C ONSTANTS IN GEP Cndida Ferreira WSC7 2002 Gepsoft A IM Analyse - - PowerPoint PPT Presentation

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F UNCTION F INDING AND THE C REATION OF N UMERICAL C ONSTANTS IN GEP Cndida Ferreira WSC7 2002 Gepsoft A IM Analyse the usefulness of numerical constants in evolutionary computation WSC7 2002 Gepsoft P ROBLEM S UITE (1) SEQUENCE INDUCTION

SLIDE 1

FUNCTION FINDING AND THE CREATION OF NUMERICAL CONSTANTS IN GEP

Cândida Ferreira

WSC7 2002 Gepsoft

SLIDE 2

AIM

Analyse the usefulness of numerical constants in evolutionary computation

WSC7 2002 Gepsoft

SLIDE 3

PROBLEM SUITE (1)

SEQUENCE INDUCTION

WSC7 2002 Gepsoft

Computer generated
Integer constants
1 variable

SLIDE 4

PROBLEM SUITE (2)

V FUNCTION

WSC7 2002 Gepsoft

Computer generated
Rational constants
1 variable

SLIDE 5

PROBLEM SUITE (3)

WOLFER SUNSPOTS

WSC7 2002 Gepsoft

Real-world problem
Rational constants
10 variables

SLIDE 6

RESULTS: Performance (1)

SEQUENCE INDUCTION

WSC7 2002 Gepsoft

With constants Without constants Number of runs 100 100 Number of generations 100 100 Population size 100 100 Average best-of-run fitness 179.827 197.232 Average best-of-run R-square 0.977612 0.999345 Success rate 16% 81%

SLIDE 7

RESULTS: Performance (2)

V FUNCTION

WSC7 2002 Gepsoft

With constants Without constants Number of runs 100 100 Number of generations 5000 5000 Population size 100 100 Average best-of-run fitness 1914.8 1931.84 Average best-of-run R-square 0.957255 0.995340

SLIDE 8

RESULTS: Performance (3)

WOLFER SUNSPOTS

WSC7 2002 Gepsoft

With constants Without constants Number of runs 100 100 Number of generations 5000 5000 Population size 100 100 Average best-of-run fitness 86215.27 89033.29 Average best-of-run R-square 0.713365 0.811863

SLIDE 9

RESULTS: Best evolved models (1)

SEQUENCE INDUCTION

WSC7 2002 Gepsoft

With constants Without constants

R-square: 1 R-square: 1

1 2 3 4 5

2 3 4

+ + + + = a a a a y 1 2 3 4 5

2 3 4

+ + + + = a a a a y

SLIDE 10

RESULTS: Best evolved models (2)

V FUNCTION

WSC7 2002 Gepsoft

With constants Without constants

R-square: 0.9999313

( )

[ ] [ ]

( ) ( )

[ ] [

] [

]

2 2

1 2 cos cos sin 2 10 2 ln

sin 2 sin 2 a a a a a

e e e e a a a a a y + + + + + + + + + + =

R-square: 0.99997001

( )

[ ]

( )

[ ] [ ] [ ] [ ]

a a a a

e e a a y + + + − + + + =

981 . 3 929 . 27278 . 1 sin 2

45714 . 2 80112 . 2 77631 . 10 10 99782 . ln

SLIDE 11

RESULTS: Best evolved models (3)

WOLFER SUNSPOTS

WSC7 2002 Gepsoft

With constants Without constants

R-square: 0.833714 R-square: 0.882831

j i j j e c g b a j i h j y + + + + + + + + + + =

2 2 2

903 . 1 847 . 995 . 2

i a ij bj d e b j i d j y 2 3 + − + + + + − + =

SLIDE 12

CONCLUSIONS

The use of numerical constants results in:

WSC7 2002 Gepsoft

worse performance
more complex implementation
worse evolution
more CPU time