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Table 1 Mean and standard deviation values of GD, SSM and OO between INSGA-II, MO-NSGA-II, SHAMODE-WO, IMOPSO, MOEA/D-URAW and IMODE over 100 runs on eight given different final points (× 10−2)

From: Multi-objective Trajectory Planning Method based on the Improved Elitist Non-dominated Sorting Genetic Algorithm

Final point Performance metric INSGA-II MO-INSGA-II SHAMODE-WO IMOPSO MOEA/D-URAW IMODE
Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD
FPH1 IGD 2.15 0.698 4.02 1.07 6.53 1.62 10.4 3.04 8.25 2.16 20.1 8.27
HV 76.4 3.23 73.3 3.19 67.1 3.59 64.9 5.20 61.7 6.37 60.1 7.62
OO 17.0 2.93 20.9 4.61 16.1 2.18 16.0 2.84 15.9 2.48 10.9 3.22
FPH2 IGD 2.24 0.636 4.17 0.997 6.79 1.82 11.8 4.53 8.31 2.20 19.8 7.92
HV 75.2 3.05 76.7 3.29 67.3 3.50 64.9 5.19 63.9 5.97 60.7 7.02
OO 17.4 2.58 20.4 4.37 15.4 2.12 11.9 2.83 15.9 2.48 11.4 3.01
FPH3 IGD 2.34 0.587 4.32 0.955 6.77 1.78 11.3 4.01 8.34 2.23 19.5 7.58
HV 78.1 2.92 76.1 3.28 67.3 3.45 64.9 5.19 66.1 5.63 61.4 6.57
OO 17.8 2.34 19.9 4.13 15.7 2.17 12.9 2.53 15.9 2.50 11.9 2.83
FPH4 IGD 2.43 0.554 4.47 0.946 6.76 1.73 10.9 3.51 8.38 2.26 19.2 7.24
HV 76.9 2.82 75.4 3.32 67.5 3.45 64.9 5.18 68.3 5.38 62.1 6.30
OO 18.2 2.23 19.4 3.90 15.9 2.25 13.9 2.36 15.9 2.53 12.4 2.68
FPH5 IGD 2.52 0.540 4.62 0.971 6.74 1.69 10.4 3.04 8.42 2.29 18.9 6.90
HV 75.8 2.77 74.8 3.39 67.3 3.51 64.9 5.11 70.6 5.21 62.8 6.23
OO 18.5 2.28 18.9 3.69 16.3 2.35 14.9 2.35 15.9 2.57 12.9 2.57
FPH6 IGD 2.62 0.546 4.76 1.03 6.73 1.65 9.93 2.60 8.45 2.33 18.6 6.57
HV 74.6 2.77 74.2 3.49 67.3 3.63 64.9 5.13 72.8 5.14 63.5 6.39
OO 18.9 2.48 18.5 3.49 16.5 2.47 15.9 2.49 15.9 2.60 13.5 2.51
FPH7 IGD 2.71 0.573 4.91 1.11 6.72 1.61 9.46 2.22 8.49 2.36 18.26 6.24
HV 73.4 2.82 73.5 3.63 67.3 3.79 64.9 5.15 75.0 5.18 64.1 6.73
OO 19.3 2.78 17.9 3.31 16.8 2.61 16.9 2.78 16.0 2.65 13.9 2.48
FPH8 IGD 2.80 0.62 5.06 1.21 6.70 1.58 8.99 1.94 8.53 2.39 17.9 5.91
HV 77.3 2.91 72.9 3.79 67.3 3.98 64.8 5.14 77.2 5.32 64.8 7.25
OO 19.7 3.18 17.5 3.15 17.1 2.77 17.9 3.15 16.1 2.69 14.5 2.51