Research On Symbolic Regression And Evolution Algorithm Based On Machine Learning

As a substantial method in regression analysis,symbolic regression searches the mathematical expression that can fit a given data set in the space of mathematical expressions.Genetic Programming(GP)is a common algorithm to solve the problem of symbolic regression.However,it has two following drawbacks:(1)The problem of population initialization: the efficiency of searching results is low as GP can not create individuals according to the characteristic of the data set;(2)The problem of local optimal: GP traps in the local optimal solution as the algorithm does not memorize the spatial distribution of the search space during searching.To address two above problems,this thesis presents Genetic Programming with Machine Learning(GPML),a novel GP algorithm based on machine learning.GPML can not only generate the initial population according to the characteristics of the data set,but also can adjust the strategy of the mutation according to the spatial distribution of the population,thus yielding a more efficient searching of appropriate expressions.For the problem of the population initialization,Deep Learning with Hierarchy Initial Method(DL-HIM)is proposed to create individuals based on the characteristics.This algorithm uses CNN and CNN-RNN to obtain a set of basic mathematical symbols of the initial population,according to different characteristics of the data set.On the basis of this set,a new initialization algorithm HierarchyInit is proposed to generate a sparser population within the search space and closer to the search target.For the problem of local optimal solution,a new mutation algorithm based on DBSCAN is proposed.This algorithm first performs clustering on the population using the DBSCAN algorithm to get the spatial distribution of the population,then adjusts the probability of mutation dynamically and generates new individuals according to the number of clusters and the positions of cluster centers.Compared with the classical GP algorithm,the experimental results indicate that the GPML algorithm features a faster convergence and higher probability to get rid of local optimal solutions.Especially,for target formula without constant,both the accuracy and the efficiency to find the global optimal solution are much higher than that of traditional GP algorithms.