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Doğrusal Olmayan Gri Bernoulli Model için Parametre ve Model Yapısı Optimizasyonu

Year 2023, , 77 - 94, 11.04.2023
https://doi.org/10.26745/ahbvuibfd.1190046

Abstract

Anlaşılması ve tahmin edilmesi kolay geleneksel gri modeller yaygın olarak kullanılmaktadırlar. Ancak, bu modeller mevcut kestirim ve öngörü hassasiyeti arttırılmak istenildiği zaman ihtiyaç duyulan uyarlamalar için gereken esneklikten yoksundurlar. Diğer taraftan, oldukça esnek olan doğrusal olmayan gri Bernoulli model tek parametresi ayarlanarak, birikim üretim operatörü uygulanmış zaman serisine uyan eğriyi etkin bir şekilde uydurulabilmektedir. Yine de, bu modelinin parametreleri ve yapısı çerçevesinde yapılabilecek iyileştirmeler mevcuttur. Bu yüzden, bu çalışmada doğrusal olmayan gri Bernoulli model için önerilen başlangıç koşulunu optimizasyonu, gri modellerin öngörü performanslarını yükseltmek adına önerilen kayan pencere yöntemi ve sezgisel algoritmalar ile model parametrelerinin optimizasyonu yaklaşımları bir arada kullanılmıştır. Doğrusal olmayan gri Bernoulli model kayan pencere yöntemine dayalı olarak tahmin edilmiştir. Diferansiyel denklemin çözümünde başlangıç koşulu olarak birinci dereceden birikim üretim operatörü uygulanmış serinin düzeltilmiş son elemanı kullanılmıştır. Geçmiş değer ve kuvvet katsayısının en iyi değerleri ise salp sürüsü optimizasyon algoritması kullanılarak bulunmuştur. Dolayısıyla, model yapısının ve parametrelerinin birlikte değerlendirildiği yeni bir optimize edilmiş doğrusal olmayan gri Bernoulli model önerilmiştir. Çalışmada, parametre tahmin yöntemi ve/veya model yapısı açısından birbirinden farklı sekiz gri model değerlendirilmiştir. Ulaşılan sonuçlar önerilen modelin diğer gri modellere göre daha başarılı olduğunu göstermektedir. Sonuç olarak, Türkiye’nin gayrisafi yurt içi hasıla hacim endeksi önerilen gri model ile daha iyi modellenmiştir.

