Table 4 The IGD 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 | 5.33 × 10–03 | 4.98 × 10–03 | 8.50 × 10–03 | 4.98 × 10–03 | 6.20 × 10–03 | 1.05 × 10–02 | 4.93 × 10–03 |
Std | 1.00 × 10–03 | 4.19 × 10–04 | 5.46 × 10–04 | 3.18 × 10–04 | 4.75 × 10–04 | 1.28 × 10–03 | 2.58 × 10–04 | |
 ZDT2 | Mean | 5.04 × 10–03 | 5.40 × 10–03 | 8.62 × 10–03 | 5.41 × 10–03 | 5.11 × 10–03 | 1.09 × 10–02 | 4.91 × 10–03 |
Std | 6.79 × 10–04 | 2.10 × 10–03 | 5.12 × 10–04 | 7.15 × 10–04 | 3.77 × 10–04 | 7.91 × 10–04 | 2.52 × 10–04 | |
 ZDT3 | Mean | 5.95 × 10–03 | 6.21 × 10–03 | 8.24 × 10–03 | 1.02 × 10–02 | 4.44 × 10–03 | 1.36 × 10–02 | 5.28 × 10–03 |
Std | 5.74 × 10–04 | 9.00 × 10–04 | 3.79 × 10–04 | 1.81 × 10–03 | 1.87 × 10–04 | 1.61 × 10–02 | 1.75 × 10–04 | |
 ZDT4 | Mean | 5.00 × 10–03 | – | 8.28 × 10–03 | 9.95 × 10–03 | 4.94 × 10–03 | – | 4.89 × 10–03 |
Std | 1.94 × 10–03 | – | 5.03 × 10–04 | 5.28 × 10–04 | 7.86 × 10–05 | – | 2.91 × 10–04 | |
 ZDT6 | Mean | 4.61 × 10–03 | 4.13 × 10–03 | 6.02 × 10–02 | 4.91 × 10–03 | 6.64 × 10–03 | 1.19 × 10–02 | 3.18 × 10–03 |
Std | 1.58 × 10–03 | 8.18 × 10–04 | 1.61 × 10–02 | 5.78 × 10–04 | 2.54 × 10–03 | 3.28 × 10–01 | 5.73 × 10–04 | |
Three-objective test function | ||||||||
 DTLZ2 | Mean | 7.36 × 10–02 | 6.82 × 10–02 | 4.65 × 10–01 | 6.80 × 10–02 | 8.47 × 10–02 | 1.29 × 10–01 | 6.49 × 10–02 |
Std | 3.58 × 10–03 | 2.99 × 10–03 | 1.25 × 10–03 | 2.19 × 10–03 | 4.14 × 10–03 | 6.72 × 10–03 | 2.46 × 10–03 | |
 DTLZ4 | Mean | 6.36 × 10–02 | 8.62 × 10–02 | 4.20 × 10–01 | 8.62 × 10–02 | 7.79 × 10–02 | 9.31 × 10–02 | 6.12 × 10–02 |
Std | 1.82 × 10–02 | 5.56 × 10–03 | 2.05 × 10–03 | 4.60 × 10–03 | 4.34 × 10–03 | 6.85 × 10–03 | 4.17 × 10–03 | |
 DTLZ5 | Mean | 4.53 × 10–03 | 1.62 × 10–02 | 3.47 × 10–01 | 6.88 × 10–02 | 7.97 × 10–03 | 4.41 × 10–02 | 5.41 × 10–03 |
Std | 1.53 × 10–04 | 2.46 × 10–04 | 1.05 × 10–04 | 9.72 × 10–05 | 8.00 × 10–04 | 3.82 × 10–03 | 2.22 × 10–05 | |
 DTLZ6 | Mean | 5.48 × 10–03 | 2.29 × 10–02 | – | 6.51 × 10–02 | 7.04 × 10–03 | 1.16 × 10–02 | 5.46 × 10–03 |
Std | 8.15 × 10–04 | 3.51 × 10–04 | – | 1.00 × 10–03 | 1.00 × 10–04 | 1.10 × 10–03 | 3.72 × 10–04 | |
 DTLZ7 | Mean | 5.94 × 10–02 | 7.63 × 10–02 | 1.67 × 10–01 | 1.48 × 10–01 | 8.01 × 10–02 | 1.03 × 10–01 | 4.33 × 10–02 |
Std | 1.78 × 10–01 | 1.85 × 10–02 | 1.69 × 10–02 | 4.39 × 10–02 | 1.73 × 10–02 | 1.05 × 10–02 | 5.41 × 10–03 | |
 WFG4 | Mean | 3.13 × 10–01 | 5.20 × 10–01 | 4.76 × 10–01 | 5.35 × 10–01 | 3.73 × 10–01 | 5.11 × 10–01 | 3.07 × 10–01 |
Std | 3.88 × 10–02 | 1.70 × 10–02 | 2.79 × 10–02 | 8.51 × 10–03 | 1.49 × 10–02 | 2.89 × 10–02 | 9.89 × 10–03 | |
 WFG5 | Mean | 2.21 × 10–01 | 2.29 × 10–01 | 3.27 × 10–01 | 2.45 × 10–01 | 2.98 × 10–01 | 3.54 × 10–01 | 1.81 × 10–02 |
Std | 4.12 × 10–02 | 1.32 × 10–02 | 3.48 × 10–02 | 3.70 × 10–02 | 2.04 × 10–02 | 1.88 × 10–02 | 8.80 × 10–03 | |
 WFG6 | Mean | 4.13 × 10–01 | 3.36 × 10–01 | 5.27 × 10–01 | 4.53 × 10–01 | 4.23 × 10–01 | 4.91 × 10–01 | 2.69 × 10–01 |
Std | 1.11 × 10–02 | 5.27 × 10–03 | 6.53 × 10–02 | 2.79 × 10–02 | 3.29 × 10–02 | 8.49 × 10–03 | 8.63 × 10–03 | |
 WFG7 | Mean | 4.02 × 10–01 | 5.21 × 10–01 | 7.01 × 10–01 | 2.92 × 10–01 | 4.19 × 10–01 | 5.27 × 10–01 | 2.69 × 10–01 |
Std | 1.37 × 10–02 | 1.51 × 10–02 | 3.12 × 10–02 | 1.95 × 10–02 | 1.95 × 10–02 | 2.82 × 10–02 | 9.34 × 10–03 | |
 WFG8 | Mean | 6.24 × 10–01 | 1.07 × 10+00 | 8.73 × 10–01 | 7.47 × 10–01 | 4.98 × 10–01 | 6.73 × 10–01 | 4.01 × 10–01 |
Std | 1.50 × 10–02 | 2.18 × 10–02 | 4.27 × 10–02 | 9.08 × 10–03 | 1.32 × 10–02 | 3.64 × 10–02 | 8.19 × 10–03 | |
