Results of the Statistical Study


Table 9: Significant levels, $ \alpha ^*$, of each term of the linear model, determination coefficient $ R^2$, and value of Levene test of the statistical analysis of CIXL2 parameters.
Function $ \mathbf{\alpha^*}$ C $ \mathbf{\alpha^*}$ B $ \mathbf{\alpha^*}$ CB $ \mathbf{R^2}$ $ \mathbf{\alpha^*}$ T. Levene
$ f_{Sph}$ 1.000 1.000 --- --- 0.000
$ f_{SchDS}$ 0.000 0.000 0.000 0.601 0.000
$ f_{Ros}$ 0.005 0.000 0.006 0.526 0.000
$ f_{Ras}$ 0.000 0.000 0.000 0.617 0.000
$ f_{Sch}$ 0.000 0.000 0.000 0.805 0.000
$ f_{Ack}$ 0.095 0.000 0.019 0.083 0.000
$ f_{Gri}$ 0.149 0.001 --- 0.040 0.000
$ f_{Fle}$ 0.410 0.000 --- 0.054 0.003
$ f_{Lan}$ 0.040 0.000 0.024 0.159 0.000



Table 10: Significance level of the crossover operator and determination coefficient $ R^2$ of the linear model, and value of Levene test of the comparative study of the crossovers.
Function $ \mathbf{\alpha^*}$ Crossover $ \mathbf{R^2}$ $ \mathbf{\alpha^*}$ Levene test
$ f_{Sph}$ 0.000 0.779 0.000
$ f_{SchDS}$ 0.000 0.786 0.000
$ f_{Ros}$ 0.573 0.024 0.000
$ f_{Ras}$ 0.000 0.971 0.000
$ f_{Sch}$ 0.000 0.987 0.000
$ f_{Ack}$ 0.000 0.884 0.000
$ f_{Gri}$ 0.000 0.421 0.000
$ f_{Fle}$ 0.000 0.137 0.091
$ f_{Lan}$ 0.000 0.486 0.000



Table 11: Significance level of the evolutionary algorithms and determination coefficient $ R^2$ of the linear model, and value of Levene test of the comparative study betwen CIXL2 and EDAs.
Function $ \mathbf{\alpha^*}$ EA $ \mathbf{R^2}$ $ \mathbf{\alpha^*}$ Levene test
$ f_{SchDS}$ 0.000 0.955 0.000
$ f_{Ros}$ 0.000 0.778 0.000
$ f_{Ras}$ 0.000 0.992 0.000
$ f_{Sch}$ 0.000 0.999 0.000
$ f_{Ack}$ 1.000 0.641 1.000
$ f_{Gri}$ 0.000 0.455 0.000
$ f_{Fle}$ 0.001 0.150 0.000
$ f_{Lan}$ 0.027 0.079 0.000



Table 12: Results for all the functions of the multiple comparison test and the ranking obtained depending on the number of best individuals $ n$.
$ \mathbf{I}$ $ \mathbf{J}$ $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$ $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$ $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$
$ \mathbf{f_{Sph}}$ $ \mathbf{f_{SchDS}}$ $ \mathbf{f_{Ros}}$
5 10 -2.683e-15 0.000 -2.540e-02 0.000 -9.433e-01 0.000
30 -4.144e-11 0.000 -1.899e-01 0.000 -1.486e+00 0.000
60 -1.836e-07 0.000 -2.371e-01 0.000 -1.058e+00 0.000
90 -5.554e-08 0.000 -1.004e+00 0.000 -8.375e-01 0.000
10 5 2.683e-15 0.000 2.540e-02 0.000 9.433e-01 0.000
30 -4.144e-11 0.000 -1.645e-01 0.000 -5.425e-01 0.000
60 -1.836e-07 0.000 -2.117e-01 0.000 -1.142e-01 0.025
90 -5.554e-08 0.000 -9.785e-01 0.000 1.058e-01 0.014
30 5 4.144e-11 0.000 1.899e-01 0.000 1.486e+00 0.000
10 4.144e-11 0.000 1.645e-01 0.000 5.425e-01 0.000
60 -1.835e-07 0.000 -4.720e-02 0.572 4.283e-01 0.000
90 -5.549e-08 0.000 -8.140e-01 0.000 6.483e-01 0.000
60 5 1.836e-07 0.000 2.371e-01 0.000 1.058e+00 0.000
10 1.836e-07 0.000 2.117e-01 0.000 1.142e-01 0.025
30 1.835e-07 0.000 4.720e-02 0.572 -4.283e-01 0.000
90 1.281e-07 0.003 -7.668e-01 0.000 2.200e-01 0.000
90 5 5.554e-08 0.000 1.004e+00 0.000 8.375e-01 0.000
10 5.554e-08 0.000 9.785e-01 0.000 -1.058e-01 0.014
