Abstract
The problem of the creation of numerical constants has haunted the Genetic Programming (GP) community for a long time and is still considered one of the principal open research issues. Many problems tackled by GP include finding mathematical formulas, which often contain numerical constants. It is, however, a great challenge for GP to create highly accurate constants as their values are normally continuous, while GP is intrinsically suited for combinatorial optimization. The prevailing attempts to resolve this issue either employ separate real-valued local optimizers or special numeric mutations. While the former yield better accuracy than the latter, they add to implementation complexity and significantly increase computational cost. In this paper, we propose a special numeric crossover operator for use with Robust Gene Expression Programming (RGEP). RGEP is a type of genotype/phenotype evolutionary algorithm closely related to GP, but employing linear chromosomes. Using normalized least squares error as a fitness measure, we show that the proposed operator is significantly better in finding highly accurate solutions than the existing numeric mutation operators on several symbolic regression problems. Another two important advantages of the proposed operator are that it is extremely simple to implement, and it comes at no additional computational cost. The latter is true because the operator is integrated into an existing crossover operator and does not call for an additional cost function evaluation.
Highlights
Gene Expression Programming (GEP) [1] is a relatively new, but established type of genotype/phenotype evolutionary algorithm closely related to Genetic Algorithms (GA) and GeneticProgramming (GP)
Using normalized least squares error as a fitness measure, we show that the proposed operator is significantly better in finding highly accurate solutions than the existing numeric mutation operators on several symbolic regression problems
The elementary difference between GA, Genetic Programming (GP) and GEP lies in the nature of the encoding of individuals: the individuals in GAs are encoded as linear strings of fixed length; the individuals in
Summary
Gene Expression Programming (GEP) [1] is a relatively new, but established type of genotype/phenotype evolutionary algorithm closely related to Genetic Algorithms (GA) and GeneticProgramming (GP). Gene Expression Programming (GEP) [1] is a relatively new, but established type of genotype/phenotype evolutionary algorithm closely related to Genetic Algorithms (GA) and Genetic. GEP can be used to solve different problems through the evolution of computer programs (phenotype), which are encoded in the form of linear gene expression strings (or chromosomes) of fixed length (genotype). GEP is considered an effective tool for searching for programs to solve real-world problems from many fields of science and engineering. These include, but are not limited to, data mining, time series prediction, classification and regression problems and knowledge discovery These include, but are not limited to, data mining, time series prediction, classification and regression problems and knowledge discovery (see, for example, ref. [2] and the references therein)
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