Salustowicz

The true underlying function HyGP had to approximate is the 1D Salustowicz function (Keijzer 2003):

f(z) = e^{-z}z^{3}cos(z)sin(z)\left[cos(z)sin^{2}(z)-1\right]

BUILDING DATA SET:
100-point Full Factorial DoE  [0.05: 0.1 : 9.95]
Available here: salustowicz_input_file

VALIDATION DATA SET:
221-point Full Factorial DoE  [-0.5: 0.05: 10.5]
Available here: salustowicz_test_dataset

HyGP hyperparameters (see salustowicz_input_file):
Population size: 300
Generations: 50
Primitives: +, -, *, / (protected), ^2, sin, cos, exp

Results:
the best model returned by HyGP is:

(3.08033e-02 + ((6.97248e+01 * (sin((1.28692e+02 * (Z1 / -6.46544e+01))))) / ((3.90905e+02 * (exp((4.70162e+01 * (Z1 / 1.69200e+02))))) + (-2.74363e+02 * Z1))))

evolved using Ed3 editing strategy.

salustowicz_m300_g50_ed3_2runs_2_r2g50
Salustowicz function (black) and HyGP-evolved model (red). The red dots represent the points of the building dataset

Performance on validation data set:
R2 = 0.9566407
max abs error = 0.1704543

salustowicz_m300_g50_ed3_2runs_2_r2g50_build

salustowicz_m300_g50_ed3_2runs_2_r2g50_val
Estimated vs Actual response plot of the evolved model on building data set (top) and validation data set (bottom)

 

 

 

References:

  • M. Keijzer. Improving symbolic regression with interval arithmetic and linear scaling. In C. Ryan, T. Soule, M. Keijzer, E. Tsang, R. Poli, and E. Costa, editors, Proceedings of EuroGP 2003, volume 2610 of LNCS, pages 70–82. Springer-Verlag, 2003.
Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s