Hideyuki Sugiura

Grammatical Evolution Using Tree Representation Learning

Grammatical evolution (GE) is one of the evolutionary computations, which evolves genotype to map phenotype by using the Backus-Naur Form (BNF) syntax. GE has been widely employed to represent syntactic structure of a function or a program in order to satisfy the design objective. As the GE decoding process parses the genotype chromosome into array or list structures with left-order traversal, encoding process could change gene codons or orders after genetic operations. For improving this issue, this paper proposes a novel GE algorithm using tree representation learning (GETRL) and presents three contributions to the original GE, genetic algorithm (GA) and genetic programming (GP). Firstly, GETRL uses a tree-based structure to represent the functions and programs for practical problems. To be different from the traditional GA, GETRL adopts a genotype-to-phenotype encoding process, which transforms the genes structures for tree traversal. Secondly, a pointer allocation mechanism is introduced in this method, which allows the GETRL to pursue the genetic operations like typical GAs. To compare with the typical GP, however GETRL still generates a tree structure, our method adopts a phenotype-to-genotype decoding process, which allows the genetic operations be able to be apply into tree-based structure. Thirdly, due to each codon in GE has different expression meaning, genetic operations are quite different from GAs, in which all codons have the same meaning. In this study, we also suggest a multi-chromosome system and apply it into GETRL, which can prevent from overriding the codons for different objectives.

Application of Grammatical Swarm to Symbolic Regression Problem

Grammatical Swarm (GS), which is one of the evolutionary computations, is designed to find the function, the program or the program segment satisfying the design objective. Since the candidate solutions are defined as the bit-strings, the use of the translation rules translates the bit-strings into the function or the program. The swarm of particles is evolved according to Particle Swarm Optimization (PSO) in order to find the better solution. The aim of this study is to improve the convergence property of GS by changing the traditional PSO in GS with the other PSOs such as Particle Swarm Optimization with constriction factor, Union of Global and Local Particle Swarm Optimizations, Comprehensive Learning Particle Swarm Optimization, Particle Swarm Optimization with Second Global best Particle and Particle Swarm Optimization with Second Personal best Particle. The improved GS algorithms, therefore, are named as Grammatical Swarm with constriction factor (GS-cf), Union of Global and Local Grammatical Swarm (UGS), Comprehensive Learning Grammatical Swarm (CLGS), Grammatical Swarm with Second Global best Particle (SG-GS) and Grammatical Swarm with Second Personal best Particle (SG-GS), respectively. Symbolic regression problem is considered as the numerical example. The original GS is compared with the other algorithms. The effect of the model parameters for the convergence properties of the algorithms are discussed in the preliminary experiments. Then, except for CLGS and UGS, the convergence speeds of the other algorithms are faster than that of the original GS. Especially, the convergence properties of GS-cf and SP-GS are fastest among them.

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

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.