In this case the true underlying function HyGP had to approximate is the 2D Kotanchek function (Korns 2011):
BUILDING DATA SET:
300-point Optimal Latin Hypercube DoE in [-50, 50] x [-50, 50] x [-50, 50] x [-50, 50]
VALIDATION DATA SET:
4096-point Full Factorial DoE [-50: 14.28 : 50] x [-50: 14.28 : 50] x [-50: 14.28 : 50] x [-50: 14.28 : 50]
Population size: 400
Primitives: +, -, *, / (protected), ^2, ^3, sin, cos, tanh, exp, log
Using editing and factorisation bonus, the best model returned by HyGP is:
resulting in a coefficient of determination =0.99974, max abs error = 0.28575 on the validation data set.
- M. F. Korns. Accuracy in symbolic regression. In R. Riolo, E. Vladislavleva, and J. H. Moore, editors, Genetic Programming Theory and Practice IX, Genetic and Evolutionary Computation. Springer New York, 2011.
- See also gpBenchmark page reporting a collection of challenging symbolic regression problems for GP, among which “Korn P10” was chosen (section “Difficult synthetic symbolic regression problems”):