https://doi.org/10.1016/j.asoc.2020.106398.

Hu, Y.C., & Jiang, P. (2017). Forecasting energy demand using neural-network-based grey residual modification models. Journal of the Operational Research Society, 68(5), 556-565. DOI: https://doi.org/10.1057/s41274-016-0130-2.

Hu, Y., Ma, X., Li, W., Wu, W., & Tu, D. (2020). Forecasting manufacturing industrial natural gas consumption of China using a novel time-delayed fractional grey model with multiple fractional order. Computational and Applied Mathematics, 39(4), 1-30. DOI: https://doi.org/10.1007/s40314-020-01315-3.

Intharathirat, R., Abdul Salam, P., Kumar, S., & Untong, A. (2015). Forecasting of municipal solid waste quantity in a developing country using multivariate grey models. Waste Management, 39, 3-14. DOI: https://doi.org/10.1016/j.wasman.2015.01.026.

Javed, S.A., Zhu, B., & Liu, S. (2020). Forecast of biofuel production and consumption in top CO2 emitting countries using a novel grey model. Journal of Cleaner Production, 276, 123997. DOI: https://doi.org/10.1016/j.jclepro.2020.123997.

Kiran, M., Shanmugam, P.V., Mishra, A., Mehendale, A., & Nadheera Sherin, H.R. (2021). A multivariate discrete grey model for estimating the waste from mobile phones, televisions, and personal computers in India. Journal of Cleaner Production, 293, 126185. DOI: https://doi.org/10.1016/j.jclepro.2021.126185.

Kumar, A., Pant, S., & Ram, M. (2018). Complex system reliability analysis and optimization. In Advanced Mathematical Techniques in Science and Engineering, pp. 185-199, River Publisher, Denmark.

Kumar, A., Pant, S., & Ram, M. (2019a). Gray wolf optimizer approach to the reliability-cost optimization of residual heat removal system of a nuclear power plant safety system. Quality and Reliability Engineering International, 35(7), 2228-2239. DOI: https://doi.org/10.1002/qre.2499.

Kumar, A., Pant, S., Ram, M., & Chaube, S. (2019b). Multi-objective grey wolf optimizer approach to the reliability-cost optimization of life support system in space capsule. International Journal of Systems Assurance Engineering and Management, 10(2), 276-284. DOI: https://doi.org/10.1007/s13198-019-00781-1.

Kumar, A., Pant, S., & Singh, S.B. (2017). Reliability optimization of complex systems using cuckoo search algorithm. In Mathematical Concepts and Applications in Mechanical Engineering and Mechatronics, IGI Global, USA, pp. 94-110. DOI: https://doi.org/10.4018/978-1-5225-1639-2.ch005.

Lee, Y.S., & Tong, L.I. (2011). Forecasting energy consumption using a grey model improved by incorporating genetic programming. Energy Conversion and Management, 52(1), 147-152. DOI: https://doi.org/10.1016/j.enconman.2010.06.053.

Li, K., & Zhang, T. (2018). Forecasting electricity consumption using an improved grey prediction model. Information, 9(8), 204. DOI: https://doi.org/10.3390/info9080204.

Li, K., & Zhang, T. (2021). A novel grey forecasting model and its application in forecasting the energy consumption in Shanghai. Energy Systems, 12(3), 357-372. DOI: https://doi.org/10.1007/s12667-019-00344-0.

Lin, J., Magnago, F., & Alemany, J.M. (2018). Optimization methods applied to power systems: current practices and challenges. In Classical and Recent Aspects of Power System Optimization, pp. 1-18, Academic Press, USA. DOI: https://doi.org/10.1016/B978-0-12-812441-3.00001-X.

Liu, X., & Xie, N. (2019). A nonlinear grey forecasting model with double shape parameters and its application. Applied Mathematics and Computation, 360, 203-212. DOI: https://doi.org/10.1016/j.amc.2019.05.012.

Mirjalili, S., Mirjalili, S.M., & Lewis, A. (2014). Grey wolf optimizer. Advances in Engineering Software, 69, 46-61. DOI: https://doi.org/10.1016/j.advengsoft.2013.12.007.

Negi, G., Kumar, A., Pant, S., & Ram, M. (2021). GWO: a review and applications. International Journal of Systems Assurance Engineering and Management, 12(1), 1-8. DOI: https://doi.org/10.1007/s13198-020-00995-8.

