Using Genetic Programming to Obtain a Closed-Form Approximation to a Recursive Function

Abstract

We demonstrate a fully automated method for obtaining a closedform approximation of a recursive function. This method resulted from a realworld problem in which we had a detector that monitors a time series and where we needed an indication of the total number of false positives expected over a fixed amount of time. The problem, because of the constraints on the available measurements on the detector, was formulated as a recursion, and conventional methods for solving the recursion failed to yield a closed form or a closed-form approximation. We demonstrate the use of genetic programming to rapidly obtain a high-accuracy approximation with minimal assumptions about the expected solution and without a need to specify problem-specific parameterizations. We analyze both the solution and the evolutionary process. This novel application shows a promising way of using genetic programming to solve recurrences in practical settings.