Research Article
A Constrained Solution Update Strategy for Multiobjective Evolutionary Algorithm Based on Decomposition
Table 1
IGD 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) | 2.26E-2 –
(1.52E-3) | 3.46E-1 –
(2.27E-2) | 2.69E-2 –
(3.53E-3) | 2.63E-2 –
(2.72E-3) | 3.62E-1 –
(7.47E-3) | 2.72E-2 –
(2.33E-3) | 1.66E-2 (4.38E-4) | | MOP2 | Mean
(Std) | 7.40E-3 –
(5.09E-4) | 2.95E-1 –
(7.83E-2) | 6.79E-2 –
(7.69E-2) | 6.02E-2 –
(6.46E-2) | 2.77E-1 –
(7.19E-2) | 3.13E-2 –
(6.67E-2) | 6.87E-3 (2.29E-3) | | MOP3 | Mean
(Std) | 1.04E-2 –
(2.20E-3) | 1.55E-1 –
(3.43E-2) | 3.85E-2 –
(5.83E-2) | 1.43E-2 –
(1.91E-2) | 1.23E-1 –
(4.82E-2) | 1.36E-2 –
(2.06E-2) | 8.14E-3 (3.76E-3) | | MOP4 | Mean
(Std) | 4.57E-3 = (3.39E-4) | 3.00E-1 –
(2.99E-2) | 3.52E-2 –
(3.23E-2) | 1.07E-1 –
(8.46E-2) | 2.76E-1 –
(3.24E-2) | 5.48E-2 –
(5.74E-2) | 4.47E-3 (1.22E-4) | | MOP5 | Mean
(Std) | 2.00E-2 –
(6.91E-4) | 3.12E-1 –
(2.78E-2) | 2.31E-2 –
(3.04E-3) | 2.16E-2 –
(2.41E-3) | 3.16E-1 –
(8.02E-3) | 2.39E-2 –
(2.31E-3) | 1.51E-2 (3.57E-4) | | MOP6 | Mean
(Std) | 4.96E-2 –
(1.58E-3) | 2.90E-1 –
(2.24E-2) | 4.90E-2 –
(2.36E-3) | 4.84E-2 –
(2.80E-3) | 2.90E-1 –
(2.56E-2) | 5.02E-2 –
(2.39E-3) | 3.30E-2 (2.80E-4) | | MOP7 | Mean
(Std) | 7.93E-2 –
(4.69E-3) | 3.51E-1 –
(8.93E-8) | 1.77E-1 –
(3.16E-2) | 1.92E-1 –
(1.86E-2) | 3.38E-1 –
(2.27E-2) | 2.33E-1 –
(2.47E-2) | 4.65E-2 (3.35E-4) | | IMB1 | Mean
(Std) | 1.04E-2 –
(6.11E-4) | 1.05E-1 –
(8.78E-2) | 1.23E-2 –
(1.33E-3) | 1.18E-2 –
(1.96E-3) | 1.76E-1 –
(7.14E-2) | 1.28E-2 –
(9.52E-4) | 7.53E-3 (1.36E-4) | | IMB2 | Mean
(Std) | 1.19E-2 –
(5.46E-4) | 1.62E-1 –
(1.16E-2) | 4.70E-2 –
(1.79E-2) | 6.64E-2 –
(2.46E-2) | 1.67E-1 –
(1.11E-2) | 5.85E-2 –
(1.84E-2) | 8.92E-3 (2.16E-4) | | IMB3 | Mean
(Std) | 1.78E-2 –
(7.66E-4) | 2.82E-1 –
(3.55E-2) | 2.56E-2 –
(3.48E-3) | 2.37E-2 –
(2.73E-3) | 2.84E-1 –
(1.42E-2) | 2.26E-2 –
(1.88E-3) | 1.19E-2 (3.16E-4) | | IMB4 | Mean
(Std) | 4.05E-2 –
(1.59E-3) | 1.33E-1 –
(6.92E-3) | 2.53E-2 +
(5.04E-4) | 2.39E-2 + (2.57E-4) | 1.37E-1 –
(6.97E-3) | 2.82E-2 =
(5.45E-4) | 2.79E-2
(2.19E-4) | | IMB5 | Mean
(Std) | 5.67E-2 –
(9.92E-3) | 8.40E-2 –
(2.47E-5) | 8.39E-2 –
(1.37E-5) | 7.90E-2 –
(4.61E-3) | 9.12E-2 –
(5.74E-5) | 7.41E-2 –
(7.50E-3) | 3.28E-2 (1.21E-4) | | IMB6 | Mean
(Std) | 3.85E-2 –
(5.24E-3) | 4.62E-2 –
(1.24E-4) | 4.61E-2 –
(2.12E-4) | 4.70E-2 –
(1.45E-4) | 5.22E-2 –
(6.28E-4) | 2.50E-2 –
(3.10E-4) | 2.37E-2 (8.71E-5) | | IMB7 | Mean
(Std) | 1.08E-2 –
(5.89E-4) | 2.98E-2 –
(2.28E-4) | 2.49E-2 –
(8.30E-3) | 2.76E-2 –
(2.76E-2) | 2.99E-2 –
(1.95E-4) | 2.85E-2 –
(6.95E-3) | 7.92E-3 (3.05E-4) | | IMB8 | Mean
(Std) | 1.24E-2 –
(5.30E-4) | 3.45E-2 –
(9.77E-4) | 2.61E-2 –
(1.06E-2) | 3.34E-2 –
(5.35E-3) | 3.38E-2 –
(3.58E-3) | 3.52E-2 –
(4.19E-3) | 9.40E-3 (3.81E-4) | | IMB9 | Mean
(Std) | 1.35E-2 –
(6.62E-4) | 3.84E-2 –
2.43E-4 | 3.25E-2 –
(9.16E-3) | 3.79E-2 –
(3.42E-3) | 3.83E-2 –
(2.29E-4) | 3.96E-2 –
(1.20E-3) | 1.18E-2 (6.18E-4) | | IMB10 | Mean
(Std) | 4.79E-2 –
(8.68E-4) | 2.82E-2 + (1.80E-3) | 3.29E-2 +
(9.61E-4) | 2.95E-2 +
(8.55E-4) | 3.63E-2 –
(1.95E-3) | 3.17E-2 +
(7.63E-4) | 3.57E-2
(3.02E-4) | | Better/Worse/Similar | 16/0/1 | 16/1/0 | 15/2/0 | 15/2/0 | 17/0/0 | 15/1/1 | |
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