Table 9 The total number, the mean and standard deviation of each cost of feasible paths obtained by each algorithm when considering path length, threat cost and smooth cost as objective functions.

Scenario

Algorithm

MOPSO

NSGAII

NSGAIII

MOJS

MOGNDO

UMOJS

Scenario 1

Total number

699

846

1016

604

485

1092

Path length

Mean

1503.44

1125.39

1153.90

1576.27

1606.15

892.84

Std

221.74

226.42

202.78

501.70

375.06

1.49

Threat cost

Mean

1.90

3.90

3.94

3.07

2.74

3.86

Std

4.70

5.13

6.24

3.69

5.67

3.02

Smooth cost

Mean

278.23

78.91

69.53

203.99

502.56

0

Std

130.20

103.08

68.49

154.10

383.74

0

Altitude cost

Mean

370.95

423.08

397.79

395.53

408.68

385.22

Std

62.69

85.14

66.06

48.78

106.26

21.38

Scenario 2

Total number

82

227

528

117

49

1097

Path length

Mean

1770.02

1131.67

1180.88

1787.42

2445.88

943.30

Std

382.74

169.43

214.45

557.83

732.35

8.34

Threat cost

Mean

1.08

9.32

11.06

8.09

4.84

6.12

Std

3.00

7.58

9.75

7.39

5.41

6.24

Smooth cost

Mean

286.33

64.84

60.40

280.94

605.81

2.93

Std

132.71

65.43

106.14

253.25

266.55

15.90

Altitude cost

Mean

325.03

385.42

397.68

383.33

420.77

412.35

Std

48.10

76.97

112.09

46.84

38.63

23.06

Scenario 3

Total number

0

268

107

84

200

1084

Path length

Mean

-

1146.55

977.18

1475.10

3037.24

930.82

Std

-

203.61

119.16

313.92

1526.78

9.57

Threat cost

Mean

-

8.55

8.12

5.36

6.31

15.48

Std

-

8.63

7.29

5.62

9.00

12.38

Smooth cost

Mean

-

109.34

57.22

214.31

522.53

7.44

Std

-

128.69

110.00

130.57

189.53

32.79

Altitude cost

Mean

-

349.65

406.45

397.67

396.77

366.86

Std

-

90.90

102.03

54.03

50.50

13.71