AdaptiveNormalization: Objective space normalization.
In MaOEA: Many Objective Evolutionary Algorithm
Description
Usage
Arguments
Value
Examples
Description
Normalize the objectives to 0-1. The origin is the ideal point. (1,...,1) is not the nadir point.
The normalization is done by using adaptive normalization used in NSGA-III.
Usage
1
AdaptiveNormalization(objectiveValue)
Arguments
objectiveValue
Set of objective vectors to normalize
Value
A list containing the following:
normalizedObjective The normalized values
idealPoint The ideal point corresponding to the origin
nadirPoint The location of nadir point in the normalized Space
Examples
1
2
3
4
5
6
7
8
9
Example output
Check required python modules:
reticulate::py_module_available('numpy') and reticulate::py_module_available('pygmo').
If not available, try using MaOEA::install_python_dependencies()
or follow the instructions in https://esa.github.io/pagmo2/install.html
and call MaOEA::load_python_dependencies().
$normalizedObjective
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.05648679 0.001472863 0.03285909 0.27293512 0.03678232 0.009515391
[2,] 0.02382927 0.005128712 0.01794660 0.13451228 0.01359563 0.015231071
[3,] 0.21095706 0.014997285 0.03939423 0.03354975 0.03574221 0.029412144
[4,] 0.19946021 0.000000000 0.02707473 0.24680090 0.02181673 0.104629247
[5,] 0.90930911 0.974883792 0.98520110 0.05742719 0.97085824 0.968249634
[,7] [,8] [,9] [,10] [,11] [,12]
[1,] 0.04975852 0.020216126 0.07910876 0.008540803 0.015160438 0.009812862
[2,] 0.01200320 0.008979619 0.05333916 0.003701728 0.008988469 0.008198087
[3,] 0.15042067 0.070533765 0.11339754 0.014853317 0.015970428 0.007770556
[4,] 0.80893407 0.161300439 0.32679459 0.089491080 0.046675695 0.013874197
[5,] 0.51348192 0.959924006 0.87198237 0.971824157 0.983580410 0.981607681
[,13] [,14] [,15] [,16] [,17] [,18]
[1,] 0.006690424 0.1410935 0.03080473 0.016045514 0.08680722 0.22749022
[2,] 0.013155203 0.1782149 0.02882942 0.008705316 0.11059544 0.02358204
[3,] 0.032313830 0.2162834 0.03228781 0.020932989 0.47378464 0.03276539
[4,] 0.260289301 0.5919080 0.85332344 0.076714505 0.24308486 0.65828273
[5,] 0.932707067 0.3617935 0.47902722 0.976647936 0.55299338 0.13171747
[,19] [,20] [,21] [,22] [,23] [,24]
[1,] 0.03902942 0.11047582 0.03023335 0.013326152 0.03667296 0.08475060
[2,] 0.02725533 0.12293776 0.01824393 0.007855445 0.02929790 0.05049393
[3,] 0.05346685 0.57485082 0.01456701 0.032705998 0.09179842 0.08307390
[4,] 0.01408240 0.05285134 0.14250373 0.111899006 0.95482649 0.87146652
[5,] 0.97821372 0.29823002 0.96889757 0.971723345 0.23843998 0.32641930
[,25] [,26] [,27] [,28] [,29] [,30]
[1,] 0.008132462 0.011482031 0.01709511 0.01838634 0.026117691 0.15329321
[2,] 0.006796376 0.005512279 0.01205346 0.01763083 0.007586351 0.07343904
[3,] 0.010874137 0.010715519 0.01878527 0.06868508 0.132076639 0.03376697
[4,] 0.012001279 0.006854380 0.01965332 0.13914933 0.842262605 0.71488844
