Symbolic regression by uniform random global search

Abstract

Purpose: To compare symbolic regression by genetic programming (SRGP) with symbolic regression by random search (SRRS), a novel method for symbolic regression described herein. Methods: We limit our problem space to N binary trees, m terminals and n functions, then use a dense enumeration of full binary trees to perform uniform random sampling from the set of all permitted equations. We compare a single basic configuration of symbolic regression by genetic programming with symbolic regression by random search using 1000 randomly generated problems. We perform a hyperparameter search with 50 randomly generated symbolic regression problems and 198 randomly generated hyperparameter configurations, examining the performance of SRGP against SRRS. Results: For the single configuration experiment, SRGP outperformed SRRS in 49.0% of problems, random search was best in 26.2% of problems, and there was a tie in 24.8% of problems. Of the cases that were not tied, genetic programming was best in 65.6% of experiments (99% CI, [60.7%, 69.2%]). Of the cases that were not tied in the hyperparameter search, SRGP was best in 44% (99% CI, [41%, 48%]) of cases. The average random configuration of SRGP performs worse than does SRRS. Conclusion: SRGP can outperform SRRS with appropriate hyperparameter selection, but our computations suggest that the average SRGP configuration performs worse than does SRRS.

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