30 5.549e-08 0.000 8.140e-01 0.000 -6.483e-01 0.000
60 -1.281e-07 0.003 7.668e-01 0.000 -2.200e-01 0.000
Ranking $ \mu_{60}>\mu_{90}>\mu_{30}>\mu_{10}>\mu_{5}$ $ \mu_{90}>\mu_{30}>\mu_{10}>\mu_{5}$ $ \mu_{30}>\mu_{60}>\mu_{10}>\mu_{90}>\mu_{5}$
$ \mu_{60}>\mu_{5}$
$ \mathbf{f_{Ras}}$ $ \mathbf{f_{Sch}}$ $ \mathbf{f_{Ack}}$
5 10 -5.79e+00 0.000 -2.691e+02 0.082 -1.063e-07 0.000
30 -6.72e+00 0.000 -7.338e+02 0.000 -2.384e-05 0.000
60 -1.01e+01 0.000 -9.559e+02 0.000 -1.508e-03 0.000
90 -1.51e+01 0.000 -1.148e+03 0.000 -6.769e-02 0.216
10 5 5.79e+00 0.000 2.691e+02 0.082 1.063e-07 0.000
30 -9.31e-01 0.807 -4.647e+02 0.000 -2.373e-05 0.000
60 -4.30e+00 0.000 -6.868e+02 0.000 -1.508e-03 0.000
90 -9.32e+00 0.000 -8.786e+02 0.000 -6.769e-02 0.216
30 5 6.72e+00 0.000 7.338e+02 0.000 2.384e-05 0.000
10 9.31e-01 0.807 4.647e+02 0.000 2.373e-05 0.000
60 -3.37e+00 0.000 -2.221e+02 0.000 -1.484e-03 0.000
90 -8.39e+00 0.000 -4.139e+02 0.000 -6.767e-02 0.216
60 5 1.01e+01 0.000 9.559e+02 0.000 1.508e-03 0.000
10 4.30e+00 0.000 6.868e+02 0.000 1.508e-03 0.000
30 3.37e+00 0.000 2.221e+02 0.000 1.484e-03 0.000
90 -5.02e+00 0.000 -1.918e+02 0.000 -6.619e-02 0.242
90 5 1.51e+01 0.000 1.148e+03 0.000 6.769e-02 0.216
10 9.32e+00 0.000 8.786e+02 0.000 6.769e-02 0.216
30 8.39e+00 0.000 4.139e+02 0.000 6.767e-02 0.216
60 5.02e+00 0.000 1.918e+02 0.000 6.619e-02 0.242
Ranking $ \mu_{90}>\mu_{60}>\mu_{10}>\mu_{5}$ $ \mu_{90}>\mu_{60}>\mu_{30}>\mu_{5}$ $ \mu_{60}>\mu_{30}>\mu_{10}>\mu_{5}$
$ \mu_{30}>\mu_{5}$ $ \mu_{10}\ge\mu_{5}$ $ \mu_{90}\ge\mu_{5}$
$ \mathbf{f_{Gri}}$ $ \mathbf{f_{Fle}}$ $ \mathbf{f_{Lan}}$
5 10 -7.207E-03 0.174 -2.776e+03 0.885 -1.354e-02 0.998
30 -3.896E-03 0.864 -7.968e+03 0.004 -5.881e-02 0.009
60 2.329E-03 1.000 -7.342e+03 0.008 -8.794e-02 0.000
90 8.649E-03 0.001 -1.268e+04 0.000 -1.142e-01 0.000
10 5 7.207E-03 0.174 2.776e+03 0.885 1.354e-02 0.998
30 3.311E-03 0.983 -5.192e+03 0.234 -4.527e-02 0.082
60 9.535E-03 0.533 -4.566e+03 0.378 -7.440e-02 0.000
90 1.586E-02 0.000 -9.899e+03 0.006 -1.007e-01 0.000
30 5 3.896E-03 0.864 7.968e+03 0.004 5.881e-02 0.009
10 -3.311E-03 0.983 5.192e+03 0.234 4.527e-02 0.082
60 6.225E-03 0.930 6.254e+02 1.000 -2.913e-02 0.354
90 1.254E-02 0.000 -4.707e+03 0.678 -5.540e-02 0.000
60 5 -2.329E-03 1.000 7.342e+03 0.008 8.794e-02 0.000
10 -9.535E-03 0.533 4.566e+03 0.378 7.440e-02 0.000
30 -6.225E-03 0.930 -6.254e+02 1.000 2.913e-02 0.354
90 6.320E-03 0.884 -5.333e+03 0.491 -2.627e-02 0.247
90 5 -8.649E-03 0.001 1.268e+04 0.000 1.142e-01 0.000
10 -1.586E-02 0.000 9.899e+03 0.006 1.007e-01 0.000
30 -1.254E-02 0.000 4.707e+03 0.678 5.540e-02 0.000
60 -6.320E-03 0.884 5.333e+03 0.491 2.627e-02 0.247
Ranking $ \mu_{60}\ge\mu_{90} \ \ \ \ \ \mu_{5}>\mu_{90}$ $ \mu_{10}\ge\mu_{5} \ \ \ \ \ \mu_{30}>\mu_{5}$ $ \mu_{10}\ge\mu_{5} \ \ \ \ \ \mu_{30}>\mu_{5}$
$ \mu_{10}>\mu_{90} \ \ \ \ \ \mu_{30}>\mu_{90}$ $ \mu_{60}>\mu_{5} \ \ \ \ \ \mu_{90}>\mu_{5} $ $ \mu_{60}>\mu_{5} \ \ \ \ \ \mu_{90}>\mu_{5} $



Table 13: Results for all the functions of the multiple comparison test and the ranking obtained depending on the confidence coefficient $ 1-\alpha $.
