The solution of ordinary differential equations using genetic programming with constant tuning

In this paper we report the solution of a benchmark set of ordinary differential equations (ODEs) using genetic programming (GP) within a collocation framework using tuning of the embedded tree constants. We report statistical comparison with a baseline GP approach without constant tuning that indicates that parameter tuning produces statistically superior results. We obtain highly accurate solutions for almost all the benchmark ODEs, but identify a hitherto unreported issue with GP finding trivial solutions. The characteristics of the individual ODEs appear to dictate whether or not solution is problematic.