Pant, S., Kumar, A., & Ram, M. (2017b). Flower pollination algorithm development: a state of art review. International Journal of Systems Assurance Engineering and Management, 8(2), 1858-1866. DOI: https://doi.org/10.1007/s13198-017-0623-7.

Pant, S., Kumar, A., & Ram, M. (2019). Solution of nonlinear systems of equations via metaheuristics. International Journal of Mathematical, Engineering and Management Sciences, 4(5), 1108-1126. DOI: https://doi.org/10.33889/IJMEMS.2019.4.5-088.

Pant, S., Kumar, A., Singh, S.B., & Ram, M. (2017a). A modified particle swarm optimization algorithm for nonlinear optimization. Nonlinear Studies, 24(1), 127-138.

Qu, Z., Mao, W., Zhang, K., Zhang, W., & Li, Z. (2019). Multi-step wind speed forecasting based on a hybrid decomposition technique and an improved back-propagation neural network. Renewable Energy, 133, 919-929. DOI: https://doi.org/10.1016/j.renene.2018.10.043.

Ren, S.J., Wang, C.P., Xiao, Y., Deng, J., Tian, Y., Song, J.J., Cheng, X.J., & Sun, G.F. (2020). Thermal properties of coal during low temperature oxidation using a grey correlation method. Fuel, 260, 116287. DOI: https://doi.org/10.1016/j.fuel.2019.116287.

Shen, X., Yue, M., Duan, P., Wu, G., & Tan, X. (2019). Application of grey prediction model to the prediction of medical consumables consumption. Grey Systems: Theory and Application, 9(2), 213-223. DOI: https://doi.org/10.1108/gs-11-2018-0059.

Sun, W., & Huang, C. (2020). A carbon price prediction model based on secondary decomposition algorithm and optimized back propagation neural network. Journal of Cleaner Production, 243, 118671. DOI: https://doi.org/10.1016/j.jclepro.2019.118671.

Tang, J., Yuan, F., Shen, X., Wang, Z., Rao, M., He, Y., Sun, Y., Li, X., Zhang, W., Li, Y., Gao, B., Qian, H., Bi, G., Song, S., Yang, J.J., & Wu, H. (2019). Bridging biological and artificial neural networks with emerging neuromorphic devices: fundamentals, progress, and challenges. Advanced Materials, 31(49), 1902761. DOI: https://doi.org/10.1002/adma.201902761.

Uniyal, N., Pant, S., & Kumar, A. (2020). An overview of few nature inspired optimization techniques and its reliability applications. International Journal of Mathematical, Engineering and Management Sciences, 5(4), 732-743. DOI: https://doi.org/10.33889/IJMEMS.2020.5.4.058.

Wang, C.H., & Hsu, L.C. (2008). Using genetic algorithms grey theory to forecast high technology industrial output. Applied Mathematics and Computation, 195(1), 256-263. DOI: https://doi.org/10.1016/j.amc.2007.04.080.

Wang, R., Xu, K., Xu, Y., & Wu, Y. (2020). Study on prediction model of hazardous chemical accidents. Journal of Loss Prevention in the Process Industries, 66, 104183. DOI: https://doi.org/10.1016/j.jlp.2020.104183.

Wu, W., Ma, X., Wang, Y., Zhang, Y., & Zeng, B. (2019). Research on a novel fractional GM( α , n ) model and its applications. Grey Systems: Theory and Application, 9(3), 356-373. DOI: https://doi.org/10.1108/gs-11-2018-0052.

Xuemei, L., Cao, Y., Wang, J., Dang, Y., & Kedong, Y. (2019). A summary of grey forecasting and relational models and its applications in marine economics and management. Marine Economics and Management, 2(2), 87-113. DOI: https://doi.org/10.1108/maem-04-2019-0002.

Yang, Y., Chen, Y., Shi, J., Liu, M., Li, C., & Li, L. (2016). An improved grey neural network forecasting method based on genetic algorithm for oil consumption of China. Journal of Renewable and Sustainable Energy, 8(2), 024104. DOI: https://doi.org/10.1063/1.4944977.

Zeng, B., Li, H., & Ma, X. (2020). A novel multi-variable grey forecasting model and its application in forecasting the grain production in China. Computers and Industrial Engineering, 150, 106915. DOI: https://doi.org/10.1016/j.cie.2020.106915.

Zhang, Q., Yu, H., Barbiero, M., Wang, B., & Gu, M. (2019). Artificial neural networks enabled by nanophotonics. Light: Science and Applications, 8(1), 1-14. DOI: https://doi.org/10.1038/s41377-019-0151-0.