[5,] 0.980770474 0.979821170 0.98662505 0.96898410 0.446982307 0.41683746
[,31] [,32] [,33] [,34] [,35] [,36]
[1,] 0.02190453 0.02847533 0.013594497 0.05076766 0.16126667 0.09164436
[2,] 0.01438159 0.02281629 0.011668447 0.01651798 0.02452596 0.02356005
[3,] 0.02554313 0.03947523 0.009040695 0.09276678 0.02221302 0.11048769
[4,] 0.05784224 0.14086877 0.086919639 0.13533402 0.18900053 0.91890338
[5,] 0.98704314 0.97552394 0.978132225 0.96224672 0.78366391 0.19419350
[,37] [,38] [,39] [,40] [,41] [,42]
[1,] 0.08033642 0.006028793 0.01341850 0.01786947 0.013715914 0.03963728
[2,] 0.01004148 0.006091121 0.02046421 0.01557593 0.008826466 0.03527891
[3,] 0.04946720 0.007891831 0.04666956 0.02649807 0.021874539 0.13588998
[4,] 0.32033346 0.049680170 0.46213527 0.02645462 0.009272554 0.73081868
[5,] 0.87793086 0.978616033 0.85034200 0.98260161 0.983996824 0.60661896
[,43] [,44] [,45] [,46] [,47] [,48]
[1,] 0.023107157 0.02235173 0.004968143 0.009068509 0.006046214 0.06638847
[2,] 0.014701788 0.01476797 0.003959312 0.007801741 0.010084248 0.02790795
[3,] 0.005226788 0.02054783 0.006094141 0.007874364 0.017057984 0.29778666
[4,] 0.059955753 0.03093773 0.019754242 0.037162605 0.052161563 0.41808932
[5,] 0.969732969 0.99100072 0.977311352 0.981247348 0.974650143 0.76537322
[,49] [,50] [,51] [,52] [,53] [,54]
[1,] 0.04189858 0.06098753 0.014206452 0.006421246 0.03696614 0.07437231
[2,] 0.04013136 0.05042851 0.009795618 0.006118715 0.03085260 0.03237073
[3,] 0.02594029 0.03911230 0.014782319 0.005445430 0.06854795 0.29459297
[4,] 0.27575601 0.11115928 0.028186626 0.016714553 0.01512257 0.85551935
[5,] 0.93979158 0.96371862 0.985352040 0.980404003 0.96637484 0.18917055
[,55] [,56] [,57] [,58] [,59] [,60]
[1,] 0.02635589 0.009815330 0.04525532 0.01891099 0.02519304 0.0431832
[2,] 0.02190955 0.008987052 0.03202343 0.01256386 0.01485276 0.0280299
[3,] 0.07225297 0.008487375 0.03622733 0.01870100 0.03144580 0.1126746
[4,] 0.68356107 0.032838010 0.68088871 0.04773532 0.04530276 0.1815596
[5,] 0.70498937 0.980418255 0.69056461 0.98819507 0.99026806 0.9545110
[,61] [,62] [,63] [,64] [,65] [,66]
[1,] 0.02124385 0.045768887 0.01720460 0.006130202 0.01760184 0.044111264
[2,] 0.01888967 0.025415722 0.01006394 0.005288618 0.01370191 0.007234155
[3,] 0.01164942 0.159387358 0.01621772 0.008608555 0.02099823 0.063238338
[4,] 0.06787048 0.008260895 0.01673265 0.054937199 0.02523185 0.366528351
[5,] 0.97929795 0.947488769 0.98485546 0.977143008 0.98603308 0.896641239
[,67] [,68] [,69] [,70] [,71] [,72]
[1,] 0.012026707 0.008465319 0.08087501 0.11590024 0.05704484 0.02620690
[2,] 0.006855235 0.005839232 0.07174809 0.07703916 0.03432513 0.01757277
[3,] 0.026476631 0.004884047 0.22939221 0.18738540 0.05738241 0.06134119
[4,] 0.044356748 0.056549814 0.17508435 0.42180673 0.70791688 0.06794099
[5,] 0.979255259 0.975699282 0.84893909 0.71515377 0.65140760 0.97738976
[,73] [,74] [,75] [,76] [,77] [,78]
