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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