$ \mathbf{I}$ $ \mathbf{J}$ $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$ $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$ $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$
$ \mathbf{f_{Sph}}$ $ \mathbf{f_{SchDS}}$ $ \mathbf{f_{Ros}}$
0.70 0.90 -1.361e-08 0.000 -3.985e-01 0.000 -1.360e-01 0.281
0.95 -4.394e-08 0.000 -3.783e-02 0.967 -1.693e-01 0.131
0.99 -1.302e-07 0.000 8.165e-02 0.114 -1.813e-01 0.310
0.90 0.70 1.361e-08 0.000 3.985e-01 0.000 1.360e-01 0.281
0.95 -3.033e-08 0.000 3.607e-01 0.001 -3.333e-02 0.995
0.99 -1.166e-07 0.000 4.802e-01 0.000 -4.533e-02 0.996
0.95 0.70 4.394e-08 0.000 3.783e-02 0.967 1.693e-01 0.131
0.90 3.033e-08 0.000 -3.607e-01 0.001 3.333e-02 0.995
0.99 -8.628e-08 0.019 1.195e-01 0.013 -1.200e-02 1.000
0.99 0.70 1.302e-07 0.000 -8.165e-02 0.114 1.813e-01 0.310
0.90 1.166e-07 0.000 -4.802e-01 0.000 4.533e-02 0.996
0.95 8.628e-08 0.019 -1.195e-01 0.013 1.200e-02 1.000
Ranking $ \mu_{0.99}>\mu_{0.95}>\mu_{0.90}>\mu_{0.70}$ $ \mu_{0.90}>\mu_{0.95}>\mu_{0.99}$ $ \mu_{0.99}\ge\mu_{0.95}\ge\mu_{0.90}\ge\mu_{0.70}$
$ \mu_{0.70}\ge\mu_{0.99}$
$ \mathbf{f_{Ras}}$ $ \mathbf{f_{Sch}}$ $ \mathbf{f_{Ack}}$
0.70 0.90 -4.23e+00 0.000 1.198e+02 0.714 -2.471e-04 0.000
0.95 -3.59e+00 0.000 8.247e+01 0.919 -1.944e-02 0.617
0.99 -5.56e+00 0.000 -3.008e+02 0.001 -3.541e-02 0.382
0.90 0.70 4.23e+00 0.000 -1.198e+02 0.714 2.471e-04 0.000
0.95 6.40e-01 0.966 -3.736e+01 0.997 -1.919e-02 0.631
0.99 -1.33e+00 0.551 -4.206e+02 0.000 -3.516e-02 0.390
0.95 0.70 3.59e+00 0.000 -8.247e+01 0.919 1.944e-02 0.617
0.90 -6.40e-01 0.966 3.736e+01 0.997 1.919e-02 0.631
0.99 -1.97e+00 0.044 -3.833e+02 0.000 -1.597e-02 0.985
0.99 0.70 5.56e+00 0.000 3.008e+02 0.001 3.541e-02 0.382
0.90 1.33e+00 0.551 4.206e+02 0.000 3.516e-02 0.390
0.95 1.97e+00 0.044 3.833e+02 0.000 1.597e-02 0.985
Ranking $ \mu_{0.99}>\mu_{0.95}>\mu_{0.70}$ $ \mu_{0.70}\ge\mu_{0.95}\ge\mu_{0.90}$ $ \mu_{0.99}\ge\mu_{0.95}\ge\mu_{0.70}$
$ \mu_{0.90}>\mu_{0.70}$ $ \mu_{0.99}>\mu_{0.90}$ $ \mu_{0.90}>\mu_{0.70}$
$ \mathbf{f_{Gri}}$ $ \mathbf{f_{Fle}}$ $ \mathbf{f_{Lan}}$
0.70 0.90 -7.196E-03 0.395 -2.986e+03 0.717 6.105e-03 0.998
0.95 -2.027E-03 0.945 -3.241e+03 0.635 2.867e-02 0.272
0.99 -5.667E-03 0.155 -3.079e+03 0.644 3.309e-02 0.133
0.90 0.70 7.196E-03 0.395 2.986e+03 0.717 -6.105e-03 0.998
0.95 5.168E-03 0.791 -2.547e+02 1.000 2.257e-02 0.585
0.99 1.529E-03 1.000 -9.255e+01 1.000 2.698e-02 0.363
0.95 0.70 2.027E-03 0.945 3.241e+03 0.635 -2.867e-02 0.272
0.90 -5.168E-03 0.791 2.547e+02 1.000 -2.257e-02 0.585
0.99 -3.640E-03 0.747 1.622e+02 1.000 4.415e-03 1.000
0.99 0.70 5.667E-03 0.155 3.079e+03 0.644 -3.309e-02 0.133
0.90 -1.529E-03 1.000 9.255e+01 1.000 -2.698e-02 0.363
0.95 3.640E-03 0.747 -1.622e+02 1.000 -4.415e-03 1.000
Ranking $ \mu_{0.90}\ge\mu_{0.99}\ge\mu_{0.95}\ge\mu_{0.70}$ $ \mu_{0.95}\ge\mu_{0.99}\ge\mu_{0.90}\ge\mu_{0.70}$ $ \mu_{0.70}\ge\mu_{0.90}\ge\mu_{0.95}\ge\mu_{0.99}$



Table 14: Results of the multiple comparison tests for $ f_{Sph}$, $ f_{SchDS}$ y $ f_{Ros}$ functions and the ranking established by the test regarding the crossover operator.