[1,] 0.02313666 0.02541980 0.04438008 0.0000000 0.1352397 0.011423401
[2,] 0.01445994 0.01614678 0.01911396 0.0000000 0.1385223 0.009777136
[3,] 0.03042705 0.02659889 0.02814720 0.0000000 0.3108743 0.016293567
[4,] 0.02447916 0.02459913 0.06526616 0.0125858 0.4827396 0.004554735
[5,] 0.98863166 0.98649795 0.97489267 0.9718209 0.3692117 0.982491498
[,79] [,80] [,81] [,82] [,83] [,84]
[1,] 0.01742173 0.05334461 0.001782884 0.01446258 0.01923808 0.14040111
[2,] 0.01254827 0.02130175 0.003524532 0.01042242 0.01197066 0.14278550
[3,] 0.02631592 0.13943735 0.012584387 0.01906726 0.01691258 0.14736112
[4,] 0.02917878 0.70363598 0.096787291 0.08070066 0.09829455 0.06798636
[5,] 0.98523684 0.61292470 0.969850001 0.98232483 0.98363360 0.75475005
[,85] [,86] [,87] [,88] [,89] [,90]
[1,] 0.009145151 0.020896615 0.01743710 0.03929354 0.1097200 0.02336824
[2,] 0.015901846 0.008504363 0.01476515 0.04646023 0.0545494 0.01693236
[3,] 0.035585921 0.061782541 0.01322467 0.12677960 0.2068573 0.05026018
[4,] 0.346173617 0.136511632 0.03249445 0.20088258 0.2378666 0.08314403
[5,] 0.904516285 0.971310198 0.97779115 0.93155073 0.7882024 0.97794231
[,91] [,92] [,93] [,94] [,95] [,96]
[1,] 0.01433764 0.28143108 0.026141944 0.02197990 0.02530400 0.04001719
[2,] 0.01671278 0.03831532 0.009211723 0.01792000 0.02529331 0.01546301
[3,] 0.08541266 0.28282231 0.026714367 0.07634812 0.02089869 0.09726278
[4,] 0.05038729 0.13552417 0.014958293 0.06122696 0.33598842 0.98091523
[5,] 0.96582875 0.09561000 0.979189748 0.96756861 0.92712475 0.00000000
[,97] [,98] [,99] [,100]
[1,] 0.13866695 0.06644982 0.03499156 0.02954007
[2,] 0.06253262 0.05069866 0.01912316 0.03085476
[3,] 0.16591766 0.33981404 0.02967760 0.15525240
[4,] 0.09300336 0.62941298 0.01736101 0.47863055
[5,] 0.81359747 0.56959566 0.98300103 0.83263443
$idealPoint
[1] 0.7532505 0.7247962 0.7501569 0.8090407 1.1394237
$nadirPoint
[1] 0.2814311 0.1782149 0.5748508 0.9809152 0.9910007
MaOEA documentation built on Aug. 31, 2020, 5:07 p.m.
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Description Usage Arguments Value Examples
Description
Normalize the objectives to 0-1. The origin is the ideal point. (1,...,1) is not the nadir point. The normalization is done by using adaptive normalization used in NSGA-III.
Usage
1 | AdaptiveNormalization(objectiveValue)
|
Arguments
objectiveValue |
Set of objective vectors to normalize |
Value
A list containing the following:
normalizedObjective The normalized values
idealPoint The ideal point corresponding to the origin
nadirPoint The location of nadir point in the normalized Space
Examples
1 2 3 4 5 6 7 8 9 |
Example output
Check required python modules:
reticulate::py_module_available('numpy') and reticulate::py_module_available('pygmo').
If not available, try using MaOEA::install_python_dependencies()
or follow the instructions in https://esa.github.io/pagmo2/install.html
and call MaOEA::load_python_dependencies().
