Computational Intelligence and Neuroscience / 2020 / Article / Tab 3

Research Article

A Search History-Driven Offspring Generation Method for the Real-Coded Genetic Algorithm

Table 3

The results of the absolute error between the optimal value and the final-generation-elite fitness over 100 runs.

MinimumMaximum
Mean
MinimumMaximumMinimumMaximum
MedianMedianMeanMedianMean
SDSD valueSD value

BLXSH-BLX_randomSH-BLX_sequential
53.37E + 001.58E + 012.07E + 001.51E + 012.45E + 001.36E + 01
8.82E + 008.92E + 007.27E + 007.26E + 007.13E + 007.35E + 00
2.87E + 002.40E + 002.76E − 052.29E + 006.54E − 05
101.03E + 012.58E + 018.60E + 002.28E + 019.20E + 002.68E + 01
1.80E + 011.84E + 011.72E + 011.68E + 011.66E + 011.69E + 01
3.20E + 002.90E + 001.11E − 033.36E + 008.49E − 04
51.07E − 013.40E + 001.19E − 021.69E + 007.60E − 022.14E + 00
7.75E − 019.28E − 015.67E − 015.57E − 014.47E − 015.63E − 01
6.39E − 013.78E − 013.07E − 064.11E − 011.67E − 06
101.02E + 001.59E + 019.51E − 019.47E + 001.29E + 008.85E + 00
5.02E + 005.33E + 004.14E + 004.24E + 003.79E + 004.09E + 00
2.18E + 001.68E + 008.78E − 051.53E + 003.00E − 06
51.61E − 019.02E + 001.51E − 019.28E + 001.58E − 015.74E + 00
2.08E + 002.62E + 001.24E + 001.60E + 001.35E + 001.69E + 00
1.66E + 001.33E + 006.50E − 081.26E + 001.17E − 06
104.57E + 005.66E + 012.41E + 004.86E + 014.04E + 004.56E + 01
2.47E + 012.60E + 011.84E + 012.11E + 012.02E + 012.06E + 01
1.02E + 019.57E + 001.33E − 048.79E + 001.90E − 04
56.96E + 011.94E + 041.21E + 028.83E + 037.78E + 018.08E + 03
1.94E + 032.80E + 038.98E + 021.74E + 038.68E + 021.40E + 03
2.80E + 032.00E + 037.07E − 051.45E + 039.29E − 07
106.89E + 033.50E + 054.44E + 032.12E + 054.89E + 031.56E + 05
6.11E + 047.19E + 044.69E + 045.35E + 043.38E + 044.21E + 04
5.19E + 043.91E + 041.73E − 033.01E + 042.16E − 07
52.45E + 015.58E + 021.81E + 016.65E + 027.61E + 004.54E + 02
1.78E + 021.93E + 021.30E + 021.63E + 021.29E + 021.45E + 02
1.15E + 021.18E + 029.22E − 038.49E + 011.15E − 03
104.00E + 022.80E + 033.94E + 022.29E + 032.98E + 022.32E + 03
1.40E + 031.37E + 031.12E + 031.18E + 031.16E + 031.22E + 03
4.28E + 023.99E + 026.21E − 044.39E + 026.82E − 03
54.00E + 002.12E + 022.06E + 008.97E + 012.70E + 008.71E + 01
2.52E + 013.36E + 011.49E + 012.05E + 011.56E + 011.87E + 01
3.25E + 011.62E + 014.48E − 061.32E + 012.58E − 07
104.03E + 011.17E + 061.63E + 011.57E + 053.60E + 018.26E + 05
3.85E + 033.75E + 049.76E + 029.57E + 031.09E + 031.31E + 04
1.33E + 052.77E + 045.04E − 058.24E + 043.11E − 04
52.84E − 011.22E + 014.40E − 011.09E + 013.23E − 011.02E + 01
