Table 3 presents the number of times that each parameter was optimized for the CDD watershed using the NSE, when moving from 1 to 19 parameters for the eight multi-objective optimizations. The vertical axis presents the 19 combinations of parameters from the Pareto front (as discussed earlier, the combinations of 20, 21, 22, and 23 parameters were not optimal, as these combinations were no better than the one with a 19-parameter model). The horizontal axis represents the number of times each of the 23 parameters was selected for each combination defining the Pareto front. For example, the first row indicates that when one parameter was selected to define the Pareto front, parameters 5, 14, and 22 were chosen twice while parameters 8 and 19 were selected once for a total of eight corresponding to the eight performed optimizations. The last column of each row is the summation of all chosen parameters divided by the number of parameters and should be equal to eight. If the number is less than eight, it simply indicates that one of the eight multi-objective optimizations did not retain this number of parameters as optimal, thus indicating better performance with a lesser number of parameters.
Number of parameters selected as being important for the eight MOGA optimizations using the NSE for the CDD watershed
PN . | P1 . | P2 . | P3 . | P4 . | P5 . | P6 . | P7 . | P8 . | P9 . | P10 . | P11 . | P12 . | P13 . | P14 . | P15 . | P16 . | P17 . | P18 . | P19 . | P20 . | P21 . | P22 . | P23 . | RN . |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Number of times that each parameter is selected during optimization for all eight multi-objective optimization runs | ||||||||||||||||||||||||
1 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 2 | 0 | 8 |
2 | 0 | 0 | 1 | 0 | 2 | 3 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 3 | 1 | 0 | 0 | 0 | 3 | 0 | 0 | 2 | 0 | 8 |
3 | 2 | 0 | 1 | 0 | 3 | 2 | 0 | 2 | 0 | 0 | 0 | 0 | 1 | 1 | 4 | 0 | 0 | 1 | 3 | 0 | 0 | 4 | 0 | 8 |
4 | 3 | 0 | 3 | 0 | 2 | 4 | 0 | 3 | 0 | 0 | 0 | 0 | 2 | 2 | 3 | 0 | 0 | 0 | 3 | 0 | 2 | 4 | 1 | 8 |
5 | 3 | 0 | 4 | 2 | 3 | 4 | 0 | 3 | 0 | 1 | 0 | 0 | 2 | 3 | 3 | 0 | 0 | 1 | 5 | 1 | 2 | 3 | 0 | 8 |