References

  • Aljarah, I., Mafarja, M., Heidari, A. A., Faris, H., Zhang, Y. ve Mirjalili, S. (2018). Asynchronous accelerating multi-leader salp chains for feature selection. Applied Soft Computing, 71, 964–979. https://doi.org/10.1016/j.asoc.2018.07.040
  • Chen, C.-I., Chen, H. L. ve Chen, S.-P. (2008). Forecasting of foreign exchange rates of Taiwan’s major trading partners by novel nonlinear Grey Bernoulli model NGBM(1,1). Communications in Nonlinear Science and Numerical Simulation, 13​(6), 1194–1204. https://doi.org/10.1016/j.cnsns.2006.08.008
  • Chen, C.-I., Hsin, P.-H. ve Wu, C.-S. (2010). Forecasting Taiwan’s major stock indices by the Nash nonlinear grey Bernoulli model. Expert Systems with Applications, 37​(12), 7557–7562. https://doi.org/10.1016/j.eswa.2010.04.088
  • Cheng, M., Liu, Y., Li, J. ve Liu, B. (2022). Nonlinear Grey Bernoulli model NGBM (1, 1)’s parameter optimisation method and model application. Journal of Industrial and Management Optimization, 18​(3), 2017. https://doi.org/10.3934/jimo.2021054
  • Chia-Nan, W. ve Van-Thanh, P. (2015). An Improved Nonlinear Grey Bernoulli Model Combined with Fourier Series. Mathematical Problems in Engineering, 2015, e740272. https://doi.org/10.1155/2015/740272
  • Comert, G., Begashaw, N. ve Huynh, N. (2021). Improved grey system models for predicting traffic parameters. Expert Systems with Applications, 177, 114972. https://doi.org/10.1016/j.eswa.2021.114972
  • Deng, J. L. (1982). Control Problems of Grey System. Systems and Control Letters, 5, 288-294.
  • Hsu, L.-C. (2003). Applying the Grey prediction model to the global integrated circuit industry. Technological Forecasting and Social Change, 70​(6), 563–574. https://doi.org/10.1016/S0040-1625(02)00195-6
  • Hsu, L.-C. (2010). A genetic algorithm based nonlinear grey Bernoulli model for output forecasting in integrated circuit industry. Expert Systems with Applications, 37​(6), 4318–4323. https://doi.org/10.1016/j.eswa.2009.11.068
  • Jiang, J., Feng, T. ve Liu, C. (2021). An Improved Nonlinear Grey Bernoulli Model Based on the Whale Optimization Algorithm and Its Application. Mathematical Problems in Engineering, 2021, e6691724. https://doi.org/10.1155/2021/6691724
  • Kayacan, E., Ulutas, B. ve Kaynak, O. (2010). Grey system theory-based models in time series prediction. Expert Systems with Applications, 37​(2, 2), 1784–1789. https://doi.org/10.1016/j.eswa.2009.07.064
  • Lu, J., Xie, W., Zhou, H. ve Zhang, A. (2016). An optimized nonlinear grey Bernoulli model and its applications. Neurocomputing, 177, 206–214. https://doi.org/10.1016/j.neucom.2015.11.032
  • Mirjalili, S., Gandomi, A. H., Mirjalili, S. Z., Saremi, S., Faris, H. ve Mirjalili, S. M. (2017). Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems. Advances in Engineering Software, 114, 163–191. https://doi.org/10.1016/j.advengsoft.2017.07.002
  • Ngo, H. A. ve Hoang, T. N. (2020). A Rolling Optimized Nonlinear Grey Bernoulli Model RONGBM (1, 1) and application in predicting total COVID-19 infected cases. https://arxiv.org/abs/2008.07581
  • Özcan, T. ve Tüysüz, F. (2018). Healthcare Expenditure Prediction in Turkey by Using Genetic Algorithm Based Grey Forecasting Models. C. Kahraman ve Y. I. Topcu içinde, Operations Research Applications in Health Care Management (159–190). Springer International Publishing. https://doi.org/10.1007/978-3-319-65455-3_7
  • Pao, H.-T., Fu, H.-C. ve Tseng, C.-L. (2012). Forecasting of CO2 emissions, energy consumption and economic growth in China using an improved grey model. Energy, 40​(1), 400–409. https://doi.org/10.1016/j.energy.2012.01.037
  • Rizk-Allah, R. M., Hassanien, A. E., Elhoseny, M. ve Gunasekaran, M. (2019). A new binary salp swarm algorithm: Development and application for optimization tasks. Neural Computing and Applications, 31​(5, 5), 1641–1663. https://doi.org/10.1007/s00521-018-3613-z
  • Tien, T.-L. (2009). A new grey prediction model FGM(1, 1). Mathematical and Computer Modelling, 49​(7, 7), 1416–1426. https://doi.org/10.1016/j.mcm.2008.11.015
  • Wang, Z.-X., Li, Q. ve Pei, L.-L. (2018). A seasonal GM(1,1) model for forecasting the electricity consumption of the primary economic sectors. Energy, 154, 522–534. https://doi.org/10.1016/j.energy.2018.04.155
  • Wu, L., Liu, S., Yao, L., Yan, S. ve Liu, D. (2013). Grey system model with the fractional order accumulation. Communications in Nonlinear Science and Numerical Simulation, 18​(7), 1775–1785. https://doi.org/10.1016/j.cnsns.2012.11.017
  • Wu, W.-Z., Zhang, T. ve Zheng, C. (2019). A Novel Optimized Nonlinear Grey Bernoulli Model for Forecasting China’s GDP. Complexity, 2019, e1731262. https://doi.org/10.1155/2019/1731262
  • Xia, M. ve Wong, W. K. (2014). A seasonal discrete grey forecasting model for fashion retailing. Knowledge-Based Systems, 57, 119–126. https://doi.org/10.1016/j.knosys.2013.12.014
  • Xie, N.-m. ve Liu, S.-f. (2009). Discrete grey forecasting model and its optimization. Applied Mathematical Modelling, 33​(2), 1173–1186. https://doi.org/10.1016/j.apm.2008.01.011
  • Zhou, J., Fang, R., Li, Y., Zhang, Y. ve Peng, B. (2009). Parameter optimization of nonlinear grey Bernoulli model using particle swarm optimization. Applied Mathematics and Computation, 207​(2), 292–299. https://doi.org/10.1016/j.amc.2008.10.045