3.33E + 003.87E + 002.48E + 002.93E + 002.16E + 002.76E + 00
2.52E + 001.97E + 003.21E − 031.99E + 005.01E − 04
107.23E + 004.17E + 017.08E + 004.04E + 015.92E + 004.00E + 01
2.39E + 012.32E + 011.98E + 012.04E + 011.95E + 011.94E + 01
7.22E + 006.47E + 001.49E − 036.75E + 007.14E − 05
5
108.70E − 011.00E + 004.90E − 011.00E + 009.16E − 011.00E + 00
1.00E + 009.95E − 011.00E + 009.86E − 011.00E + 009.93E − 01
1.87E − 026.23E − 023.65E − 061.41E − 027.74E − 07
54.50E + 002.22E + 013.68E + 002.01E + 014.74E + 002.13E + 01
1.28E + 011.34E + 011.15E + 011.15E + 011.13E + 011.14E + 01
3.52E + 003.40E + 002.35E − 043.46E + 005.41E − 05
102.44E + 015.91E + 012.61E + 015.87E + 012.61E + 015.60E + 01
4.44E + 014.40E + 014.31E + 014.22E + 014.22E + 014.24E + 01
6.68E + 006.01E + 001.93E − 027.00E + 006.44E − 02
56.18E + 019.74E + 02
5.93E + 025.75E + 02
1.78E + 022.82E − 39
105.69E + 022.15E + 035.93E + 022.23E + 037.63E + 022.24E + 03
1.77E + 031.71E + 031.78E + 031.76E + 031.85E + 031.79E + 03
2.62E + 022.45E + 028.94E − 012.35E + 029.91E − 01
54.10E + 014.31E + 014.06E + 014.22E + 014.08E + 014.25E + 01
4.18E + 014.18E + 014.15E + 014.15E + 014.14E + 014.14E + 01
4.15E − 013.47E − 019.67E − 083.11E − 012.23E − 10
101.83E + 021.87E + 021.83E + 021.86E + 021.83E + 021.86E + 02
1.85E + 021.85E + 021.85E + 021.85E + 021.85E + 021.85E + 02
6.42E − 016.27E − 012.70E − 066.55E − 012.38E − 08
53.70E + 009.50E + 002.80E + 008.91E + 002.88E + 009.80E + 00
6.69E + 006.82E + 005.68E + 005.66E + 005.84E + 005.87E + 00
1.46E + 001.30E + 001.19E − 071.23E + 002.67E − 06
105.99E + 001.30E + 016.06E + 001.13E + 015.01E + 001.24E + 01
1.00E + 019.84E + 008.95E + 009.13E + 009.08E + 009.12E + 00
1.23E + 001.12E + 004.53E − 061.39E + 007.36E − 05
52.97E − 019.57E − 011.51E − 018.28E − 011.60E − 017.97E − 01
5.41E − 015.59E − 015.08E − 014.92E − 014.77E − 014.85E − 01
1.27E − 011.44E − 011.16E − 031.36E − 019.77E − 05
108.82E − 011.28E + 007.98E − 011.24E + 006.04E − 011.23E + 00
1.11E + 001.11E + 001.08E + 001.08E + 001.07E + 001.06E + 00
7.04E − 027.46E − 021.14E − 039.55E − 021.91E − 05
53.09E − 012.52E + 004.48E − 012.03E + 003.56E − 012.63E + 00
1.34E + 001.37E + 001.20E + 001.18E + 001.20E + 001.19E + 00
3.93E − 013.52E − 013.88E − 043.59E − 012.14E − 04
101.73E + 004.20E + 001.80E + 004.22E + 001.58E + 003.68E + 00
2.96E + 002.97E + 002.72E + 002.71E + 002.71E + 002.66E + 00
4.74E − 014.77E − 016.94E − 054.66E − 015.25E − 06
55.04E − 021.55E − 014.53E − 021.21E − 014.44E − 021.08E − 01
7.84E − 028.18E − 027.22E − 027.21E − 026.74E − 026.88E − 02
