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Table 3

Features of 10 runs of the MOALOA and NSGAII

AlgorithmFeatureRun 1Run 2Run 3Run 4Run 5Run 6Run 7Run 8Run 9Run 10
MOALOA Mean Euclidean distance between Pareto front and the origin of the coordinate system 0.40 0.61 0.58 0.62 0.53 0.57 0.50 0.47 0.45 0.51 
Number of points on the Pareto front 100 93 94 92 98 89 92 100 100 86 
Run Time (s) 2,950 2,743 2,695 2,849 2,615 2,754 2,917 2,825 2,990 2,890 
 Hyper Volume indicator for objective functions (1) and (2) 0.2 0.28 0.25 0.29 0.26 0.28 0.24 0.23 0.22 0.26 
 Hyper Volume indicator for objective functions (2) and (3) 0.1 0.13 0.13 0.12 0.11 0.11 0.12 0.1 0.11 0.12 
NSGAII Mean Euclidean distance between Pareto front and the origin of the coordinate system 0.57 0.53 0.58 0.69 0.58 0.61 0.59 0.60 0.60 0.60 
Number of points on the Pareto front 20 18 18 18 18 16 20 18 15 15 
Run Time (s) 2,985 2,864 2,689 2,762 2,889 2,850 2,828 2,735 2,963 2,912 
 Hyper Volume indicator for objective functions (1) and (2) 0.28 0.25 0.26 0.3 0.28 0.28 0.28 0.27 0.28 0.28 
 Hyper Volume indicator for objective functions (2) and (3) 0.1 0.1 0.11 0.13 0.1 0.13 0.11 0.13 0.11 0.12 
AlgorithmFeatureRun 1Run 2Run 3Run 4Run 5Run 6Run 7Run 8Run 9Run 10
MOALOA Mean Euclidean distance between Pareto front and the origin of the coordinate system 0.40 0.61 0.58 0.62 0.53 0.57 0.50 0.47 0.45 0.51 
Number of points on the Pareto front 100 93 94 92 98 89 92 100 100 86 
Run Time (s) 2,950 2,743 2,695 2,849 2,615 2,754 2,917 2,825 2,990 2,890 
 Hyper Volume indicator for objective functions (1) and (2) 0.2 0.28 0.25 0.29 0.26 0.28 0.24 0.23 0.22 0.26 
 Hyper Volume indicator for objective functions (2) and (3) 0.1 0.13 0.13 0.12 0.11 0.11 0.12 0.1 0.11 0.12 
NSGAII Mean Euclidean distance between Pareto front and the origin of the coordinate system 0.57 0.53 0.58 0.69 0.58 0.61 0.59 0.60 0.60 0.60 
Number of points on the Pareto front 20 18 18 18 18 16 20 18 15 15 
Run Time (s) 2,985 2,864 2,689 2,762 2,889 2,850 2,828 2,735 2,963 2,912 
 Hyper Volume indicator for objective functions (1) and (2) 0.28 0.25 0.26 0.3 0.28 0.28 0.28 0.27 0.28 0.28 
 Hyper Volume indicator for objective functions (2) and (3) 0.1 0.1 0.11 0.13 0.1 0.13 0.11 0.13 0.11 0.12 
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