Parameter optimization of nonlinear grey Bernoulli model using particle swarm optimization. (English) Zbl 1158.65307
Summary: The nonlinear grey Bernoulli model (NGBM) is a novel grey forecasting model which is a simple modification of the grey model GM(1,1) together with a Bernoulli differential equation. This paper presents a new parameter optimization scheme of NGBM using the particle swarm optimization (PSO) algorithm. The power index of the Bernoulli differential equation and the production coefficient of the background value are considered as decision variables and the forecasting error is taken as the optimization objective.
The parameter optimization of the NGBM is formulated as a combinatorial optimization problem and is solved collectively using the PSO technique. Once the PSO finds the optimal parameters of the NGBM, the model can be optimized. The NGBM with this parameter optimization algorithm is then applied in long-term power load forecasting. Results show that the NGBM has remarkably improved the forecasting accuracy and PSO is an effective global optimization algorithm suitable for the parameter optimization of NGBM.
The parameter optimization of the NGBM is formulated as a combinatorial optimization problem and is solved collectively using the PSO technique. Once the PSO finds the optimal parameters of the NGBM, the model can be optimized. The NGBM with this parameter optimization algorithm is then applied in long-term power load forecasting. Results show that the NGBM has remarkably improved the forecasting accuracy and PSO is an effective global optimization algorithm suitable for the parameter optimization of NGBM.
MSC:
| 65C60 | Computational problems in statistics (MSC2010) |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62M20 | Inference from stochastic processes and prediction |
| 90C15 | Stochastic programming |
| 90C27 | Combinatorial optimization |
| 90C59 | Approximation methods and heuristics in mathematical programming |
Keywords:
nonlinear grey Bernoulli model; parameter optimization; particle swarm optimization; long-term load forecasting; time series; numerical examples; prediction; combinatorial optimizationReferences:
| [1] | Deng, J. L., Introduction of grey system, J. Grey Syst., 1, 1, 1-24 (1989) · Zbl 0701.90057 |
| [2] | Deng, J. L., The Primary Methods of Grey System Theory (2005), Huazhong University of Science and Technology Press: Huazhong University of Science and Technology Press Wuhan, (in Chinese) |
| [3] | Yu, P. S.; Chen, C. J., Applicaiton of grey and fuzzy methods for rainfall forecasting, J. Hydrol. Eng., 5, 4, 339-345 (2000) |
| [4] | Lin, C. T.; Yang, S. Y., Forecast of the output value of Taiwan’s optoelectronics industry using the grey forecasting model, Technol. Forecast. Soc. Change, 70, 2, 177-186 (2003) |
| [5] | Yao, A. W.L.; Chi, S. C.; Chen, J. H., An improved grey-based approach for electricity demand forecasting, Elec. Power Syst. Res., 67, 3, 217-224 (2003) |
| [6] | Wang, Y. F., Predicting stock price using fuzzy grey prediction system, Expert Syst. Appl., 22, 1, 33-39 (2002) |
| [7] | Yao, A. W.L.; Chi, S. C., Analysis and design of a Taguchi-Grey based electricity demand predictor for energy management systems, Energy Convers. Manage., 45, 7-8, 1205-1217 (2004) |
| [8] | Yong, H., A new forecasting model for agricultural commodities, J. Agric. Eng. Res., 60, 227-235 (1995) |
| [9] | Tan, C. L.; Chang, S. P., Residual correction method of Fourier series to GM(1,1) model, Proc. of the First National Conf on Grey Theory and Applications, Kauhsiung, Taiwan, 93-101 (1996) |
| [10] | Tan, C. L.; Lu, B. F., Grey Markov chain forecasting model, Proc. of the First National Conf on Grey Theory and Applications, Kauhsiung, Taiwan, 157-162 (1996) |
| [11] | Hsu, Y. T.; Cheng, C. S.; Wu, C. C., Grey modeling using neural network, J. Grey Syst., 9, 3, 219-232 (1997) |
| [12] | Chen, C. K.; Tien, T. L., The indirect measurement of tensile strength by the deterministic grey dynamic model DGDM(1,1,1), Int. J. Syst. Sci., 28, 7, 683-690 (1997) · Zbl 0875.93031 |
| [13] | Chen, C. I.; Chen, H. L.; Chen, S. P., Forecasting of foreign exchange rates of Taiwan’s major trading partners by novel nonlinear grey Bernoulli model NGBM(1,1), Commun. Nonlinear Sci. Numer. Simul., 13, 6, 1194-1204 (2008) |
| [14] | Chen, C. I., Application of the novel nonlinear grey Bernoulli model for forecasting unemployment rate, Chaos Soliton Fract., 37, 1, 278-287 (2008) · Zbl 1390.91253 |
| [15] | Kennedy, J.; Eberhart, R. C., Particle swarm optimization, Proc. IEEE Int Conf on Neural Networks, Piscataway, NJ, 1942-1948 (1995) |
| [16] | Eberhart, R. C.; Kennedy, J., A new optimizer using particle swarm theory, Proc. 6th Int Symposium on Micro Machine and Human Science, Nagoya, Japan, 39-43 (1995) |
| [17] | Liu, S. F.; Dang, Y. G.; Fang, Z. G., The Theory of Grey System and its Applications (2004), Science Press: Science Press Beijing, (in Chinese) |
| [18] | Shi, Y.; Eberhart, R. C., Empirical study of particle swarm optimization, Proc. of the Congress on Evolutionary Computation, 1945-1950 (1999) |
| [19] | Boeringer, D. W.; Werner, D. H., Particle swarm optimization versus genetic algorithms for phased array synthesis, IEEE Trans. Antennas Propagat., 52, 771-779 (2004) |
| [20] | Zhuang, H. Y., Mechanism and application of GM(1,1) and improvement methods, Syst. Eng. Theor. Methodol. Appl., 2, 3, 56-62 (1993), (in Chinese) |
| [21] | Chang, S. C.; Lai, H. C.; Yu, H. C., A variable \(P\) value rolling grey forecasting model for Taiwan semiconductor industry production, Technol. Forecast Social Change, 72, 5, 623-640 (2005) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