1.99E − 021.59E − 022.67E − 041.44E − 025.03E − 07
101.86E − 031.27E − 021.17E − 031.07E − 021.26E − 031.12E − 02
5.75E − 035.66E − 035.28E − 035.43E − 034.93E − 035.12E − 03
2.04E − 032.03E − 032.58E − 011.95E − 032.84E − 02

SPXSH-SPX_randomSH-SPX_sequential
52.73E − 012.23E + 001.71E − 011.48E + 001.83E − 012.99E + 00
9.30E − 019.76E − 016.46E − 017.10E − 015.77E − 016.90E − 01
4.08E − 012.74E − 013.92E − 074.21E − 015.93E − 09
102.11E − 018.83E − 011.76E − 019.73E − 011.64E − 018.63E − 01
4.73E − 015.03E − 013.55E − 013.78E − 012.81E − 013.07E − 01
1.29E − 011.26E − 014.24E − 131.22E − 013.26E − 21
53.00E − 036.10E − 021.09E − 036.74E − 023.67E − 043.57E − 02
1.54E − 021.97E − 027.82E − 031.11E − 024.51E − 037.39E − 03
1.33E − 029.97E − 032.63E − 096.87E − 035.70E − 17
109.45E − 041.11E − 025.33E − 047.35E − 031.68E − 045.32E − 03
3.70E − 034.22E − 031.64E − 031.89E − 031.08E − 031.30E − 03
2.06E − 031.07E − 031.29E − 208.56E − 042.16E − 27
54.02E − 034.15E − 012.48E − 033.84E − 012.41E − 034.92E − 01
4.10E − 025.50E − 022.21E − 023.68E − 021.86E − 024.22E − 02
5.67E − 025.17E − 026.57E − 067.39E − 027.37E − 07
105.20E − 038.20E − 022.42E − 031.88E − 011.66E − 031.36E − 01
2.07E − 022.31E − 021.31E − 021.93E − 026.25E − 031.38E − 02
1.23E − 022.19E − 021.04E − 052.30E − 024.27E − 17
55.72E + 001.10E + 032.49E + 006.26E + 022.50E + 002.62E + 03
2.12E + 015.79E + 011.80E + 016.39E + 011.27E + 017.01E + 01
1.29E + 021.18E + 021.74E − 012.77E + 021.89E − 05
101.04E + 018.49E + 018.69E + 002.67E + 027.58E + 003.46E + 02
1.64E + 011.88E + 011.19E + 012.13E + 011.06E + 011.95E + 01
9.64E + 003.56E + 016.19E − 113.77E + 013.70E − 14
53.63E − 013.58E + 011.59E − 011.27E + 027.85E − 023.06E + 01
2.12E + 003.44E + 001.92E + 005.01E + 001.58E + 004.20E + 00
4.57E + 001.41E + 019.05E − 026.01E + 002.58E − 02
102.80E − 016.40E + 007.15E − 026.69E + 004.67E − 021.13E + 01
9.01E − 011.20E + 005.28E − 018.65E − 015.03E − 011.19E + 00
1.04E + 009.14E − 016.06E − 071.79E + 009.06E − 06
51.46E + 002.49E + 015.51E − 011.84E + 011.93E − 011.90E + 01
5.66E + 006.28E + 003.13E + 003.72E + 002.71E + 004.45E + 00
3.41E + 002.47E + 001.05E − 154.19E + 002.78E − 10
102.16E + 001.11E + 011.42E + 003.24E + 019.44E − 018.43E + 00
4.13E + 004.37E + 002.65E + 003.26E + 002.03E + 002.42E + 00
1.35E + 003.25E + 001.25E − 171.32E + 001.58E − 21
55.87E − 031.12E + 004.99E − 031.34E + 003.09E − 033.30E + 00
8.86E − 021.65E − 015.66E − 021.38E − 018.61E − 022.95E − 01
1.96E − 012.15E − 013.69E − 035.54E − 011.90E − 01
