Title: Grammatical evolution using two-dimensional gene for symbolic regression: an advanced improvement with conditional statement grammar

Authors: Hideyuki Sugiura; Masahiro Nagao; Yi Zuo; Eisuke Kita

Addresses: Graduate School of Information Sciences, Nagoya University, Nagoya 464-8601, Japan ' Graduate School of Environmental Sciences, Nagoya University, Nagoya 464-8601, Japan ' Institute of Innovation for Future Society, Nagoya University, Nagoya 464-8601, Japan ' Graduate School of Information Sciences, Nagoya University, Nagoya 464-8601, Japan

Abstract: Symbolic regression problems can be solved using grammatical evolution (GE), an evolutionary computation (EC) method, to find a function that coincides satisfactorily with the given datasets. The evolutional approach of GE is based on the grammar learning paradigm, which can translate the genotype (binary digit) into the phenotype (terminals and non-terminals). Unlike traditional codons in a genotype, the fittest codons in phenotype represented by the Backus-Naur form (BNF) are difficult for next generation genes to inherit the traits of parents, accounting for crossover and mutation. For this issue, this article presents a proposal of an advanced improvement to GE using a two-dimensional gene (GE2DG). In contrast to multi-chromosomal GE (GEMC), our proposal not only encloses the two-dimensional gene-expression for symbolic regression, but also introduces one independent gene defined as a conditional statement to express a new BNF grammar of an if-then (-else) branch. In the experiments described herein, continuous/discontinuous non-branch functions and continuous/discontinuous branch functions, four testing patterns, are considered as numerical examples. Results show that GE2DG has better performance than the original GE or GEMC. Especially for the case of branch functions, GE with hybrid chromosome (GEHC), where GE2DG is incorporated with GEMC, has faster convergence in symbolic regression than other methods.

Keywords: symbolic regression; grammatical evolution; multi chromosome; hybrid chromosome; conditional statement grammar.

DOI: 10.1504/IJCISTUDIES.2016.083572

International Journal of Computational Intelligence Studies, 2016 Vol.5 No.3/4, pp.237 - 251

Received: 31 Aug 2015
Accepted: 09 Jan 2016

Published online: 06 Apr 2017 *

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