6 | 4 | 0 | 5 | 4 | 3 | 4 | 0 | 2 | 0 | 1 | 0 | 0 | 4 | 3 | 2 | 1 | 0 | 1 | 4 | 5 | 1 | 4 | 0 | 8 |
7 | 5 | 0 | 5 | 5 | 2 | 5 | 0 | 2 | 0 | 1 | 1 | 1 | 3 | 3 | 3 | 1 | 0 | 1 | 5 | 5 | 2 | 6 | 0 | 8 |
8 | 7 | 0 | 4 | 5 | 5 | 5 | 0 | 5 | 0 | 0 | 1 | 1 | 6 | 2 | 1 | 1 | 1 | 1 | 5 | 6 | 2 | 6 | 0 | 8 |
9 | 8 | 0 | 5 | 6 | 4 | 6 | 0 | 4 | 0 | 0 | 3 | 2 | 5 | 2 | 1 | 1 | 0 | 2 | 6 | 8 | 2 | 6 | 1 | 8 |
10 | 7 | 3 | 5 | 6 | 4 | 6 | 1 | 6 | 0 | 0 | 3 | 3 | 5 | 2 | 1 | 2 | 1 | 1 | 7 | 8 | 2 | 6 | 1 | 8 |
11 | 8 | 1 | 7 | 6 | 4 | 6 | 1 | 7 | 0 | 0 | 5 | 4 | 6 | 1 | 1 | 2 | 1 | 3 | 7 | 8 | 3 | 6 | 1 | 8 |
12 | 8 | 4 | 7 | 6 | 4 | 7 | 1 | 7 | 0 | 0 | 5 | 2 | 6 | 1 | 3 | 2 | 2 | 3 | 7 | 8 | 5 | 6 | 2 | 8 |
13 | 8 | 5 | 8 | 7 | 6 | 6 | 1 | 7 | 0 | 0 | 5 | 3 | 6 | 2 | 4 | 2 | 1 | 6 | 8 | 8 | 3 | 6 | 2 | 8 |
14 | 6 | 5 | 6 | 5 | 4 | 5 | 1 | 5 | 0 | 2 | 4 | 3 | 5 | 1 | 3 | 1 | 1 | 3 | 6 | 6 | 5 | 5 | 2 | 6 |
15 | 7 | 6 | 7 | 6 | 5 | 6 | 2 | 7 | 2 | 3 | 4 | 3 | 6 | 1 | 4 | 2 | 1 | 3 | 7 | 7 | 5 | 6 | 5 | 7 |
16 | 4 | 2 | 4 | 3 | 2 | 3 | 2 | 4 | 1 | 3 | 4 | 3 | 3 | 1 | 3 | 2 | 0 | 3 | 4 | 4 | 2 | 4 | 3 | 4 |
17 | 4 | 2 | 4 | 3 | 3 | 4 | 1 | 4 | 1 | 1 | 4 | 3 | 3 | 2 | 3 | 2 | 2 | 3 | 4 | 4 | 3 | 4 | 4 | 4 |
18 | 5 | 4 | 5 | 4 | 4 | 3 | 2 | 5 | 2 | 5 | 5 | 5 | 3 | 3 | 3 | 4 | 3 | 4 | 5 | 5 | 3 | 5 | 3 | 5 |
19 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
Sum | 90 | 33 | 82 | 69 | 63 | 80 | 12 | 76 | 6 | 18 | 45 | 34 | 67 | 35 | 44 | 24 | 14 | 37 | 91 | 84 | 43 | 86 | 25 | 131 |
Ratio | 0.69 | 0.25 | 0.63 | 0.53 | 0.48 | 0.61 | 0.09 | 0.58 | 0.05 | 0.14 | 0.34 | 0.26 | 0.51 | 0.27 | 0.34 | 0.18 | 0.11 | 0.28 | 0.70 | 0.64 | 0.33 | 0.66 | 0.19 |
PN . | P1 . | P2 . | P3 . | P4 . | P5 . | P6 . | P7 . | P8 . | P9 . | P10 . | P11 . | P12 . | P13 . | P14 . | P15 . | P16 . | P17 . | P18 . | P19 . | P20 . | P21 . | P22 . | P23 . | RN . |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Number of times that each parameter is selected during optimization for all eight multi-objective optimization runs | ||||||||||||||||||||||||
1 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 2 | 0 | 8 |
2 | 0 | 0 | 1 | 0 | 2 | 3 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 3 | 1 | 0 | 0 | 0 | 3 | 0 | 0 | 2 | 0 | 8 |