101.36E − 021.19E + 004.93E − 031.22E + 004.72E − 031.86E + 00
6.32E − 021.24E − 012.42E − 027.25E − 023.80E − 021.35E − 01
1.66E − 011.55E − 017.46E − 092.49E − 012.72E − 03
5
103.58E − 031.92E − 011.20E − 039.98E − 019.28E − 049.98E − 01
1.73E − 022.54E − 026.69E − 035.27E − 028.29E − 036.27E − 02
2.82E − 021.88E − 011.08E − 101.96E − 019.22E − 05
52.42E + 002.32E + 019.43E − 012.03E + 016.68E − 012.03E + 01
1.12E + 011.18E + 011.02E + 011.02E + 018.62E + 008.86E + 00
3.95E + 003.89E + 004.58E − 033.45E + 008.84E − 09
101.44E + 014.54E + 013.53E + 003.65E + 018.75E − 012.79E + 01
3.47E + 013.37E + 011.52E + 011.71E + 018.14E + 009.53E + 00
6.66E + 007.99E + 006.39E − 275.97E + 001.87E − 33
5
109.16E + 002.86E + 03
1.88E + 031.83E + 03
4.94E + 022.82E − 39
54.04E + 014.13E + 014.03E + 014.15E + 014.02E + 014.11E + 01
4.07E + 014.07E + 014.06E + 014.06E + 014.05E + 014.05E + 01
1.90E − 011.60E − 014.35E − 101.65E − 018.70E − 15
101.81E + 021.81E + 021.80E + 021.81E + 021.80E + 021.81E + 02
1.81E + 021.81E + 021.81E + 021.81E + 021.81E + 021.81E + 02
1.29E − 011.08E − 014.36E − 181.28E − 011.14E − 25
54.05E − 013.28E + 002.13E − 013.14E + 001.97E − 012.65E + 00
1.87E + 001.84E + 001.45E + 001.49E + 001.12E + 001.23E + 00
5.88E − 016.29E − 014.46E − 055.57E − 011.65E − 11
102.67E − 011.39E + 001.57E − 012.07E + 008.07E − 025.88E − 01
5.83E − 016.16E − 013.50E − 013.96E − 012.36E − 012.45E − 01
2.25E − 012.25E − 012.84E − 169.53E − 024.47E − 30
51.04E − 016.17E − 014.94E − 025.92E − 019.47E − 025.98E − 01
3.49E − 013.52E − 013.12E − 013.20E − 013.31E − 013.27E − 01
1.11E − 011.12E − 012.86E − 021.09E − 017.84E − 02
106.96E − 024.84E − 011.43E − 023.90E − 011.22E − 022.88E − 01
1.93E − 012.08E − 017.37E − 029.07E − 025.03E − 026.06E − 02
1.00E − 016.20E − 026.30E − 204.44E − 026.33E − 28
52.00E − 017.73E − 011.21E − 017.01E − 012.00E − 017.10E − 01
4.13E − 014.24E − 014.00E − 013.98E − 014.00E − 013.86E − 01
1.39E − 011.30E − 011.16E − 011.22E − 013.43E − 02
102.00E − 017.03E − 012.00E − 015.14E − 012.00E − 016.16E − 01
3.65E − 013.66E − 013.10E − 013.25E − 013.08E − 013.35E − 01
8.08E − 026.94E − 022.20E − 049.77E − 021.57E − 03
54.37E − 021.27E − 014.24E − 021.32E − 014.28E − 028.59E − 02
7.25E − 027.30E − 025.54E − 025.82E − 025.12E − 025.45E − 02
1.63E − 021.36E − 022.32E − 129.05E − 035.28E − 18
101.08E − 039.64E − 036.29E − 045.55E − 036.01E − 043.29E − 03
4.23E − 034.38E − 031.22E − 031.52E − 038.99E − 041.01E − 03
1.89E − 038.58E − 042.60E − 274.11E − 042.82E − 33

UNDXSH-UNDX_randomSH-UNDX_sequential
51.20E + 006.82E + 008.26E − 015.16E + 007.35E − 015.54E + 00
