Semantic Sub-tree Crossover Operator for Postfix Genetic Programming

Abstract

Design of crossover operator plays a crucial role in Genetic Programming (GP). The most studied issues related to crossover operator in GP are: (1) ensuring that crossover operator always produces syntactically valid individuals (2) improving search efficiency of crossover operator. These issues become crucial when the individuals are represented using linear string representation. This paper aims to introduce postfix GP approach to symbolic regression for solving empirical modeling problems. The main contribution includes (1) a linear string (postfix notation) based genome representation method and stack based evaluation to reduce space–time complexity of GP algorithm (2) ensuring that sub-tree crossover operator always produces syntactically valid genomes in linear string representation (3) using semantic information of sub-trees, to be swapped, while designing crossover operator for linear genome representation to provide additional search guidance. The proposed method is tested on two real valued symbolic regression problems. Two different constant creation techniques for Postfix GP, one that explicitly use list of constants and another without use of the list, are presented to evolve useful numeric constants for symbolic regression problems. The results on tested problems show that postfix GP comprised of semantic sub-tree crossover offers a new possibility for efficiently solving empirical modeling problems.KeywordsPostfix genetic programmingSymbolic regressionEmpirical modelingSemantic sub-tree crossover operator