Crossover $ \mathbf{f_{Sph}}$ $ \mathbf{f_{SchDS}}$ $ \mathbf{f_{Ros}}$
I J $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$ $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$ $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$
CIXL2 BLX(0.3) 3.109e-16 0.000 -1.583e-02 0.000 -4.283e+00 0.997
BLX(0.5) 1.628e-16 0.212 -7.337e-03 0.028 -6.667e+00 0.933
SBX(2) -1.644e-12 0.000 -2.014e-01 0.000 -2.809e+00 0.958
SBX(5) -4.873e-12 0.000 -3.913e-01 0.000 -6.165e+00 0.944
Fuzzy -2.102e-15 0.000 -3.968e+01 0.000 -2.487e+00 1.000
Logical -3.689e-13 0.000 -1.098e+01 0.000 -2.092e+00 0.000
UNDX -2.910e-05 0.000 -2.080e+01 0.000 -3.460e+00 0.000
BLX(0.3) CIXL2 -3.109e-16 0.000 1.583e-02 0.000 4.283e+00 0.997
BLX(0.5) -1.480e-16 0.074 8.495e-03 0.357 -2.384e+00 1.000
SBX(2) -1.644e-12 0.000 -1.855e-01 0.000 1.473e+00 1.000
SBX(5) -4.873e-12 0.000 -3.755e-01 0.000 -1.882e+00 1.000
Fuzzy -2.413e-15 0.000 -3.966e+01 0.000 1.796e+00 1.000
Logical -3.692e-13 0.000 -1.097e+01 0.000 2.191e+00 1.000
UNDX -2.910e-05 0.000 -2.078e+01 0.000 8.225e-01 1.000
BLX(0.5) CIXL2 -1.628e-16 0.212 7.337e-03 0.028 6.667e+00 0.933
BLX(0.3) 1.480e-16 0.074 -8.495e-03 0.357 2.384e+00 1.000
SBX(2) -1.644e-12 0.000 -1.940e-01 0.000 3.857e+00 1.000
SBX(5) -4.873e-12 0.000 -3.840e-01 0.000 5.019e-01 1.000
Fuzzy -2.265e-15 0.000 -3.967e+01 0.000 4.179e+00 1.000
Logical -3.690e-13 0.000 -1.098e+01 0.000 4.575e+00 1.000
UNDX -2.910e-05 0.000 -2.079e+01 0.000 3.206e+00 1.000
SBX(2) CIXL2 1.644e-12 0.000 2.014e-01 0.000 2.809e+00 0.958
BLX(0.3) 1.644e-12 0.000 1.855e-01 0.000 -1.473e+00 1.000
BLX(0.5) 1.644e-12 0.000 1.940e-01 0.000 -3.857e+00 1.000
SBX(5) -3.229e-12 0.000 -1.900e-01 0.115 -3.355e+00 1.000
Fuzzy 1.642e-12 0.000 -3.948e+01 0.000 3.222e-01 1.000
Logical 1.275e-12 0.000 -1.078e+01 0.000 7.179e-01 1.000
UNDX -2.910e-05 0.000 -2.060e+01 0.000 -6.508e-01 1.000
SBX(5) CIXL2 4.873e-12 0.000 3.913e-01 0.000 6.165e+00 0.944
BLX(0.3) 4.873e-12 0.000 3.755e-01 0.000 1.882e+00 1.000
BLX(0.5) 4.873e-12 0.000 3.840e-01 0.000 -5.019e-01 1.000
SBX(2) 3.229e-12 0.000 1.900e-01 0.115 3.355e+00 1.000
Fuzzy 4.871e-12 0.000 -3.929e+01 0.000 3.678e+00 1.000
Logical 4.504e-12 0.000 -1.059e+01 0.000 4.073e+00 1.000
UNDX -2.910e-05 0.000 -2.041e+01 0.000 2.705e+00 1.000
Fuzzy CIXL2 2.102e-15 0.000 3.968e+01 0.000 2.487e+00 1.000
BLX(0.3) 2.413e-15 0.000 3.966e+01 0.000 -1.796e+00 1.000
BLX(0.5) 2.265e-15 0.000 3.967e+01 0.000 -4.179e+00 1.000
SBX(2) -1.642e-12 0.000 3.948e+01 0.000 -3.222e-01 1.000
SBX(5) -4.871e-12 0.000 3.929e+01 0.000 -3.678e+00 1.000
Logical -3.668e-13 0.000 2.870e+01 0.000 3.957e-01 1.000
UNDX -2.910e-05 0.000 1.888e+01 0.000 -9.730e-01 1.000
Logical CIXL2 3.689e-13 0.000 1.098e+01 0.000 2.092e+00 0.000
