The Estimation Of Fractional Grey Models Driven By Gravitational Search Algorithm

Since the grey model was proposed,it has been attached more importance by scholars in the fields of fitting and forecasting with limited data.Fractional accumulated generating operator(FAGO)has been one of effective methods to optimize the grey model due to the high performance of fitting and forecasting.However,using FAGO to improve the accuracy of the existing grey model is one of difficulties in research.Therefore,in this paper,it combines FAGO to expand a series of grey models to enhance the accuracy.Moreover,it firstly chooses gravitational search algorithm(GSA)to estimate the parameters of fractional grey models.The main context and results in this paper are organized as follows:Firstly,we analyze the stability of the classical grey model GM(1,1)and the fractional accumulated grey model of its variant.Comparing their the perturbation bound of the grey parameters solution by the matrix perturbation lemma is to determine which model is more stable.The results show that the stability of the fractional accumulated model is better than the classical grey model GM(1,1)with the same perturbations.Secondly,we promote the existing integer rolling grey parameter model by two different methods.One is to combine the rolling mechanism and the fractional accumulated grey model to propose fractional rolling grey accumulated model.Due to the GSA's characteristic that is more suitable for high-dimensional optimization problems,the other is expanding directly the integer-order rolling grey parameter model to the fractional rolling grey parameter model to extend the dimension of the objective function to be two.Numerical simulations show that comparing the existing results,the accuracy of fractional rolling grey accumulated model and the fractional rolling grey parameter model are higher.Moreover,compared the GSA with the PSO algorithm in the grey model estimation,GSA has a good application for the grey model estimation.Finally,the integer-order time sequence variation regression grey model is improved.Fractional grey model GSA-TSGM(1,1)with time sequence variation regression driven by GSA is proposed by expanding the one-order accumulated operator in the original model.Numerical simulations show that the errors in the simulation of the time sequence variation regression grey model in[???,???.????.2011]are corrected at first.Then the forecasting accuracy of the novel model has higher prediction accuracy in multiple point's prediction.In conclusion,firstly,the GSA is feasible in the estimation of the fractional grey model,and it can provide guidance for the GSA to estimate the fractional grey model.Secondly,through utilizing the FAGO into the existing a series of grey models improves the accuracy of the existing grey model.Therefore,this paper extends the grey forecasting model and enriches the existing grey theory.