Gene Expression Programming Solution Space Model Based on Phenotype
The theory of solution space model has practical significance to improve the performance of Gene Expression Programming (GEP) algorithms.There are few studies on the GEP solution space model,and the theoretical research on GEP phenotype is also scarce.To address this problem,a GEP solution space model based on phenotype was proposed.Firstly,by defining the height of GEP chromosome phenotype,a theorem and the proof of the upper bound of single gene chromosome and polygene chromosome manifestation were given.To ensure the boundedness and calculability of the GEP phenotype solution space model,the general formula of height upper bound of GEP chromosome phenotype with the minimum number of operators 1 or 2 was calculated,by using the ability of GEP algorithm to find out the function.Secondly,on basis of the definition for upper bound theorem of GEP phenotype height,the GEP solution space model based on phenotype was constructed,and the properties and theorems ofGEP phenotype solution space model were summarized.By further defining the concept of the complete solution space of the GEP phenotype,the distribution of the optimal solution in the GEP phenotype solution space and the complete solution space were explored.It was found that the optimal solution of the subspace in the complete solution space largely increased in proportion to the order number of subspace.Based on the knowledge of phenotypic spatial model,the basic idea and control strategy of limiting the GEP population search space were put forward,and the effectiveness of various GEP improvement algorithms in the literature was explained by the theories of space model.
gene expression programmingphenotypesymbolic regressionspace model
国家科技期刊平台
NSTL
万方数据
维普
