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Creation of Numerical Constants in Robust Gene Expression Programming

University of Ljubljana, Faculty of Electrical Engineering, Tržaška 25, 1000 Ljubljana, Slovenia
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Entropy 2018, 20(10), 756; https://doi.org/10.3390/e20100756
Received: 23 August 2018 / Revised: 24 September 2018 / Accepted: 29 September 2018 / Published: 1 October 2018
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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. View Full-Text
Keywords: genetic programming; gene expression programming; genetic algorithms; genotype/phenotype evolutionary algorithms; symbolic regression; constant creation; ephemeral random constants; numeric mutation; numeric crossover; digit-wise crossover genetic programming; gene expression programming; genetic algorithms; genotype/phenotype evolutionary algorithms; symbolic regression; constant creation; ephemeral random constants; numeric mutation; numeric crossover; digit-wise crossover
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Fajfar, I.; Tuma, T. Creation of Numerical Constants in Robust Gene Expression Programming. Entropy 2018, 20, 756.

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