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

F UNCTION F INDING AND THE C REATION OF N UMERICAL C ONSTANTS IN GEP Cândida 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 • Computer generated • Integer constants • 1 variable WSC7 2002 Gepsoft

P ROBLEM S UITE (2) V FUNCTION • Computer generated • Rational constants • 1 variable WSC7 2002 Gepsoft

P ROBLEM S UITE (3) WOLFER SUNSPOTS • Real-world problem • Rational constants • 10 variables WSC7 2002 Gepsoft

R ESULTS: Performance (1) SEQUENCE INDUCTION 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% WSC7 2002 Gepsoft

R ESULTS: Performance (2) V FUNCTION 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 WSC7 2002 Gepsoft

R ESULTS: Performance (3) WOLFER SUNSPOTS 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 WSC7 2002 Gepsoft

R ESULTS: Best evolved models (1) SEQUENCE INDUCTION With constants = + + + + 4 3 2 5 4 3 2 1 y a a a a R-square: 1 Without constants = + + + + 4 3 2 5 4 3 2 1 y a a a a R-square: 1 WSC7 2002 Gepsoft

R ESULTS: Best evolved models (2) V FUNCTION With constants [ ] [ ] [ ] ( ) ( ) = + + + 2 sin 1 . 27278 0 . 929 a a y ln 0 . 99782 a 10 10 [ ] [ ] − + + + 3 0 . 981 a a 0 . 77631 2 . 80112 a 2 . 45714 e e R-square: 0.9999313 Without constants [ ] [ ] ( ) = + + + + + 2 sin a 2 y ln 2 a 10 2 a sin a a [ ] [ ] [ ] ( ( ) ) + + + + + 2 2 sin a a a a cos cos 2 1 a e e e e R-square: 0.99997001 WSC7 2002 Gepsoft

R ESULTS: Best evolved models (3) WOLFER SUNSPOTS With constants + + + 2 2 2 j a b g 1 . 903 j j = + + y + + + + + 2 h i j 0 . 995 0 . 847 c e i j R-square: 0.833714 Without constants − + + − d i 3 j d bj ij = + + y j + + b e a 2 i R-square: 0.882831 WSC7 2002 Gepsoft

C ONCLUSIONS The use of numerical constants results in: • worse performance • more complex implementation • worse evolution • more CPU time WSC7 2002 Gepsoft