1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
|
analysis= class=MultiObjectiveOptimizationAnalysis name=optim physicalModel=aModelPhys algorithmName=nsga2 number of generations=10 blockSize=1 starting population size=50 bounds=[[0, 5],[0, 0],[0, 5]] variable inputs=[X0,X1] variable types=[0,0,2] variables of interest=[Y0,Y1] minimization=[Y0,Y2,Y1] constraints=[Y0<3.] maximumConstraintError=1e-05 seed=0
results=
class=MultiObjectiveOptimizationAnalysisResult fronts=[ [ Y0 Y1 ]
0 : [ 0.0118802 0.992246 ], [ Y0 Y1 ]
0 : [ 0.0151824 1.00528 ], [ Y0 Y1 ]
0 : [ 0.0157035 1.00746 ], [ Y0 Y1 ]
0 : [ 0.0157035 18.5931 ]
1 : [ 0.0323259 1.08665 ]
2 : [ 0.0323148 9.71416 ], [ Y0 Y1 ]
0 : [ 0.0323438 1.08674 ], [ Y0 Y1 ]
0 : [ 0.0323446 1.08675 ]
1 : [ 0.0323446 1.08675 ]
2 : [ 0.0323446 1.08675 ]
3 : [ 0.0323446 1.08675 ]
4 : [ 0.0323446 1.08675 ], [ Y0 Y1 ]
0 : [ 0.0323446 9.71416 ]
1 : [ 0.032388 1.08697 ]
2 : [ 0.032388 1.08697 ]
3 : [ 0.032388 1.08697 ]
4 : [ 0.0323446 9.71416 ], [ Y0 Y1 ]
0 : [ 0.0325405 1.08775 ]
1 : [ 0.0323446 18.5012 ]
2 : [ 0.0323446 18.5012 ]
3 : [ 0.032388 18.501 ]
4 : [ 0.032388 18.501 ]
5 : [ 0.032383 18.5011 ], [ Y0 Y1 ]
0 : [ 0.0325574 18.5005 ]
1 : [ 0.0326313 1.08822 ]
2 : [ 0.0323446 36.1928 ], [ Y0 Y1 ]
0 : [ 0.0327228 9.7141 ]
1 : [ 0.0345148 1.09795 ], [ Y0 Y1 ]
0 : [ 0.0328649 18.4994 ]
1 : [ 0.0345376 1.09806 ], [ Y0 Y1 ]
0 : [ 0.0345533 1.09814 ]
1 : [ 0.0345533 1.09814 ]
2 : [ 0.0345533 1.09814 ]
3 : [ 0.0345533 1.09814 ], [ Y0 Y1 ]
0 : [ 0.0356064 1.10362 ]
1 : [ 0.0345533 9.71409 ]
2 : [ 0.0356064 1.10362 ]
3 : [ 0.0356064 1.10362 ], [ Y0 Y1 ]
0 : [ 0.0356052 18.491 ]
1 : [ 0.0356064 9.71426 ]
2 : [ 0.0356279 1.10374 ]
3 : [ 0.0356064 9.71426 ], [ Y0 Y1 ]
0 : [ 0.0358094 1.10468 ]
1 : [ 0.0356064 18.491 ]
2 : [ 0.0357194 18.4907 ], [ Y0 Y1 ]
0 : [ 0.0358179 1.10473 ], [ Y0 Y1 ]
0 : [ 0.0359637 1.10549 ]
1 : [ 0.0359635 9.71435 ]]#17 finalPop=class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=48 dimension=8 description=[X0,X2,X1,Y0,Y1,Y2,_feasibility_,_front_index_] data=[[0.0118802,0,0,0.0118802,0.992246,0,1,0],[0.0151824,0,0,0.0151824,1.00528,0,1,1],[0.0157035,0,0,0.0157035,1.00746,0,1,2],[0.0157035,0,2,0.0157035,18.5931,2,1,3],[0.0323259,0,0,0.0323259,1.08665,0,1,3],[0.0323148,0,1,0.0323148,9.71416,1,1,3],[0.0323438,0,0,0.0323438,1.08674,0,1,4],[0.0323446,0,0,0.0323446,1.08675,0,1,5],[0.0323446,0,0,0.0323446,1.08675,0,1,5],[0.0323446,0,0,0.0323446