Evolving Simple Symbolic Regression Models 17
Ta b l e 7 Analysis of the functions in the best models in terms of the subtree size
affected by the symbol grouped into three categories (trigonometric: sin;cos;tan—
exponential: exp;log—power:x^2 ;
p
x)
Trigonometric Exponential Power
MedianIQR Median IQR MedianIQR
Breiman
GP Length 20 0:00 2:00 2:00 6:00 0:00 2:75
GP Length 50 21:00 39:25 15:00 23:50 9:50 35:75
GP Length 100 123:00 139:50 87:50 70:50 38:00 82:75
NSGA-II Complexity 0:00 0:00 0:00 0:00 0:00 0:00
NSGA-II Visitation Length 0:00 5:50 10:00 10:00 0:00 0:00
NSGA-II Tree Size 0:00 1:50 8:00 11:00 0:00 4:75
NSGA-II Variables 151:50 182:00 96:50 130:50 79:50 113:00
Friedman
GP Length 20 4:50 5:50 0:00 2:75 3:00 7:00
GP Length 50 44:00 41:25 8:50 20:50 9:00 30:00
GP Length 100 127:00 106:25 42:50 69:00 38:50 71:25
NSGA-II Complexity 2:00 8:25 0:00 0:00 2:50 7:75
NSGA-II Visitation Length 12:00 29:50 0:00 2:00 2:50 4:00
NSGA-II Tree Size 10:50 19:75 0:00 4:00 2:00 6:75
NSGA-II Variables 214:50 203:75 51:50 81:50 79:00 68:50
Housing
GP Length 20 4:00 4:75 4:00 15:75 0:00 6:00
GP Length 50 19:50 20:50 31:50 53:75 26:00 33:75
GP Length 100 127:00 94:50 111:50 139:75 99:00 148:50
NSGA-II Complexity 2:00 17:50 6:00 12:75 0:00 2:00
NSGA-II Visitation Length 14:50 48:25 16:00 35:75 6:50 14:00
NSGA-II Tree Size 16:50 33:50 29:50 56:00 7:00 36:50
NSGA-II Variables 203:00 179:00 120:00 126:75 109:50 145:00
Chemical
GP Length 20 0:00 2:00 0:00 0:00 0:00 6:00
GP Length 50 12:00 23:25 1:00 8:75 8:00 21:25
GP Length 100 58:00 91:50 24:00 65:75 57:00 68:75
NSGA-II Complexity 0:00 1:50 0:00 0:00 0:00 4:00
NSGA-II Visitation Length 0:00 22:50 0:00 0:00 5:00 51:75
NSGA-II Tree Size 0:00 1:50 0:00 0:00 12:50 36:75
NSGA-II Variables 252:50 256:25 84:00 101:75 149:50 140:00
To w e r
GP Length 20 0:00 3:50 0:00 0:00 0:00 2:00
GP Length 50 14:00 27:00 7:50 20:00 7:50 14:00
GP Length 100 61:50 112:75 42:00 78:25 38:50 92:50
NSGA-II Complexity 0:00 0:00 0:00 0:00 0:00 0:00
NSGA-II Visitation Length 6:00 19:00 2:00 12:50 0:00 4:00
NSGA-II Tree Size 6:00 27:75 3:00 24:50 0:00 7:75
NSGA-II Variables 513:00 442:25 122:50 146:00 109:50 156:75