Table 13 Statistical results of optimization methods on different benchmark functions.
Function | Global optima | Â | HS | DMOA | HS-DMOA | LUS |
|---|---|---|---|---|---|---|
F1 | 0 | Max | 9.88E + 02 | 0 | 0 | 9.90E-07 |
Min | 2.91E + 02 | 0 | 0 | 5.55E-07 | ||
Avg | 5.88E + 02 | 0 | 0 | 8.78E-07 | ||
Std | 2.13E + 02 | 0 | 0 | 1.34E-07 | ||
F2 | 0 | Max | 0 | 0 | 0 | 1.37E + 00 |
Min | 0 | 0 | 0 | 5.54E-02 | ||
Avg | 0 | 0 | 0 | 5.70E-01 | ||
Std | 0 | 0 | 0 | 4.72E-01 | ||
F3 | 0 | Max | 6.38E + 03 | 2.57E-04 | 3.09E-05 | 1.18E + 01 |
Min | 3.11E + 03 | 3.36E-05 | 1.11E-06 | 4.50E-01 | ||
Avg | 4.82E + 03 | 1.12E-04 | 9.25E-06 | 4.87E + 00 | ||
Std | 1.25E + 03 | 8.05E-05 | 8.92E-06 | 4.49E + 00 | ||
F4 | 0 | Max | 5.40E + 01 | 1.20E + 01 | 2.22E-02 | 8.42E-01 |
Min | 1.46E-08 | 2.90E-07 | 1.72E-09 | 1.83E-03 | ||
Avg | 1.78E + 01 | 1.20E + 00 | 2.22E-03 | 3.35E-01 | ||
Std | 1.51E + 01 | 3.80E + 00 | 7.04E-03 | 3.22E-01 | ||
F5 | 0 | Max | 4.50E + 05 | 1.62E + 01 | 6.23E + 00 | 8.97E + 00 |
Min | 2.86E + 03 | 1.86E + 00 | 1.31E-01 | 4.34E + 00 | ||
Avg | 1.28E + 05 | 5.79E + 00 | 2.84E + 00 | 6.63E + 00 | ||
Std | 1.27E + 05 | 3.81E + 00 | 2.26E + 00 | 1.55E + 00 | ||
F6 | 0 | Max | 7.70E + 02 | 0 | 0 | 9.92E-07 |
Min | 2.66E + 02 | 0 | 0 | 6.48E-07 | ||
Avg | 5.58E + 02 | 0 | 0 | 8.70E-07 | ||
Std | 1.52E + 02 | 0 | 0 | 1.04E-07 | ||
F7 | 0 | Max | 2.95E-01 | 6.09E-03 | 4.67E-03 | 5.42E-01 |
Min | 5.75E-02 | 2.46E-03 | 2.35E-03 | 2.63E-02 | ||
Avg | 1.69E-01 | 4.07E-03 | 3.39E-03 | 2.23E-01 | ||
Std | 8.12E-02 | 1.31E-03 | 7.51E-04 | 1.64E-01 |
