Solution Modeling Using Postfix Genetic Programming

This article introduces Postfix Genetic Programming (GP), a postfix notation-based GP, approach to symbolic regression for solving empirical modeling problems. The main features of Postfix-GP are presented. These features include (1) postfix-based, variable-length individual-representation and its stack-based evaluation and (2) subtree crossover operator and semantic-aware subtree crossover operator. The article also presents two different constant creation approaches to evolve useful numeric constants for symbolic regression problems. The first approach uses an explicit list of constants and the second allows the Postfix-GP algorithm to evolve constants. Use of Postfix-GP as a solution modeling tool is demonstrated by solving two function identification problems and two deterministic chaotic time series modeling problems. Effectiveness of the evolved models is tested by statistically analyzing their performance on training and out-of-sample datasets of the problems. Experimental results on test problems suggest that Postfix-GP offers a new possibility for solving empirical modeling problems. We also compared the performance of Postfix-GP with the lil-GP system for all four problems. The results suggest that the quality of solutions found by Postfix-GP was better than that found by lil-GP, for the tested problems.