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Table 3 Case Study 1: Evaluation of selected predicted Pareto solutions and derived quantities, iterations \(k=1\) (runs 16–24) and \(k=2\) (runs 25–33)

From: Simulation and multi-objective optimization to improve the final shape and process efficiency of a laser-based material accumulation process

Run

P

s

v

Δl

\(\Delta c_{xyz}\)

E

l − s

l/E

P/v

[W]

[mm]

[mm/s]

[mm]

[μm]

[J]

[mm]

[mm/J]

J/mm

16

36.16

2.89

44.94

−0.1476

30.29

2.32

−0.036

1.23

0.80

17

41.82

2.43

32.16

0.1693

29.24

3.17

0.735

1.00

1.30

18

51.52

2.53

46.77

−0.0082

21.91

2.78

0.467

1.08

1.10

19

57.98

2.53

57.72

−0.1198

2.80

2.54

0.355

1.14

1.00

20

66.87

2.51

68.68

−0.1810

19.86

2.44

0.314

1.16

0.97

21

89.50

2.95

156.31

−2.3755

175.73

1.69

−2.325

0.37

0.57

22

90.30

2.49

116.15

−0.5962

28.42

1.94

−0.091

1.24

0.78

23

95.96

2.59

132.58

−0.5483

52.90

1.87

−0.134

1.31

0.72

24

96.77

2.55

110.67

−0.3243

29.20

2.23

0.130

1.20

0.87

25

65.25

3.00

72.33

0.2082

20.50

2.71

0.208

1.19

0.90

26

74.14

3.00

81.46

0.2734

13.64

2.73

0.273

1.20

0.91

27

87.88

2.47

99.72

−0.3816

5.40

2.18

0.144

1.20

0.88

28

89.49

3.00

159.97

−2.5515

112.34

1.68

−2.551

0.27

0.56

29

93.54

2.60

130.75

−0.5173

60.11

1.86

−0.113

1.34

0.72

30

94.34

2.70

141.71

−0.4854

81.51

1.80

−0.182

1.40

0.67

31

98.38

2.99

172.75

−2.3875

171.07

1.70

−2.377

0.36

0.57

32

100.00

2.37

112.50

−0.5043

7.95

2.11

0.122

1.18

0.89

33

100.00

2.43

123.45

−0.6117

6.04

1.97

−0.046

1.21

0.81