,1.08675,0,1,5],[0.0323446,0,0,0.0323446,1.08675,0,1,5],[0.0323446,0,0,0.0323446,1.08675,0,1,5],[0.0323446,0,1,0.0323446,9.71416,1,1,6],[0.032388,0,0,0.032388,1.08697,0,1,6],[0.032388,0,0,0.032388,1.08697,0,1,6],[0.032388,0,0,0.032388,1.08697,0,1,6],[0.0323446,0,1,0.0323446,9.71416,1,1,6],[0.0325405,0,0,0.0325405,1.08775,0,1,7],[0.0323446,0,2,0.0323446,18.5012,2,1,7],[0.0323446,0,2,0.0323446,18.5012,2,1,7],[0.032388,0,2,0.032388,18.501,2,1,7],[0.032388,0,2,0.032388,18.501,2,1,7],[0.032383,0,2,0.032383,18.5011,2,1,7],[0.0325574,0,2,0.0325574,18.5005,2,1,8],[0.0326313,0,0,0.0326313,1.08822,0,1,8],[0.0323446,0,4,0.0323446,36.1928,4,1,8],[0.0327228,0,1,0.0327228,9.7141,1,1,9],[0.0345148,0,0,0.0345148,1.09795,0,1,9],[0.0328649,0,2,0.0328649,18.4994,2,1,10],[0.0345376,0,0,0.0345376,1.09806,0,1,10],[0.0345533,0,0,0.0345533,1.09814,0,1,11],[0.0345533,0,0,0.0345533,1.09814,0,1,11],[0.0345533,0,0,0.0345533,1.09814,0,1,11],[0.0345533,0,0,0.0345533,1.09814,0,1,11],[0.0356064,0,0,0.0356064,1.10362,0,1,12],[0.0345533,0,1,0.0345533,9.71409,1,1,12],[0.0356064,0,0,0.0356064,1.10362,0,1,12],[0.0356064,0,0,0.0356064,1.10362,0,1,12],[0.0356052,0,2,0.0356052,18.491,2,1,13],[0.0356064,0,1,0.0356064,9.71426,1,1,13],[0.0356279,0,0,0.0356279,1.10374,0,1,13],[0.0356064,0,1,0.0356064,9.71426,1,1,13],[0.0358094,0,0,0.0358094,1.10468,0,1,14],[0.0356064,0,2,0.0356064,18.491,2,1,14],[0.0357194,0,2,0.0357194,18.4907,2,1,14],[0.0358179,0,0,0.0358179,1.10473,0,1,15],[0.0359637,0,0,0.0359637,1.10549,0,1,16],[0.0359635,0,1,0.0359635,9.71435,1,1,16]]
final population=
[ X0 X2 X1 Y0 Y1 Y2 _feasibility_ _front_index_ ]
0 : [ 0.0118802 0 0 0.0118802 0.992246 0 1 0 ]
1 : [ 0.0151824 0 0 0.0151824 1.00528 0 1 1 ]
2 : [ 0.0157035 0 0 0.0157035 1.00746 0 1 2 ]
3 : [ 0.0157035 0 2 0.0157035 18.5931 2 1 3 ]
4 : [ 0.0323259 0 0 0.0323259 1.08665 0 1 3 ]
5 : [ 0.0323148 0 1 0.0323148 9.71416 1 1 3 ]
6 : [ 0.0323438 0 0 0.0323438 1.08674 0 1 4 ]
7 : [ 0.0323446 0 0 0.0323446 1.08675 0 1 5 ]
8 : [ 0.0323446 0 0 0.0323446 1.08675 0 1 5 ]
9 : [ 0.0323446 0 0 0.0323446 1.08675 0 1 5 ]
10 : [ 0.0323446 0 0 0.0323446 1.08675 0 1 5 ]
11 : [ 0.0323446 0 0 0.0323446 1.08675 0 1 5 ]
12 : [ 0.0323446 0 1 0.0323446 9.71416 1 1 6 ]
13 : [ 0.032388 0 0 0.032388 1.08697 0 1 6 ]
14 : [ 0.032388 0 0 0.032388 1.08697 0 1 6 ]
15 : [ 0.032388 0 0 0.032388 1.08697 0 1 6 ]
16 : [ 0.0323446 0 1 0.0323446 9.71416 1 1 6 ]
17 : [ 0.0325405 0 0 0.0325405 1.08775 0 1 7 ]
