Application of Symbolic Regression to Unsolved Mathematical Problems

Abstract

This study proposes a method for solving unsolved mathematical games using symbolic regression libraries. We aimed to demonstrate the effectiveness of genetic programming in mathematics in rendering the process of finding formulas more efficient. In the first part of the study, we customized the Python symbolic regression library “gplearn” by adding new features, such as conditional branching. The library uses genetic programming to obtain formulas from data, and we found that the performance of the customized version was better than that of the original. However, the user of this library must be experienced in mathematics to set the conditions for branching. The second part of the study involved the creation of a Swift symbolic regression library using genetic programming. We implemented a new method that combines two criteria for selecting the best formulas: the mean absolute error and the percentage of data described by the formula without error. This new library can discover formulas as good as those discovered using the customized “gplearn” library without requiring specialized knowledge. In some cases, the Swift library discovered formulas that better described the data better than the “gplearn” library.The results of this study suggest the potential for using genetic programming in mathematics and expanding the scope of research on symbolic regression.