Table 3 The GD values obtained by all algorithms.
From: NSCSO: a novel multi-objective non-dominated sorting chicken swarm optimization algorithm
Problem | Â | LMEA | WOF | MOSMA | DGEA | MOAHA | MOSPO | NSCSO |
|---|---|---|---|---|---|---|---|---|
Bi-objective test function | ||||||||
 ZDT1 | Mean | 6.63 × 10–05 | 4.51 × 10–05 | 2.48 × 10–04 | 4.93 × 10–05 | 2.07 × 10–04 | 6.38 × 10–04 | 6.03 × 10–05 |
Std | 4.35 × 10–05 | 4.48 × 10–05 | 3.53 × 10–05 | 1.74 × 10–04 | 3.57 × 10–05 | 2.29 × 10–04 | 3.48 × 10–05 | |
 ZDT2 | Mean | 9.47 × 10–05 | 9.45 × 10–05 | 3.12 × 10–04 | 9.45 × 10–05 | 1.43 × 10–04 | 5.14 × 10–04 | 9.29 × 10–05 |
Std | 6.25 × 10–06 | 5.70 × 10–06 | 2.94 × 10–05 | 5.17 × 10–06 | 2.18 × 10–05 | 2.35 × 10–04 | 4.72 × 10–06 | |
 ZDT3 | Mean | 1.98 × 10–04 | 2.12 × 10–04 | 2.21 × 10–04 | 5.78 × 10–03 | 1.93 × 10–04 | 4.26 × 10–04 | 1.77 × 10–04 |
Std | 1.38 × 10–05 | 1.67 × 10–04 | 1.26 × 10–05 | 2.56 × 10–05 | 1.51 × 10–05 | 1.19 × 10–04 | 1.44 × 10–05 | |
 ZDT4 | Mean | 1.68 × 10–04 | – | 1.81 × 10–04 | 5.14 × 10–05 | 1.63 × 10–04 | – | 5.00 × 10–05 |
Std | 3.57 × 10–04 | – | 3.61 × 10–05 | 1.83 × 10–04 | 4.93 × 10–05 | – | 5.32 × 10–05 | |
 ZDT6 | Mean | 1.15 × 10–03 | 1.22 × 10–03 | 6.02 × 10–02 | 1.11 × 10–03 | 3.72 × 10–02 | 9.29 × 10–02 | 3.18 × 10–03 |
Std | 1.86 × 10–03 | 5.18 × 10–04 | 1.61 × 10–02 | 4.24 × 10–04 | 3.39 × 10–02 | 9.21 × 10–02 | 5.73 × 10–04 | |
Three-objective test function | ||||||||
 DTLZ2 | Mean | 6.78 × 10–04 | 7.77 × 10–04 | 1.94 × 10–01 | 7.64 × 10–04 | 1.94 × 10–01 | 1.43 × 10–02 | 3.33 × 10–05 |
Std | 1.07 × 10–01 | 3.18 × 10–03 | 3.05 × 10–02 | 3.43 × 10–03 | 3.05 × 10–02 | 3.43 × 10–03 | 2.84 × 10–03 | |
 DTLZ4 | Mean | 4.88 × 10–03 | 5.67 × 10–03 | 2.04 × 10–01 | 5.67 × 10–03 | 2.04 × 10–01 | 8.73 × 10–03 | 6.73 × 10–05 |
Std | 8.15 × 10–04 | 5.87 × 10–04 | 3.71 × 10–02 | 1.05 × 10–03 | 3.71 × 10–02 | 3.85 × 10–03 | 2.70 × 10–04 | |
 DTLZ5 | Mean | 9.16 × 10–05 | 4.71 × 10–04 | 1.74 × 10–01 | 0.26 × 10–01 | 1.74 × 10–01 | 3.91 × 10–03 | 1.07 × 10–04 |
Std | 4.86 × 10–04 | 5.07 × 10–05 | 4.06 × 10–02 | 1.87 × 10–04 | 4.06 × 10–02 | 7.06 × 10–03 | 4.35 × 10–05 | |
 DTLZ6 | Mean | 4.86 × 10–04 | 4.31 × 10–04 | – | 0.53 × 10–01 | – | 3.46 × 10–02 | 2.91 × 10–04 |
Std | 8.57 × 10–05 | 4.16 × 10–05 | – | 2.87 × 10–04 | – | 8.08 × 10–02 | 3.72 × 10–05 | |
 DTLZ7 | Mean | 1.63 × 10–03 | 3.07 × 10–03 | 5.47 × 10–03 | 1.26 × 10–02 | 5.47 × 10–03 | 3.22 × 10–03 | 4.02 × 10–04 |
Std | 6.86 × 10–04 | 1.16 × 10–03 | 9.92 × 10–04 | 2.57 × 10–04 | 9.92 × 10–04 | 1.42 × 10–03 | 1.27 × 10–04 | |
 WFG4 | Mean | 2.25 × 10–02 | 1.65 × 10–02 | 3.79 × 10–02 | 2.44 × 10–02 | 2.56 × 10–02 | 3.90 × 10–02 | 1.68 × 10–02 |
Std | 5.38 × 10–03 | 9.05 × 10–03 | 3.51 × 10–03 | 6.87 × 10–03 | 1.16 × 10–03 | 1.63 × 10–03 | 1.08 × 10–03 | |
 WFG5 | Mean | 7.02 × 10–03 | 7.57 × 10–03 | 1.60 × 10–02 | 7.18 × 10–03 | 1.85 × 10–02 | 1.41 × 10–02 | 6.52 × 10–03 |
Std | 1.57 × 10–04 | 1.25 × 10–04 | 4.42 × 10–03 | 5.99 × 10–04 | 3.19 × 10–03 | 9.30 × 10–04 | 6.92 × 10–05 | |
 WFG6 | Mean | 5.19 × 10–03 | 1.02 × 10–02 | 2.57 × 10–02 | 9.66 × 10–03 | 2.48 × 10–02 | 3.49 × 10–02 | 9.34 × 10–04 |
Std | 4.83 × 10–03 | 3.82 × 10–03 | 3.89 × 10–03 | 5.41 × 10–03 | 1.17 × 10–03 | 1.52 × 10–03 | 1.39 × 10–03 | |
 WFG7 | Mean | 2.17 × 10–02 | 2.06 × 10–02 | 7.37 × 10–02 | 2.14 × 10–02 | 3.46 × 10–02 | 4.85 × 10–02 | 1.08 × 10–02 |
Std | 1.99 × 10–03 | 1.74 × 10–03 | 4.86 × 10–03 | 6.03 × 10–03 | 1.47 × 10–03 | 1.84 × 10–03 | 1.46 × 10–03 | |
 WFG8 | Mean | 6.77 × 10–02 | 8.41 × 10–02 | 6.83 × 10–02 | 8.37 × 10–02 | 4.44 × 10–02 | 6.42 × 10–02 | 3.12 × 10–02 |
Std | 1.53 × 10–03 | 2.80 × 10–03 | 4.53 × 10–03 | 1.04 × 10–03 | 2.09 × 10–03 | 2.20 × 10–03 | 8.83 × 10–04 | |