BLX(0.3) 3.692e-13 0.000 1.097e+01 0.000 -2.191e+00 1.000
BLX(0.5) 3.690e-13 0.000 1.098e+01 0.000 -4.575e+00 1.000
SBX(2) -1.275e-12 0.000 1.078e+01 0.000 -7.179e-01 1.000
SBX(5) -4.504e-12 0.000 1.059e+01 0.000 -4.073e+00 1.000
Fuzzy 3.668e-13 0.000 -2.870e+01 0.000 -3.957e-01 1.000
UNDX -2.910e-05 0.000 -9.812e+00 0.000 -1.369e+00 0.000
UNDX CIXL2 2.910e-05 0.000 2.080e+01 0.000 3.460e+00 0.000
BLX(0.3) 2.910e-05 0.000 2.078e+01 0.000 -8.225e-01 1.000
BLX(0.5) 2.910e-05 0.000 2.079e+01 0.000 -3.206e+00 1.000
SBX(2) 2.910e-05 0.000 2.060e+01 0.000 6.508e-01 1.000
SBX(5) 2.910e-05 0.000 2.041e+01 0.000 -2.705e+00 1.000
Fuzzy 2.910e-05 0.000 -1.888e+01 0.000 9.730e-01 1.000
Logical 2.910e-05 0.000 9.812e+00 0.000 1.369e+00 0.000
Function Ranking
$ f_{Sph}$ $ \mu_{UNDX} > \mu_{SBX(5)} > \mu_{SBX(2)} > \mu_{Logical} > \mu_{Ext.F.} > \mu_{CIXL2} \ge \mu_{BLX(0.5)} \ge \mu_{BLX(0.3)}$
$ f_{SchDS}$ $ \mu_{Ext.F.} > \mu_{UNDX} > \mu_{Logical} > \mu_{SBX(5)} \ge \mu_{SBX(2)} > \mu_{BLX(0.3)} \ge \mu_{BLX(0.5)} > \mu_{CIXL2}$
$ f_{Ros}$ $ \mu_{BLX(0.5)} \ge \mu_{SBX(5)} \ge \mu_{BLX(0.3)} \ge \mu_{UNDX} \ge \mu_{SBX(2)} \ge \mu_{Ext.F.} \ge \mu_{Logical} > \mu_{CIXL2}$



Table 15: Results of the multiple comparison tests for $ f_{Ras}$, $ f_{Sch}$ and $ f_{Ack}$ functions and the ranking established by the test regarding the crossover operator.
Crossover $ \mathbf{f_{Ras}}$ $ \mathbf{f_{Sch}}$ $ \mathbf{f_{Ack}}$
I J $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$ $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$ $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$
CIXL2 BLX(0.3) 7.296e-01 0.923 2.715e+02 0.000 -2.830e-08 0.000
BLX(0.5) -9.950e-02 1.000 2.210e+02 0.010 -5.090e-08 0.000
SBX(2) -1.552e+01 0.000 -8.287e+02 0.000 -5.322e-06 0.000
SBX(5) -1.128e+01 0.000 -4.631e+02 0.000 -9.649e-06 0.000
Fuzzy -1.953e+01 0.000 -2.408e+03 0.000 -1.659e-07 0.000
Logical -6.033e+01 0.000 -1.988e+03 0.000 -2.517e-06 0.000
UNDX -1.078e+02 0.000 -7.409e+03 0.000 -3.550e-02 0.000
BLX(0.3) CIXL2 -7.296e-01 0.923 -2.715e+02 0.000 2.830e-08 0.000
BLX(0.5) -8.291e-01 0.713 -5.050e+01 1.000 -2.261e-08 0.000
SBX(2) -1.625e+01 0.000 -1.100e+03 0.000 -5.293e-06 0.000
SBX(5) -1.201e+01 0.000 -7.346e+02 0.000 -9.620e-06 0.000
Fuzzy -2.026e+01 0.000 -2.680e+03 0.000 -1.376e-07 0.000
Logical -6.106e+01 0.000 -2.260e+03 0.000 -2.488e-06 0.000
UNDX -1.085e+02 0.000 -7.680e+03 0.000 -3.550e-02 0.000
BLX(0.5) CIXL2 9.950e-02 1.000 -2.210e+02 0.010 5.090e-08 0.000
BLX(0.3) 8.291e-01 0.713 5.050e+01 1.000 2.261e-08 0.000
SBX(2) -1.542e+01 0.000 -1.050e+03 0.000 -5.271e-06 0.000
SBX(5) -1.118e+01 0.000 -6.841e+02 0.000 -9.598e-06 0.000
Fuzzy -1.943e+01 0.000 -2.629e+03 0.000 -1.150e-07 0.000
