Evolving Simple Symbolic Regression Models 11
Ta b l e 3 Performance of the best models of each algorithm variant in terms of the
NMSE on the training and test partition and the model length as well as the minimal
model length to solve the problem optimally (bold font)
Training Test Length
Median IQR Median IQR Median IQR
ProblemF 1 18 : 00
GP Length 20 0.001 0.027 0.002 0.031 23:50 1:00
GP Length 50 0.002 0.207 0.002 0.323 51:00 6:00
GP Length 100 0.023 0.209 0.092 0.533 100:50 11:50
NSGA-II Complexity 0.000 0.001 0.001 0.001 27:00 18:50
NSGA-II Visitation Length 0.029 0.246 0.034 0.336 27:00 38:00
NSGA-II Tree Size 0.043 0.199 0.050 0.357 33:00 45:25
NSGA-II Variables 0.165 0.171 0.418 0.504 102:00 8:25
ProblemF 2 18 : 00
GP Length 20 0.000 0.000 0.000 0.000 23:00 1:00
GP Length 50 0.000 0.007 0.000 0.006 52:00 2:00
GP Length 100 0.039 0.418 0.053 0.951 100:00 6:50
NSGA-II Complexity 0.001 0.093 0.001 0.114 32:50 28:25
NSGA-II Visitation Length 0.001 0.001 0.001 0.001 29:50 14:75
NSGA-II Tree Size 0.001 0.001 0.001 0.001 24:00 10:75
NSGA-II Variables 0.001 0.004 0.001 0.006 70:00 45:50
ProblemF 3 20 : 00
GP Length 20 0.005 0.008 0.008 0.016 24:00 1:00
GP Length 50 0.002 0.006 0.006 0.015 52:00 7:75
GP Length 100 0.003 0.101 0.009 0.483 101:50 8:00
NSGA-II Complexity 0.004 0.011 0.006 0.021 31:50 24:50
NSGA-II Visitation Length 0.005 0.019 0.008 0.047 31:00 18:25
NSGA-II Tree Size 0.003 0.011 0.006 0.025 30:50 18:75
NSGA-II Variables 0.051 0.141 0.188 0.557 99:00 27:00
ProblemF 4 11 : 00
GP Length 20 0.000 0.000 0.000 0.052 23:00 2:00
GP Length 50 0.000 0.210 0.042 0.452 51:00 7:00
GP Length 100 0.076 0.354 0.225 0.632 99:00 10:00
NSGA-II Complexity 0.000 0.000 0.010 0.040 11:00 3:00
NSGA-II Visitation Length 0.000 0.000 0.009 0.011 11:00 0:00
NSGA-II Tree Size 0.000 0.000 0.009 0.013 11:00 0:00
NSGA-II Variables 0.000 0.000 0.014 0.014 22:00 19:50
ProblemF 5 12 : 00
GP Length 20 0.025 0.033 0.041 0.045 23:50 2:00
GP Length 50 0.029 0.032 0.046 0.279 52:00 3:00
GP Length 100 0.055 0.112 0.846 8.233 98:00 10:00
NSGA-II Complexity 0.021 0.033 0.042 0.044 22:00 15:25
NSGA-II Visitation Length 0.025 0.033 0.041 0.045 21:00 8:00
NSGA-II Tree Size 0.029 0.033 0.041 0.044 18:50 8:00
NSGA-II Variables 0.034 0.071 0.154 1.065 80:00 60:25