In this case the true underlying function HyGP had to approximate is the 2D Hock function (Hock and Schittkowski 1981):
BUILDING DATA SET:
20-point Optimal Latin Hypercube DoE in [0, 5] x [0, 5]
VALIDATION DATA SET:
441-point Full Factorial DoE [-0.5: 0.3 : 5.5] x [-0.5: 0.3 : 5.5]
Population size: 200
Primitives: +, -, *, / (protected), ^2, ^3, sin, cos, exp
The best model returned by HyGP was:
which corresponds to a coefficient of determination = 0.97672 on the validation data set.
- W. Hock and K. Schittkowski. Test examples for nonlinear programming codes. Lecture notes in economics and mathematical systems, 187, 1981. http://www.klaus-schittkowski.de.