Parameter and Model Structure Optimization for the Nonlinear Grey Bernoulli Model

Year 2023, , 77 - 94, 11.04.2023
https://doi.org/10.26745/ahbvuibfd.1190046

Abstract

Traditional grey models, easy to understand and estimate, are widely used. However, these models lack the flexibility with regard to the adaptations required to increase the current prediction and forecast accuracy. However, the highly flexible non-linear grey Bernoulli model can effectively fit the curve for the accumulated generating operation series by adjusting its single parameter. Nevertheless, there are still improvements that can be made within the framework of the structure and parameters of this model. Therefore, in this study, initial condition optimization proposed for the non-linear grey Bernoulli model, the rolling window method proposed to improve the forecasting performance of the grey models and, optimization of the model parameters with heuristic algorithm combined. The non-linear grey Bernoulli model was estimated by using the rolling window method. The corrected last element of the accumulated generating operation series was used as the initial condition in the solution of the differential equation. The optimal values of the background value and power index were determined by using the salp swarm optimization algorithm. Therefore, a new optimized non-linear grey Bernoulli model is proposed by considering the structure and parameters of the model together. In the study, eight different grey models were evaluated in terms of parameter estimation method and/or model structure. The results showed that the proposed model outperformed the other grey models. Consequently, gross domestic product volume index of Turkey was better modeled with the proposed grey model.