Logical -6.023e+01 0.000 -2.209e+03 0.000 -2.466e-06 0.000
UNDX -1.077e+02 0.000 -7.630e+03 0.000 -3.550e-02 0.000
SBX(2) CIXL2 1.552e+01 0.000 8.287e+02 0.000 5.322e-06 0.000
BLX(0.3) 1.625e+01 0.000 1.100e+03 0.000 5.293e-06 0.000
BLX(0.5) 1.542e+01 0.000 1.050e+03 0.000 5.271e-06 0.000
SBX(5) 4.245e+00 0.005 3.655e+02 0.006 -4.327e-06 0.000
Fuzzy -4.013e+00 0.042 -1.579e+03 0.000 5.156e-06 0.000
Logical -4.481e+01 0.000 -1.159e+03 0.000 2.805e-06 0.000
UNDX -9.227e+01 0.000 -6.580e+03 0.000 -3.550e-02 0.000
SBX(5) CIXL2 1.128e+01 0.000 4.631e+02 0.000 9.649e-06 0.000
BLX(0.3) 1.201e+01 0.000 7.346e+02 0.000 9.620e-06 0.000
BLX(0.5) 1.118e+01 0.000 6.841e+02 0.000 9.598e-06 0.000
SBX(2) -4.245e+00 0.005 -3.655e+02 0.006 4.327e-06 0.000
Fuzzy -8.258e+00 0.000 -1.945e+03 0.000 9.483e-06 0.000
Logical -4.905e+01 0.000 -1.525e+03 0.000 7.132e-06 0.000
UNDX -9.651e+01 0.000 -6.946e+03 0.000 -3.550e-02 0.000
Fuzzy CIXL2 1.953e+01 0.000 2.408e+03 0.000 1.659e-07 0.000
BLX(0.3) 2.026e+01 0.000 2.680e+03 0.000 1.376e-07 0.000
BLX(0.5) 1.943e+01 0.000 2.629e+03 0.000 1.150e-07 0.000
SBX(2) 4.013e+00 0.042 1.579e+03 0.000 -5.156e-06 0.000
SBX(5) 8.258e+00 0.000 1.945e+03 0.000 -9.483e-06 0.000
Logical -4.079e+01 0.000 4.199e+02 0.000 -2.351e-06 0.000
UNDX -8.826e+01 0.000 -5.001e+03 0.000 -3.550e-02 0.000
Logical CIXL2 6.033e+01 0.000 1.988e+03 0.000 2.517e-06 0.000
BLX(0.3) 6.106e+01 0.000 2.260e+03 0.000 2.488e-06 0.000
BLX(0.5) 6.023e+01 0.000 2.209e+03 0.000 2.466e-06 0.000
SBX(2) 4.481e+01 0.000 1.159e+03 0.000 -2.805e-06 0.000
SBX(5) 4.905e+01 0.000 1.525e+03 0.000 -7.132e-06 0.000
Fuzzy 4.079e+01 0.000 -4.199e+02 0.000 2.351e-06 0.000
UNDX -4.746e+01 0.000 -5.421e+03 0.000 -3.550e-02 0.000
UNDX CIXL2 1.078e+02 0.000 7.409e+03 0.000 3.550e-02 0.000
BLX(0.3) 1.085e+02 0.000 7.680e+03 0.000 3.550e-02 0.000
BLX(0.5) 1.077e+02 0.000 7.630e+03 0.000 3.550e-02 0.000
SBX(2) 9.227e+01 0.000 6.580e+03 0.000 3.550e-02 0.000
SBX(5) 9.651e+01 0.000 6.946e+03 0.000 3.550e-02 0.000
Fuzzy 8.826e+01 0.000 5.001e+03 0.000 3.550e-02 0.000
Logical 4.746e+01 0.000 5.421e+03 0.000 3.550e-02 0.000
Function Ranking
$ f_{Ras}$ $ \mu_{UNDX} > \mu_{Logical} > \mu_{Ext.F.} > \mu_{SBX(2)} > \mu_{SBX(5)} > \mu_{BLX(0.5)} \ge \mu_{CIXL2} \ge \mu_{BLX(0.3)}$
$ f_{Sch}$ $ \mu_{UNDX} > \mu_{Ext.F.} > \mu_{Logical} > \mu_{SBX(2)} > \mu_{SBX(5)} > \mu_{CIXL2} > \mu_{BLX(0.5)} \ge \mu_{BLX(0.3)}$
$ f_{Ack}$ $ \mu_{UNDX} > \mu_{SBX(5)} > \mu_{SBX(2)} > \mu_{Logical} > \mu_{Ext.F.} > \mu_{BLX(0.5)} > \mu_{BLX(0.3)} > \mu_{CIXL2}$



Table 16: Results of the multiple comparison tests for $ f_{Gri}$, $ f_{Fle}$ and $ f_{Lan}$ functions and the ranking established by the test regarding the crossover operator.
