Research Article
A Constrained Solution Update Strategy for Multiobjective Evolutionary Algorithm Based on Decomposition
Table 2
HV comparison of results of MOEA/D-CSU and six competitors on all the MOP and IMB test problems.
| | | MOEA/D-M2M | MOEA/D-STM | MOEA/D-AGR | MOEA/D-IR | MOEA/D-DE | MOEA/D-ACD | MOEA/D-CSU |
| | MOP1 | Mean
(Std) | 6.95E-1 –
(1.78E-3) | 2.63E-1 –
(3.61E-2) | 6.92E-1 –
(4.23E-3) | 6.93E-1 –
(2.83E-3) | 2.38E-1 –
(1.37E-2) | 6.92E-1 –
(2.44E-3) | 7.03E-1 5.13E-4 | | MOP2 | Mean
(Std) | 4.39E-1 = (3.41E-4) | 2.02E-1 –
(4.86E-2) | 3.79E-1 –
(8.12E-2) | 3.86E-1 –
(6.67E-2) | 2.06E-1 –
(4.05E-2) | 4.12E-1 –
(6.60E-2) | 4.39E-1 3.60E-3 | | MOP3 | Mean
(Std) | 3.40E-1 –
(3.21E-3) | 2.15E-1 –
(2.90E-2) | 3.11E-1 –
(5.75E-2) | 3.32E-1 –
(2.64E-2) | 2.41E-1 –
(3.98E-2) | 3.33E-1 –
(2.68E-2) | 3.41E-1 4.00E-3 | | MOP4 | Mean
(Std) | 5.95E-1 = (8.24E-4) | 2.90E-1 –
(1.62E-2) | 5.69E-1 –
(3.57E-2) | 4.74E-1 –
(9.65E-2) | 3.01E-1 –
(2.31E-2) | 5.36E-1 –
(6.66E-2) | 5.95E-1 2.48E-4 | | MOP5 | Mean
(Std) | 6.96E-1 –
(1.13E-3) | 4.04E-1 –
(2.08E-2) | 6.94E-1 –
(4.87E-3) | 6.96E-1 –
(2.74E-3) | 4.00E-1 –
(1.03E-17) | 6.94E-1 –
(2.72E-3) | 7.03E-1 4.65E-4 | | MOP6 | Mean
(Std) | 8.22E-1 –
(1.74E-3) | 6.34E-1 –
(2.48E-2) | 8.24E-1 –
(3.62E-3) | 8.28E-1 –
(2.42E-3) | 6.34E-1 –
(2.97E-2) | 8.28E-1 –
(2.21E-3) | 8.40E-1 2.71E-4 | | MOP7 | Mean
(Std) | 5.41E-1 –
(4.43E-3) | 4.07E-1 –
(1.89E-7) | 4.97E-1 –
(3.39E-2) | 4.94E-1 –
(4.91E-3) | 4.12E-1 –
(1.02E-2) | 4.94E-1 –
(1.45E-2) | 5.45E-1 5.26E-4 | | IMB1 | Mean
(Std) | 7.11E-1 –
(7.41E-4) | 6.15E-1 –
(8.87E-2) | 7.09E-1 –
(1.56E-3) | 7.10E-1 –
(2.04E-3) | 5.43E-1 –
(6.95E-2) | 7.09E-1 –
(1.00E-3) | 7.15E-1 1.56E-4 | | IMB2 | Mean
(Std) | 5.70E-1 –
(7.03E-4) | 3.91E-1 –
(9.14E-3) | 5.25E-1 –
(2.33E-2) | 5.01E-1 –
(3.02E-2) | 3.90E-1 –
(7.18E-3) | 5.10E-1 –
(2.34E-2) | 5.74E-1 2.90E-4 | | IMB3 | Mean
(Std) | 3.29E-1 –
(7.63E-4) | 1.33E-1 –
(2.20E-2) | 3.24E-1 –
(1.97E-3) | 3.23E-1 –
(2.62E-3) | 1.28E-1 –
(7.18E-3) | 3.24E-1 –
(1.69E-3) | 3.35E-1 3.90E-4 | | IMB4 | Mean
(Std) | 8.23E-1 –
(2.44E-3) | 7.71E-1 –
(3.03E-3) | 8.49E-1 +
(7.80E-4) | 8.53E-1 + (4.54E-4) | 7.64E-1 –
(3.10E-3) | 8.46E-1 =
(9.63E-4) | 8.46E-1
2.45E-4 | | IMB5 | Mean
(Std) | 5.48E-1 –
(6.76E-3) | 5.45E-1 –
(2.31E-5) | 5.45E-1 –
(2.34E-5) | 5.43E-1 –
(7.91E-4) | 5.32E-1 –
(2.43E-4) | 5.42E-1 –
(8.46E-4) | 5.71E-1 2.71E-4 | | IMB6 | Mean
(Std) | 8.31E-1 –
(3.07E-3) | 8.41E-1 –
(3.53E-5) | 8.40E-1 –
(4.28E-5) | 8.40E-1 –
(1.44E-4) | 8.32E-1 –
(1.25E-3) | 8.52E-1 –
(3.58E-4) | 8.53E-1 1.11E-4 | | IMB7 | Mean
(Std) | 7.09E-1 –
(8.19E-4) | 6.95E-1 –
(5.16E-4) | 6.99E-1 –
(6.91E-3) | 6.97E-1 –
(5.58E-3) | 6.95E-1 –
(4.67E-4) | 6.96E-1 –
(5.87E-3) | 7.14E-1 5.14E-4 | | IMB8 | Mean
(Std) | 5.67E-1 –
(8.33E-4) | 5.45E-1 –
(1.14E-3) | 5.55E-1 –
(1.18E-2) | 5.46E-1 –
(6.04E-3) | 5.46E-1 –
(3.94E-3) | 5.44E-1 –
(4.77E-3) | 5.73E-1 5.41E-4 | | IMB9 | Mean
(Std) | 3.31E-1 –
(1.14E-3) | 3.13E-1 –
(8.88E-4) | 3.18E-1 –
(6.82E-3) | 3.14E-1 –
(2.49E-3) | 3.14E-1 –
(7.83E-4) | 3.11E-1 –
(2.02E-3) | 3.34E-1 9.06E-4 | | IMB10 | Mean
(Std) | 8.17E-1 –
(2.19E-3) | 8.48E-1 + (1.35E-3) | 8.39E-1 +
(1.23E-3) | 8.46E-1 +
(1.01E-3) | 8.34E-1 –
(3.05E-3) | 8.43E-1 +
(9.98E-4) | 8.36E-1
3.35E-4 | | Better/Worse/Similar | 15/0/2 | 16/1/0 | 15/2/0 | 15/2/0 | 17/0/0 | 15/1/1 | |
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