References

  • Aljarah, I., Mafarja, M., Heidari, A. A., Faris, H., Zhang, Y. ve Mirjalili, S. (2018). Asynchronous accelerating multi-leader salp chains for feature selection. Applied Soft Computing, 71, 964–979. https://doi.org/10.1016/j.asoc.2018.07.040
  • Chen, C.-I., Chen, H. L. ve Chen, S.-P. (2008). Forecasting of foreign exchange rates of Taiwan’s major trading partners by novel nonlinear Grey Bernoulli model NGBM(1,1). Communications in Nonlinear Science and Numerical Simulation, 13​(6), 1194–1204. https://doi.org/10.1016/j.cnsns.2006.08.008
  • Chen, C.-I., Hsin, P.-H. ve Wu, C.-S. (2010). Forecasting Taiwan’s major stock indices by the Nash nonlinear grey Bernoulli model. Expert Systems with Applications, 37​(12), 7557–7562. https://doi.org/10.1016/j.eswa.2010.04.088
  • Cheng, M., Liu, Y., Li, J. ve Liu, B. (2022). Nonlinear Grey Bernoulli model NGBM (1, 1)’s parameter optimisation method and model application. Journal of Industrial and Management Optimization, 18​(3), 2017. https://doi.org/10.3934/jimo.2021054
  • Chia-Nan, W. ve Van-Thanh, P. (2015). An Improved Nonlinear Grey Bernoulli Model Combined with Fourier Series. Mathematical Problems in Engineering, 2015, e740272. https://doi.org/10.1155/2015/740272
  • Comert, G., Begashaw, N. ve Huynh, N. (2021). Improved grey system models for predicting traffic parameters. Expert Systems with Applications, 177, 114972. https://doi.org/10.1016/j.eswa.2021.114972
  • Deng, J. L. (1982). Control Problems of Grey System. Systems and Control Letters, 5, 288-294.
  • Hsu, L.-C. (2003). Applying the Grey prediction model to the global integrated circuit industry. Technological Forecasting and Social Change, 70​(6), 563–574. https://doi.org/10.1016/S0040-1625(02)00195-6
  • Hsu, L.-C. (2010). A genetic algorithm based nonlinear grey Bernoulli model for output forecasting in integrated circuit industry. Expert Systems with Applications, 37​(6), 4318–4323. https://doi.org/10.1016/j.eswa.2009.11.068
  • Jiang, J., Feng, T. ve Liu, C. (2021). An Improved Nonlinear Grey Bernoulli Model Based on the Whale Optimization Algorithm and Its Application. Mathematical Problems in Engineering, 2021, e6691724. https://doi.org/10.1155/2021/6691724
  • Kayacan, E., Ulutas, B. ve Kaynak, O. (2010). Grey system theory-based models in time series prediction. Expert Systems with Applications, 37​(2, 2), 1784–1789. https://doi.org/10.1016/j.eswa.2009.07.064
  • Lu, J., Xie, W., Zhou, H. ve Zhang, A. (2016). An optimized nonlinear grey Bernoulli model and its applications. Neurocomputing, 177, 206–214. https://doi.org/10.1016/j.neucom.2015.11.032
  • Mirjalili, S., Gandomi, A. H., Mirjalili, S. Z., Saremi, S., Faris, H. ve Mirjalili, S. M. (2017). Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems. Advances in Engineering Software, 114, 163–191. https://doi.org/10.1016/j.advengsoft.2017.07.002
  • Ngo, H. A. ve Hoang, T. N. (2020). A Rolling Optimized Nonlinear Grey Bernoulli Model RONGBM (1, 1) and application in predicting total COVID-19 infected cases. https://arxiv.org/abs/2008.07581
  • Özcan, T. ve Tüysüz, F. (2018). Healthcare Expenditure Prediction in Turkey by Using Genetic Algorithm Based Grey Forecasting Models. C. Kahraman ve Y. I. Topcu içinde, Operations Research Applications in Health Care Management (159–190). Springer International Publishing. https://doi.org/10.1007/978-3-319-65455-3_7
  • Pao, H.-T., Fu, H.-C. ve Tseng, C.-L. (2012). Forecasting of CO2 emissions, energy consumption and economic growth in China using an improved grey model. Energy, 40​(1), 400–409. https://doi.org/10.1016/j.energy.2012.01.037
  • Rizk-Allah, R. M., Hassanien, A. E., Elhoseny, M. ve Gunasekaran, M. (2019). A new binary salp swarm algorithm: Development and application for optimization tasks. Neural Computing and Applications, 31​(5, 5), 1641–1663. https://doi.org/10.1007/s00521-018-3613-z
  • Tien, T.-L. (2009). A new grey prediction model FGM(1, 1). Mathematical and Computer Modelling, 49​(7, 7), 1416–1426. https://doi.org/10.1016/j.mcm.2008.11.015
  • Wang, Z.-X., Li, Q. ve Pei, L.-L. (2018). A seasonal GM(1,1) model for forecasting the electricity consumption of the primary economic sectors. Energy, 154, 522–534. https://doi.org/10.1016/j.energy.2018.04.155
  • Wu, L., Liu, S., Yao, L., Yan, S. ve Liu, D. (2013). Grey system model with the fractional order accumulation. Communications in Nonlinear Science and Numerical Simulation, 18​(7), 1775–1785. https://doi.org/10.1016/j.cnsns.2012.11.017
  • Wu, W.-Z., Zhang, T. ve Zheng, C. (2019). A Novel Optimized Nonlinear Grey Bernoulli Model for Forecasting China’s GDP. Complexity, 2019, e1731262. https://doi.org/10.1155/2019/1731262
  • Xia, M. ve Wong, W. K. (2014). A seasonal discrete grey forecasting model for fashion retailing. Knowledge-Based Systems, 57, 119–126. https://doi.org/10.1016/j.knosys.2013.12.014
  • Xie, N.-m. ve Liu, S.-f. (2009). Discrete grey forecasting model and its optimization. Applied Mathematical Modelling, 33​(2), 1173–1186. https://doi.org/10.1016/j.apm.2008.01.011
  • Zhou, J., Fang, R., Li, Y., Zhang, Y. ve Peng, B. (2009). Parameter optimization of nonlinear grey Bernoulli model using particle swarm optimization. Applied Mathematics and Computation, 207​(2), 292–299. https://doi.org/10.1016/j.amc.2008.10.045
There are 24 citations in total.

Details

Primary Language Turkish
Subjects Operation
Journal Section Main Section
Authors

Serkan Taştan 0000-0002-0889-9191

Publication Date April 11, 2023
Published in Issue Year 2023

Cite

APA Taştan, S. (2023). Doğrusal Olmayan Gri Bernoulli Model için Parametre ve Model Yapısı Optimizasyonu. Ankara Hacı Bayram Veli Üniversitesi İktisadi Ve İdari Bilimler Fakültesi Dergisi, 25(1), 77-94. https://doi.org/10.26745/ahbvuibfd.1190046