2.77E + 002.83E + 002.18E + 002.30E + 001.96E + 002.13E + 00
1.09E + 008.41E − 011.60E − 048.74E − 013.29E − 07
102.04E + 006.43E + 001.36E + 005.53E + 001.71E + 005.33E + 00
4.25E + 004.25E + 003.65E + 003.66E + 003.54E + 003.50E + 00
1.01E + 007.54E − 019.57E − 067.34E − 012.52E − 08
51.30E − 026.07E − 011.24E − 024.28E − 014.48E − 036.26E − 01
1.30E − 011.60E − 016.85E − 028.27E − 027.20E − 028.83E − 02
1.16E − 016.00E − 027.89E − 098.50E − 021.94E − 08
109.42E − 021.26E + 007.07E − 026.85E − 014.32E − 026.42E − 01
4.10E − 014.74E − 012.98E − 013.03E − 012.49E − 012.68E − 01
2.39E − 011.43E − 013.09E − 081.22E − 012.28E − 12
54.93E − 021.77E + 001.51E − 021.81E + 002.90E − 028.85E − 01
3.45E − 014.71E − 012.17E − 012.96E − 012.03E − 012.71E − 01
3.48E − 012.77E − 012.17E − 062.04E − 016.85E − 07
103.27E − 015.08E + 002.47E − 016.39E + 004.47E − 014.88E + 00
2.30E + 002.30E + 001.47E + 001.72E + 001.49E + 001.69E + 00
9.70E − 019.66E − 016.77E − 078.96E − 017.28E − 07
54.89E + 001.54E + 036.89E + 001.21E + 036.88E + 001.17E + 03
1.51E + 022.41E + 028.81E + 011.93E + 021.00E + 021.60E + 02
2.70E + 022.38E + 022.12E − 021.80E + 028.40E − 03
101.04E + 023.64E + 038.64E + 011.54E + 039.04E + 013.07E + 03
6.38E + 027.67E + 024.29E + 024.78E + 023.65E + 024.71E + 02
5.61E + 022.72E + 025.55E − 064.01E + 026.08E − 08
56.70E − 018.64E + 012.11E + 002.42E + 022.50E + 006.09E + 01
2.07E + 012.40E + 011.58E + 012.33E + 011.49E + 011.80E + 01
1.64E + 012.85E + 014.19E − 021.30E + 013.00E − 03
102.25E + 012.33E + 022.88E + 012.05E + 021.91E + 012.01E + 02
1.02E + 021.04E + 027.97E + 018.55E + 018.47E + 018.99E + 01
4.18E + 013.30E + 012.52E − 043.96E + 014.88E − 03
52.16E + 004.98E + 013.22E + 004.47E + 011.94E + 005.04E + 01
1.44E + 011.62E + 019.27E + 001.16E + 011.22E + 011.28E + 01
9.25E + 006.70E + 003.06E − 057.34E + 002.07E − 03
101.54E + 013.08E + 031.46E + 015.00E + 021.39E + 011.19E + 03
5.27E + 011.50E + 023.49E + 015.30E + 013.08E + 015.44E + 01
3.87E + 027.00E + 011.12E − 051.22E + 024.08E − 09
51.00E − 015.44E + 002.71E − 023.31E + 002.87E − 025.63E + 00
8.04E − 011.16E + 005.35E − 018.39E − 015.39E − 019.49E − 01
1.02E + 007.72E − 013.33E − 039.58E − 011.35E − 02
101.84E + 001.60E + 012.16E + 001.40E + 018.81E − 011.48E + 01
6.18E + 006.60E + 005.08E + 005.83E + 005.21E + 005.65E + 00
2.97E + 002.90E + 001.62E − 023.05E + 005.28E − 03
5
108.00E − 011.00E + 007.95E − 011.00E + 004.05E − 011.00E + 00
1.00E + 009.92E − 019.96E − 019.78E − 019.99E − 019.72E − 01
2.60E − 024.13E − 026.41E − 088.29E − 021.42E − 04