Crossover $ \mathbf{f_{Gri}}$ $ \mathbf{f_{Fle}}$ $ \mathbf{f_{Lan}}$
I J $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$ $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$ $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$
CIXL2 BLX(0.3) -3.224e-02 0.021 -4.779e+02 1.000 9.384e-02 0.091
BLX(0.5) -2.235e-02 0.012 -2.789e+03 1.000 1.392e-01 0.007
SBX(2) -6.710e-03 0.973 -1.740e+04 0.034 -1.253e-02 1.000
SBX(5) -1.603e-02 0.167 -1.810e+04 0.022 -1.982e-02 1.000
Fuzzy 1.394e-02 0.000 -1.686e+03 1.000 -1.000e-01 0.000
Logical 9.173e-03 0.057 -1.196e+04 0.709 -2.064e-01 0.000
UNDX -6.312e-02 0.000 -1.947e+04 0.009 6.557e-03 1.000
BLX(0.3) CIXL2 3.224e-02 0.021 4.779e+02 1.000 -9.384e-02 0.091
BLX(0.5) 9.893e-03 1.000 -2.311e+03 1.000 4.540e-02 1.000
SBX(2) 2.553e-02 0.188 -1.693e+04 0.046 -1.064e-01 0.046
SBX(5) 1.621e-02 0.952 -1.763e+04 0.029 -1.137e-01 0.013
Fuzzy 4.618e-02 0.000 -1.208e+03 1.000 -1.938e-01 0.000
Logical 4.142e-02 0.001 -1.148e+04 0.888 -3.003e-01 0.000
UNDX -3.088e-02 0.252 -1.899e+04 0.012 -8.728e-02 0.151
BLX(0.5) CIXL2 2.235e-02 0.012 2.789e+03 1.000 -1.392e-01 0.007
BLX(0.3) -9.893e-03 1.000 2.311e+03 1.000 -4.540e-02 1.000
SBX(2) 1.564e-02 0.361 -1.461e+04 0.179 -1.518e-01 0.004
SBX(5) 6.320e-03 1.000 -1.531e+04 0.121 -1.591e-01 0.001
Fuzzy 3.629e-02 0.000 1.104e+03 1.000 -2.392e-01 0.000
Logical 3.152e-02 0.000 -9.169e+03 1.000 -3.457e-01 0.000
UNDX -4.077e-02 0.003 -1.668e+04 0.054 -1.327e-01 0.012
SBX(2) CIXL2 6.710e-03 0.973 1.740e+04 0.034 1.253e-02 1.000
BLX(0.3) -2.553e-02 0.188 1.693e+04 0.046 1.064e-01 0.046
BLX(0.5) -1.564e-02 0.361 1.461e+04 0.179 1.518e-01 0.004
SBX(5) -9.320e-03 0.980 -7.002e+02 1.000 -7.285e-03 1.000
Fuzzy 2.065e-02 0.000 1.572e+04 0.095 -8.747e-02 0.008
Logical 1.588e-02 0.003 5.446e+03 1.000 -1.939e-01 0.000
UNDX -5.641e-02 0.000 -2.061e+03 1.000 1.909e-02 1.000
SBX(5) CIXL2 1.603e-02 0.167 1.810e+04 0.022 1.982e-02 1.000
BLX(0.3) -1.621e-02 0.952 1.763e+04 0.029 1.137e-01 0.013
BLX(0.5) -6.320e-03 1.000 1.531e+04 0.121 1.591e-01 0.001
SBX(2) 9.320e-03 0.980 7.002e+02 1.000 7.285e-03 1.000
Fuzzy 2.997e-02 0.000 1.642e+04 0.063 -8.018e-02 0.004
Logical 2.520e-02 0.001 6.146e+03 1.000 -1.866e-01 0.000
UNDX -4.709e-02 0.000 -1.361e+03 1.000 2.637e-02 1.000
Fuzzy CIXL2 -1.394e-02 0.000 1.686e+03 1.000 1.000e-01 0.000
BLX(0.3) -4.618e-02 0.000 1.208e+03 1.000 1.938e-01 0.000
BLX(0.5) -3.629e-02 0.000 -1.104e+03 1.000 2.392e-01 0.000
SBX(2) -2.065e-02 0.000 -1.572e+04 0.095 8.747e-02 0.008
SBX(5) -2.997e-02 0.000 -1.642e+04 0.063 8.018e-02 0.004
Logical -4.763e-03 0.025 -1.027e+04 1.000 -1.064e-01 0.000
UNDX -7.706e-02 0.000 -1.778e+04 0.027 1.066e-01 0.000
Logical CIXL2 -9.173e-03 0.057 1.196e+04 0.709 2.064e-01 0.000
BLX(0.3) -4.142e-02 0.001 1.148e+04 0.888 3.003e-01 0.000
BLX(0.5) -3.152e-02 0.000 9.169e+03 1.000 3.457e-01 0.000
SBX(2) -1.588e-02 0.003 -5.446e+03 1.000 1.939e-01 0.000
SBX(5) -2.520e-02 0.001 -6.146e+03 1.000 1.866e-01 0.000
Fuzzy 4.763e-03 0.025 1.027e+04 1.000 1.064e-01 0.000
UNDX -7.229e-02 0.000 -7.507e+03 1.000 2.130e-01 0.000
UNDX CIXL2 6.312e-02 0.000 1.947e+04 0.009 -6.557e-03 1.000
BLX(0.3) 3.088e-02 0.252 1.899e+04 0.012 8.728e-02 0.151
BLX(0.5) 4.077e-02 0.003 1.668e+04 0.054 1.327e-01 0.012
SBX(2) 5.641e-02 0.000 2.061e+03 1.000 -1.909e-02 1.000
SBX(5) 4.709e-02 0.000 1.361e+03 1.000 -2.637e-02 1.000
Fuzzy 7.706e-02 0.000 1.778e+04 0.027 -1.066e-01 0.000
Logical 7.229e-02 0.000 7.507e+03 1.000 -2.130e-01 0.000
Function Ranking
$ f_{Gri}$ $ \mu_{UNDX} \ge \mu_{BLX(0.3)} \ge \mu_{BLX(0.5)} \ge \mu_{SBX(5)} \ge \mu_{SBX(2)} \ge \mu_{CIXL2} \ge \mu_{Logical} > \mu_{Ext.F.}$
$ f_{Fle}$ $ \mu_{UNDX} \ge \mu_{SBX(5)} \ge \mu_{SBX(2)} \ge \mu_{Logical} \ge \mu_{BLX(0.5)} \ge \mu_{Ext.F.} \ge \mu_{BLX(0.3)} \ge \mu_{CIXL2}$
$ f_{Lan}$ $ \mu_{Logical} > \mu_{Ext.F.} > \mu_{SBX(5)} \ge \mu_{SBX(2)} \ge \mu_{CIXL2} \ge \mu_{UNDX} \ge \mu_{BLX(0.3)} \ge \mu_{BLX(0.5)}$



Table 17: Results for all the functions of the multiple comparison test and the ranking obtained depending on the evolutionary algorithm.
