## Penalty Functions for Genetic Programming Algorithms

Talk Layout. 1 The Symbolic Regression Problem. 2 Model Selection. 3 Experimental Results. C.E. Borges. Penalty Functions for Genetic Programming Algorithms. 2/12 ...
Penalty Functions for Genetic Programming Algorithms José L. Montaña,1 César L. Alonso,2 Cruz E. Borges,1 and Javier de la Dehesa.1 [email protected], [email protected], [email protected], [email protected] Dept. Matemáticas, Estadística y Computación1

Centro de Inteligencia Artificial2

11th ICCSA 2011, 20-23 June 2011, Santander, Spain.

Talk Layout

C.E. Borges

1

The Symbolic Regression Problem

2

Model Selection

3

Experimental Results

Penalty Functions for Genetic Programming Algorithms

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Talk Layout

C.E. Borges

1

The Symbolic Regression Problem

2

Model Selection

3

Experimental Results

Penalty Functions for Genetic Programming Algorithms

2/12

Talk Layout

C.E. Borges

1

The Symbolic Regression Problem

2

Model Selection

3

Experimental Results

Penalty Functions for Genetic Programming Algorithms

2/12

Regression Problems. Regressions Problems. Given a set of points and a space of functions, find the best function that fits the set of points. f (x)

f (x)

x x1 x2 x3 4

x0

x5

x7

x8 x x10 9

x6

x C.E. Borges

Penalty Functions for Genetic Programming Algorithms

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Regression Problems. Regressions Problems. Given a set of points and a space of functions, find the best function that fits the set of points. f (x)

g(x)

x C.E. Borges

Penalty Functions for Genetic Programming Algorithms

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How we solve it?

When the Function Set. . . is Known: Interpolation, Least Squares. is Unknown: Symbolic Regression.

C.E. Borges

Penalty Functions for Genetic Programming Algorithms

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How we solve it?

When the Function Set. . . is Known: Interpolation, Least Squares. is Unknown: Symbolic Regression.

C.E. Borges

Penalty Functions for Genetic Programming Algorithms

4/12

How we solve it?

When the Function Set. . . is Known: Interpolation, Least Squares. is Unknown: Symbolic Regression.

C.E. Borges

Penalty Functions for Genetic Programming Algorithms

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Symbolic Regression Problems

Symbolic Regression. Looks for a symbolic expression of the regressor. Looks for a computer program that evaluate the regressor. Genetic Programming.

C.E. Borges

Penalty Functions for Genetic Programming Algorithms

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Symbolic Regression Problems

Symbolic Regression. Looks for a symbolic expression of the regressor. Looks for a computer program that evaluate the regressor. Genetic Programming.

C.E. Borges

Penalty Functions for Genetic Programming Algorithms

5/12

Symbolic Regression Problems

Symbolic Regression. Looks for a symbolic expression of the regressor. Looks for a computer program that evaluate the regressor. Genetic Programming.

C.E. Borges

Penalty Functions for Genetic Programming Algorithms

5/12

Genetic Programming with Trees.

Figure: Example of a computer program, encoded as a tree, that evaluate the function f := x 4 + x 3 + x 2 + x.

f ≡

+ +

+ ∗ ∗

x x

∗ x

x x

C.E. Borges

∗ x

x