3 | 2 | 0 | 1 | 0 | 3 | 2 | 0 | 2 | 0 | 0 | 0 | 0 | 1 | 1 | 4 | 0 | 0 | 1 | 3 | 0 | 0 | 4 | 0 | 8 |
4 | 3 | 0 | 3 | 0 | 2 | 4 | 0 | 3 | 0 | 0 | 0 | 0 | 2 | 2 | 3 | 0 | 0 | 0 | 3 | 0 | 2 | 4 | 1 | 8 |
5 | 3 | 0 | 4 | 2 | 3 | 4 | 0 | 3 | 0 | 1 | 0 | 0 | 2 | 3 | 3 | 0 | 0 | 1 | 5 | 1 | 2 | 3 | 0 | 8 |
6 | 4 | 0 | 5 | 4 | 3 | 4 | 0 | 2 | 0 | 1 | 0 | 0 | 4 | 3 | 2 | 1 | 0 | 1 | 4 | 5 | 1 | 4 | 0 | 8 |
7 | 5 | 0 | 5 | 5 | 2 | 5 | 0 | 2 | 0 | 1 | 1 | 1 | 3 | 3 | 3 | 1 | 0 | 1 | 5 | 5 | 2 | 6 | 0 | 8 |
8 | 7 | 0 | 4 | 5 | 5 | 5 | 0 | 5 | 0 | 0 | 1 | 1 | 6 | 2 | 1 | 1 | 1 | 1 | 5 | 6 | 2 | 6 | 0 | 8 |
9 | 8 | 0 | 5 | 6 | 4 | 6 | 0 | 4 | 0 | 0 | 3 | 2 | 5 | 2 | 1 | 1 | 0 | 2 | 6 | 8 | 2 | 6 | 1 | 8 |
10 | 7 | 3 | 5 | 6 | 4 | 6 | 1 | 6 | 0 | 0 | 3 | 3 | 5 | 2 | 1 | 2 | 1 | 1 | 7 | 8 | 2 | 6 | 1 | 8 |
11 | 8 | 1 | 7 | 6 | 4 | 6 | 1 | 7 | 0 | 0 | 5 | 4 | 6 | 1 | 1 | 2 | 1 | 3 | 7 | 8 | 3 | 6 | 1 | 8 |
12 | 8 | 4 | 7 | 6 | 4 | 7 | 1 | 7 | 0 | 0 | 5 | 2 | 6 | 1 | 3 | 2 | 2 | 3 | 7 | 8 | 5 | 6 | 2 | 8 |
13 | 8 | 5 | 8 | 7 | 6 | 6 | 1 | 7 | 0 | 0 | 5 | 3 | 6 | 2 | 4 | 2 | 1 | 6 | 8 | 8 | 3 | 6 | 2 | 8 |
14 | 6 | 5 | 6 | 5 | 4 | 5 | 1 | 5 | 0 | 2 | 4 | 3 | 5 | 1 | 3 | 1 | 1 | 3 | 6 | 6 | 5 | 5 | 2 | 6 |
15 | 7 | 6 | 7 | 6 | 5 | 6 | 2 | 7 | 2 | 3 | 4 | 3 | 6 | 1 | 4 | 2 | 1 | 3 | 7 | 7 | 5 | 6 | 5 | 7 |
16 | 4 | 2 | 4 | 3 | 2 | 3 | 2 | 4 | 1 | 3 | 4 | 3 | 3 | 1 | 3 | 2 | 0 | 3 | 4 | 4 | 2 | 4 | 3 | 4 |
17 | 4 | 2 | 4 | 3 | 3 | 4 | 1 | 4 | 1 | 1 | 4 | 3 | 3 | 2 | 3 | 2 | 2 | 3 | 4 | 4 | 3 | 4 | 4 | 4 |
18 | 5 | 4 | 5 | 4 | 4 | 3 | 2 | 5 | 2 | 5 | 5 | 5 | 3 | 3 | 3 | 4 | 3 | 4 | 5 | 5 | 3 | 5 | 3 | 5 |
19 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
Sum | 90 | 33 | 82 | 69 | 63 | 80 | 12 | 76 | 6 | 18 | 45 | 34 | 67 | 35 | 44 | 24 | 14 | 37 | 91 | 84 | 43 | 86 | 25 | 131 |
Ratio | 0.69 | 0.25 | 0.63 | 0.53 | 0.48 | 0.61 | 0.09 | 0.58 | 0.05 | 0.14 | 0.34 | 0.26 | 0.51 | 0.27 | 0.34 | 0.18 | 0.11 | 0.28 | 0.70 | 0.64 | 0.33 | 0.66 | 0.19 |
Note: Roman, italic, bold, and underline denote the most important, important, average, and least important, respectively.
PN, the number of free parameters; RN, number of runs using PN; Sum, summation of the number of times the parameter was present in a Pareto-optimal set.