$ \mathbf{I}$ $ \mathbf{J}$ $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$ $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$ $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$ $ \mathbf{\mu_I - \mu_J}$ $ \mathbf{\alpha^*}$
$ \mathbf{f_{SchDS}}$ $ \mathbf{f_{Ros}}$ $ \mathbf{f_{Ras}}$ $ \mathbf{f_{Sch}}$
CIXL2 $ UMDA_c$ -2.221e+01 0.000 -2.928e+00 0.000 -1.547e+02 0.000 -1.089e+04 0.000
$ EGNA_{BGe}$ -2.076e-01 0.000 -2.906e+00 0.000 -1.533e+02 0.000 -1.091e+04 0.000
$ UMDA_c$ CIXL2 2.221e+01 0.000 2.928e+00 0.000 1.547e+02 0.000 1.089e+04 0.000
$ EGNA_{BGe}$ 2.200e+01 0.000 2.207e-02 0.856 1.360e+00 0.888 -2.390e+01 0.677
$ EGNA_{BGe}$ CIXL2 2.076e-01 0.000 2.906e+00 0.000 1.533e+02 0.000 1.091e+04 0.000
$ UMDA_c$ -2.200e+01 0.000 -2.207e-02 0.856 -1.360e+00 0.888 2.390e+01 0.677
Function Ranking
$ f_{SchDS}$ $ \mu_{UMDA_c} > \mu_{EGNA_{BGe}} > \mu_{CIXL2}$
$ f_{Ros}$ $ \mu_{UMDA_c}\ge\mu_{EGNA_{BGe}}>\mu_{CIXL2}$
$ f_{Ras}$ $ \mu_{UMDA_c}\ge\mu_{EGNA_{BGe}}>\mu_{CIXL2}$
$ f_{Sch}$ $ \mu_{EGNA_{BGe}}\ge\mu_{UMDA_c}>\mu_{CIXL2}$
$ \mathbf{f_{Ack}}$ $ \mathbf{f_{Gri}}$ $ \mathbf{f_{Fle}}$ $ \mathbf{f_{Lan}}$
CIXL2 $ UMDA_c$ -1.101e-08 0.000 1.525e-02 0.000 9.803e+03 0.004 -3.306e-02 0.176
$ EGNA_{BGe}$ -9.194e-09 0.000 1.525e-02 0.000 6.157e+03 0.150 -3.306e-02 0.176
$ UMDA_c$ CIXL2 1.101e-08 0.000 -1.525e-02 0.000 -9.803e+03 0.004 3.306e-02 0.176
$ EGNA_{BGe}$ 1.817e-09 0.175 1.266e-16 0.000 -3.646e+03 0.049 1.33781e-11 0.325
$ EGNA_{BGe}$ CIXL2 9.194e-09 0.000 -1.525e-02 0.000 -6.157e+03 0.150 3.306e-02 0.176
$ UMDA_c$ -1.817e-09 0.175 -1.266e-16 0.000 3.646e+03 0.049 -1.33781e-11 0.325
Function Ranking
$ f_{Ack}$ $ \mu_{UMDA_c}\ge\mu_{EGNA_{BGe}}>\mu_{CIXL2}$
$ f_{Gri}$ $ \mu_{CIXL2}>\mu_{UMDA_c}>\mu_{EGNA_{BGe}}$
$ f_{Fle}$ $ \mu_{CIXL2}\ge\mu_{EGNA_{BGe}}>\mu_{UMDA_c}$
$ f_{Lan}$ $ \mu_{UMDA_c}\ge\mu_{EGNA_{BGe}}\ge\mu_{CIXL2}$


Domingo 2005-07-11