53.55E + 001.95E + 013.51E + 001.96E + 011.81E + 001.89E + 01
1.06E + 011.10E + 011.10E + 011.09E + 011.00E + 011.01E + 01
3.58E + 003.30E + 004.28E − 013.50E + 004.51E − 02
101.74E + 014.84E + 011.95E + 014.38E + 011.70E + 014.69E + 01
3.64E + 013.64E + 013.45E + 013.40E + 013.45E + 013.43E + 01
6.45E + 005.52E + 001.98E − 036.07E + 007.45E − 03
56.48E + 011.16E + 03
7.66E + 027.24E + 02
2.55E + 022.82E − 39
105.25E + 022.48E + 03
1.70E + 031.60E + 03
4.68E + 022.82E − 39
54.06E + 014.22E + 014.06E + 014.19E + 014.05E + 014.19E + 01
4.12E + 014.13E + 014.11E + 014.11E + 014.11E + 014.11E + 01
3.29E − 012.95E − 012.24E − 042.75E − 014.55E − 04
101.82E + 021.84E + 021.82E + 021.84E + 021.82E + 021.84E + 02
1.83E + 021.83E + 021.83E + 021.83E + 021.83E + 021.83E + 02
4.72E − 014.03E − 015.09E − 074.09E − 012.62E − 08
52.04E + 005.83E + 001.69E + 004.95E + 001.27E + 005.92E + 00
3.89E + 003.81E + 003.23E + 003.24E + 003.30E + 003.26E + 00
7.79E − 016.47E − 011.07E − 078.19E − 011.42E − 06
103.04E + 006.14E + 002.47E + 005.22E + 001.85E + 005.06E + 00
4.32E + 004.38E + 003.87E + 003.85E + 003.81E + 003.81E + 00
6.26E − 015.59E − 012.45E − 085.87E − 014.85E − 09
51.54E − 016.60E − 011.07E − 015.25E − 011.55E − 016.38E − 01
3.74E − 013.81E − 013.73E − 013.64E − 013.39E − 013.55E − 01
1.06E − 019.63E − 022.13E − 011.01E − 013.81E − 02
104.11E − 019.76E − 014.01E − 019.11E − 014.77E − 018.96E − 01
8.37E − 018.09E − 017.95E − 017.73E − 017.59E − 017.47E − 01
1.06E − 019.53E − 029.46E − 041.06E − 012.73E − 06
52.01E − 011.13E + 002.15E − 019.63E − 011.46E − 011.03E + 00
7.05E − 017.00E − 015.80E − 015.79E − 015.41E − 015.68E − 01
1.94E − 011.72E − 016.01E − 061.83E − 011.40E − 06
106.09E − 011.69E + 005.27E − 011.40E + 005.00E − 011.31E + 00
1.00E + 001.04E + 009.04E − 019.09E − 018.95E − 018.80E − 01
2.16E − 011.72E − 011.79E − 051.58E − 019.29E − 08
54.42E − 021.08E − 014.62E − 021.09E − 014.67E − 021.13E − 01
7.04E − 027.25E − 026.97E − 027.06E − 026.76E − 026.93E − 02
1.45E − 021.34E − 021.99E − 011.39E − 026.66E − 02
101.44E − 037.63E − 031.89E − 038.04E − 031.35E − 038.53E − 03
4.31E − 034.33E − 034.02E − 034.24E − 034.12E − 034.23E − 03
1.30E − 031.31E − 032.75E − 011.38E − 032.68E − 01

The best results in each row are emphasized in bold. The emphasized values in bold indicate that the Mann–Whitney U test with the significance level shows significance against the result without SHX. “—” represents invalid solutions (trapped by local optimum or out of parameter range

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