RatPol2D

In this case the true underlying function HyGP had to approximate is the 2D RatPol2D function (Keijzer 2003):

f(z_{1}, z_{2}) = \dfrac{(z_{1}-3)^4 + (z_{2}-3)^3 - (z_{2}-3)}{(z_{2}-2)^4 + 10}

RatPol2D_3D

BUILDING DATA SET:
40-point Optimal Latin hypercube DoE in [0 , 6.0] x [0 , 6.0]
Available here: ratpol2d_input_file

RatPol2D_2D_points_png
VALIDATION DATA SET:
1156-point Full Factorial DoE  [-0.25: 0.2 : 6.35] x [-0.25: 0.2 : 6.35]
Available here: ratpol2d_test_dataset

HyGP hyperparameters (see ratpol2d_input_file):
Population size: 200
Generations: 50
Primitives: +, -, *, / (protected), ^2, ^3, sin, cos, exp, reciprocal

Results:
Using the editing strategy (Ed2) and factorisation bonus, the best model returned by HyGP was:

\tilde{f}(z_{1},z_{2}) = -0.352041 + \dfrac{532.069 - 72.9607\, \mathrm{z_{2}}}  {  (598.117 / (52.1197 + 8.27273 \mathrm{z_{1}}\, \mathrm{z_{1}} -49.3048\, \mathrm{z_{1}} -5.24910\,\mathrm{z_{2}}\mathrm{z_{2}} + 27.3669\, \mathrm{z_{2}}))^2}

resulting in a coefficient of determination R^2 = 0.95361 and max abs error = 3.60808 on the validation data set.

wp_RatPol2D_fact_edit_best
Ratpol2D function (black) and model generated by HyGP (red)

 

ratpol2d_omegalim_ed2_f_r8g50_build
RatPol2D test function: Actual vs Estimated response returned by HyGP best model on building data set
ratpol2d_omegalim_ed2_f_r8g50_test
RatPol2D test function: Actual vs Estimated response returned by HyGP best model on test data set

 

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