18 : [ 0.0323446 0 2 0.0323446 18.5012 2 1 7 ]
19 : [ 0.0323446 0 2 0.0323446 18.5012 2 1 7 ]
20 : [ 0.032388 0 2 0.032388 18.501 2 1 7 ]
21 : [ 0.032388 0 2 0.032388 18.501 2 1 7 ]
22 : [ 0.032383 0 2 0.032383 18.5011 2 1 7 ]
23 : [ 0.0325574 0 2 0.0325574 18.5005 2 1 8 ]
24 : [ 0.0326313 0 0 0.0326313 1.08822 0 1 8 ]
25 : [ 0.0323446 0 4 0.0323446 36.1928 4 1 8 ]
26 : [ 0.0327228 0 1 0.0327228 9.7141 1 1 9 ]
27 : [ 0.0345148 0 0 0.0345148 1.09795 0 1 9 ]
28 : [ 0.0328649 0 2 0.0328649 18.4994 2 1 10 ]
29 : [ 0.0345376 0 0 0.0345376 1.09806 0 1 10 ]
30 : [ 0.0345533 0 0 0.0345533 1.09814 0 1 11 ]
31 : [ 0.0345533 0 0 0.0345533 1.09814 0 1 11 ]
32 : [ 0.0345533 0 0 0.0345533 1.09814 0 1 11 ]
33 : [ 0.0345533 0 0 0.0345533 1.09814 0 1 11 ]
34 : [ 0.0356064 0 0 0.0356064 1.10362 0 1 12 ]
35 : [ 0.0345533 0 1 0.0345533 9.71409 1 1 12 ]
36 : [ 0.0356064 0 0 0.0356064 1.10362 0 1 12 ]
37 : [ 0.0356064 0 0 0.0356064 1.10362 0 1 12 ]
38 : [ 0.0356052 0 2 0.0356052 18.491 2 1 13 ]
39 : [ 0.0356064 0 1 0.0356064 9.71426 1 1 13 ]
40 : [ 0.0356279 0 0 0.0356279 1.10374 0 1 13 ]
41 : [ 0.0356064 0 1 0.0356064 9.71426 1 1 13 ]
42 : [ 0.0358094 0 0 0.0358094 1.10468 0 1 14 ]
43 : [ 0.0356064 0 2 0.0356064 18.491 2 1 14 ]
44 : [ 0.0357194 0 2 0.0357194 18.4907 2 1 14 ]
45 : [ 0.0358179 0 0 0.0358179 1.10473 0 1 15 ]
46 : [ 0.0359637 0 0 0.0359637 1.10549 0 1 16 ]
47 : [ 0.0359635 0 1 0.0359635 9.71435 1 1 16 ]
#!/usr/bin/env python
import openturns as ot
import persalys
myStudy = persalys.Study('myStudy')
persalys.Study.Add(myStudy)
X0 = persalys.Input('X0', 0, '')
X2 = persalys.Input('X2', 0, '')
X1 = persalys.Input('X1', 0, '')
Y0 = persalys.Output('Y0', '')
Y2 = persalys.Output('Y2', '')
Y1 = persalys.Output('Y1', '')
inputs = [X0, X2, X1]
outputs = [Y0, Y2, Y1]
formulas = ['X0', 'X1', 'var g := 1.0 + 9.0 * (X0 + X1); g * (1.0 - sqrt(X0 / g))']
aModelPhys = persalys.SymbolicPhysicalModel('aModelPhys', inputs, outputs, formulas)
myStudy.add(aModelPhys)
optim = persalys.MultiObjectiveOptimizationAnalysis('optim', aModelPhys, 'nsga2')
interestVariables = ['Y0', 'Y1']
optim.setInterestVariables(interestVariables)
optim.setMinimization(['Y0', 'Y2', 'Y1'])
bounds = ot.Interval([0, 0, 0], [5, 0, 5])
optim.addConstraint("Y0<3.")
optim.setBounds(bounds)
optim.setPopulationSize(50)
optim.setGenerationNumber(10)
optim.setBlockSize(1)
optim.setVariableInputs(['X0', 'X1'])
optim.setVariablesType([0, 0, 2])
myStudy.add(optim)
|
