Evaluating Methods for Constant Optimization of Symbolic Regression Benchmark Problems

Constant optimization in symbolic regression is an important task addressed by several researchers. It has been demonstrated that continuous optimization techniques are adequate to find good values for the constants by minimizing the prediction error. In this paper, we evaluate several continuous optimization methods that can be used to perform constant optimization in symbolic regression. We have selected 14 well-known benchmark problems and tested the performance of diverse optimization methods in finding the expected constant values, assuming that the correct formula has been found. The results show that Levenberg-Marquardt presented the highest success rate among the evaluated methods, followed by Powell's and Nelder-Mead's Simplex. However, two benchmark problems were not solved, and for two other problems the Levenberg-Marquardt was largely outperformed by Nelder-Mead Simplex in terms of success rate. We conclude that even though a symbolic regression technique may find the correct formula, constant optimization may fail, thus, this may also happen during the search for a formula and may guide the method towards the wrong solution. Also, the efficiency of LM in finding high-quality solutions by using only a few function evaluations could serve as inspiration for the development of better symbolic regression methods.