Application of Grammatical Swarm to Symbolic Regression Problem

Abstract

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.