Design And Application Of Non-equidistant Grey Prediction Evolutionary Algorithm

Prediction-based evolutionary algorithms become an important branch of recently developed meta-heuristics.Hu Zhongbo et al.first proposed a kind of grey prediction evolution algorithm(GPEs)in 2020,using grey prediction models as as a reproduction operator to predict the next generation population.The core of the GPE is derived from an insight that population evolution is guided by the number of iterations of the population sequence as the interval of time series.It has been observed that the quality of a fitness value based on a given task reflects the degree to which the population is optimized in almost any evolutionary process,and it guide the population to move towards promising areas,and the speed of movement is closely related to the speed and direction of evolution.It is reasonable(for the minimization problem)that population evolution is essentially regarded as a process in which fitness values have variable-speed decrease with the increase of the number of iterations.In order to further explore the practical significance of GPEs,this paper improved the non-equidistant grey prediction model,and finally three improved grey prediction evolutionary algorithms are designed.The main research work of this paper is as follows:1.A simplified non-equidistant grey prediction evolution algorithm is proposed(NeGPE-s).Firstly,the interval in the fitting stage of NeGM(1,1)is simplified to an approximately equidistant time interval.To be specific,the unordered non-equidistant original data is transformed into a simplified sequence with the property of an approximate exponential function.Secondly,a simplified reproduction operator which employs a parameter to preserve the non-equidistant nature in the prediction stage of the NeGM(1,1)is developed.Significantly,the necessity and rationality of model simplification process are analyzed in theory.2.Non-equidistant grey prediction evolution algorithm is proposed(NeGPE).NeGPE is derived from an insight that the evolutionary population sequence with the property of variable-speed evolution should be modeled more properly as a non-equidistant time series.Its design is based on an ideological basis that the approximate exponential function trends,which may exist in consecutive populations,can be mined by a nonequidistant grey model(NeGM(1,1))for guiding the current population searches along the evolutionary direction.Consequently,the proposed algorithm is identified by its reproduction operator which is developed by the following two steps.Firstly,NeGM(1,1)based on the average fitness value of each generation population to preserve the nonequidistant nature is modeled.Secondly,the interval in the fitting stage of the NeGM(1,1)is defined as an increasing time interval.To be specific,the unordered non-equidistant original data is transformed into a sequence of increasing intervals with the property of an approximate exponential function.3.A hybrid non-equidistant grey prediction evolution algorithm for PV model parameter identification is proposed(hNeGPE).hNeGPE searches the distance information of vectors in the population to dynamically select suitable propagation operators to dig out the optimal solution of population evolution.The algorithm is developed by combining the following two parts to balance its exploration and development capabilities.Firstly,the non-equidistant model is combined with the average fitness prediction model to predict the evolution trend of mining search population,that is,to maintain the global search ability in the early stage of search.Second,it is based on the DE/current-to-best/1variant to ensure local search capability later in the search.In order to verify the effectiveness of the algorithms designed by the evolutionary properties of the evolved population,the performance of the proposed algorithms are tested on CEC2014,CEC2019,CEC2020 benchmark function sets,practical engineering constraints and photovoltaic model parameter identification problems.The experimental results showed that: 1)NeGPE-s ranks first in CEC2014 and CECE2019 benchmark functions.The proposed algorithm can achieve a better solution with fewer computational overhead than some state-of-the-art algorithms on six engineering constrained design problems.2)The performance of NeGPE is evaluated on CEC2019 and CEC2020 benchmark functions,NeGPE is superior to other more complex and notable approaches,in terms of solving accuracy as well as the rate of convergence.3)The results of extensive comparison with DE,GPE and GPEed show that hNeGPE is superior to the comparison algorithm in solving the problem of PV model parameter identification in terms of accuracy.