Table 1 IGD metrics and HV metrics of each algorithm with 6 test functions.
Test Function | \(M\) | \(D\) | Metrics | MSNSGA-III | NSGA-III |
|---|---|---|---|---|---|
DLTZ1 | 4 | 13 | IGD | 3.2570e−01(1.916e−01) +  | 3.9852e−01(2.928e−01) |
HV | 3.2084e−01(3.351e−01) +  | 3.2673e−01(3.521e−01) | |||
DLTZ2 | 4 | 13 | IGD | 1.2848e−01(1.456e−03) +  | 1.4118e−01(3.080e−04) |
HV | 7.2513e−01(4.450e−03) +  | 6.8325e−01(2.021e−03) | |||
DLTZ4 | 4 | 13 | IGD | 2.2041e−01(1.361e−01) +  | 2.4312e−01(1.478e−01) |
HV | 6.7899e−01(7.395e−02) +  | 6.3334e−01(7.261e−02) | |||
DLTZ5 | 4 | 13 | IGD | 5.8220e−02(1.004e−02) +  | 6.6119e−02(1.215e−02) |
HV | 1.3447e−01(5.339e−03) +  | 1.2735e−01(5.356e−03) | |||
DLTZ6 | 4 | 13 | IGD | 4.5909e−01(3.937e−01) +  | 4.8814e−01(4.410e−01) |
HV | 3.1342e−02(4.148e−02) +  | 2.9201e−02(4.065e−02) | |||
DTLZ7 | 4 | 13 | IGD | 1.9929e−01(2.046e−02) +  | 2.2189e−01(1.365e−02) |
HV | 2.5397e−01(8.075e−03) +  | 2.4567e−01(8.168e−03) |