Geoscience Reference
In-Depth Information
TABLE 8.1
Data Set Used for Developing Solutions 1 and 2
Independent Variables
Dependent
Variable (
V
)
Record
D
0
D
1
D
2
D
3
D
4
1
4
6
8
0
2
3.0
2
6
4
2
7
9
75.0
3
2
5
8
2
6
13.2
4
9
5
2
5
8
62.5
5
3
6
4
7
8
60.5
6
1
5
3
7
9
64.6
7
5
3
6
7
5
37.5
8
2
5
4
6
8
50.5
9
2
5
3
7
8
59.3
Solution 1
:
V =
(
D
1
- D
1)
+
(
D
4
* D
3)
+
((
D
1
* D
0)/
D
2)
(8.2)
Solution 2
:
(
)
43
3
2
)
+
D
D
+
(
)
(
)
(
=
(
(
)
)
VDD
*
DD DDDD
10 3
* −−−
4
4
2
(8.3)
Note that with some simple rearranging and/or removal of redundant components, the solutions are
identical. This is a feature of the simplicity of the problem and may or may not occur when problem
complexity increases:
V
= (
D
4 ×
D
3) + (
D
1 ×
D
0)/
D
2
(8.4)
For more complex problems, the fundamentals of symbolic regression remain the same in that a
multivariate and multifunctional solution is evolved from a data set using a mix of default and user-
defined software settings. Some further examples of software that can be downloaded and used to
experiment with include
•
Eureqa
(http://creativemachines.cornell.edu/eureqa)
•
Open BEAGLE
(http://code.google.com/p/beagle/)
•
DEAP
(http://code.google.com/p/deap/)
•
ECF
(http://gp.zemris.fer.hr/ecf/)
•
ECJ
(http://www.cs.gmu.edu/~eclab/projects/ecj/)
•
EpochX
(http://www.epochx.org/)
•
GenetiK
(http://code.google.com/p/genetik/)
•
GPLAB
(http://gplab.sourceforge.net/)
8.3 GETTING THE MODELLING RIGHT
Despite the prominence of GP, guidelines for the parameterisation and customisation of its models
have only just started to be published (Graff and Poli, 2010). The consequence of not having a com-
mon methodological framework is that some of the key assumptions for applying GP to a problem
are being ignored. For example, before being accepted as valid, potential solutions should be judged