$normalizedObjective
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.05648679 0.001472863 0.03285909 0.27293512 0.03678232 0.009515391
[2,] 0.02382927 0.005128712 0.01794660 0.13451228 0.01359563 0.015231071
[3,] 0.21095706 0.014997285 0.03939423 0.03354975 0.03574221 0.029412144
[4,] 0.19946021 0.000000000 0.02707473 0.24680090 0.02181673 0.104629247
[5,] 0.90930911 0.974883792 0.98520110 0.05742719 0.97085824 0.968249634
[,7] [,8] [,9] [,10] [,11] [,12]
[1,] 0.04975852 0.020216126 0.07910876 0.008540803 0.015160438 0.009812862
[2,] 0.01200320 0.008979619 0.05333916 0.003701728 0.008988469 0.008198087
[3,] 0.15042067 0.070533765 0.11339754 0.014853317 0.015970428 0.007770556
[4,] 0.80893407 0.161300439 0.32679459 0.089491080 0.046675695 0.013874197
[5,] 0.51348192 0.959924006 0.87198237 0.971824157 0.983580410 0.981607681
[,13] [,14] [,15] [,16] [,17] [,18]
[1,] 0.006690424 0.1410935 0.03080473 0.016045514 0.08680722 0.22749022
[2,] 0.013155203 0.1782149 0.02882942 0.008705316 0.11059544 0.02358204
[3,] 0.032313830 0.2162834 0.03228781 0.020932989 0.47378464 0.03276539
[4,] 0.260289301 0.5919080 0.85332344 0.076714505 0.24308486 0.65828273
[5,] 0.932707067 0.3617935 0.47902722 0.976647936 0.55299338 0.13171747
[,19] [,20] [,21] [,22] [,23] [,24]
[1,] 0.03902942 0.11047582 0.03023335 0.013326152 0.03667296 0.08475060
[2,] 0.02725533 0.12293776 0.01824393 0.007855445 0.02929790 0.05049393
[3,] 0.05346685 0.57485082 0.01456701 0.032705998 0.09179842 0.08307390
[4,] 0.01408240 0.05285134 0.14250373 0.111899006 0.95482649 0.87146652
[5,] 0.97821372 0.29823002 0.96889757 0.971723345 0.23843998 0.32641930
[,25] [,26] [,27] [,28] [,29] [,30]
[1,] 0.008132462 0.011482031 0.01709511 0.01838634 0.026117691 0.15329321
[2,] 0.006796376 0.005512279 0.01205346 0.01763083 0.007586351 0.07343904
[3,] 0.010874137 0.010715519 0.01878527 0.06868508 0.132076639 0.03376697
[4,] 0.012001279 0.006854380 0.01965332 0.13914933 0.842262605 0.71488844
[5,] 0.980770474 0.979821170 0.98662505 0.96898410 0.446982307 0.41683746
[,31] [,32] [,33] [,34] [,35] [,36]
[1,] 0.02190453 0.02847533 0.013594497 0.05076766 0.16126667 0.09164436
[2,] 0.01438159 0.02281629 0.011668447 0.01651798 0.02452596 0.02356005
[3,] 0.02554313 0.03947523 0.009040695 0.09276678 0.02221302 0.11048769
[4,] 0.05784224 0.14086877 0.086919639 0.13533402 0.18900053 0.91890338
[5,] 0.98704314 0.97552394 0.978132225 0.96224672 0.78366391 0.19419350
[,37] [,38] [,39] [,40] [,41] [,42]
[1,] 0.08033642 0.006028793 0.01341850 0.01786947 0.013715914 0.03963728
[2,] 0.01004148 0.006091121 0.02046421 0.01557593 0.008826466 0.03527891
[3,] 0.04946720 0.007891831 0.04666956 0.02649807 0.021874539 0.13588998
[4,] 0.32033346 0.049680170 0.46213527 0.02645462 0.009272554 0.73081868
[5,] 0.87793086 0.978616033 0.85034200 0.98260161 0.983996824 0.60661896
[,43] [,44] [,45] [,46] [,47] [,48]
[1,] 0.023107157 0.02235173 0.004968143 0.009068509 0.006046214 0.06638847
[2,] 0.014701788 0.01476797 0.003959312 0.007801741 0.010084248 0.02790795
[3,] 0.005226788 0.02054783 0.006094141 0.007874364 0.017057984 0.29778666
[4,] 0.059955753 0.03093773 0.019754242 0.037162605 0.052161563 0.41808932
[5,] 0.969732969 0.99100072 0.977311352 0.981247348 0.974650143 0.76537322
[,49] [,50] [,51] [,52] [,53] [,54]
[1,] 0.04189858 0.06098753 0.014206452 0.006421246 0.03696614 0.07437231
[2,] 0.04013136 0.05042851 0.009795618 0.006118715 0.03085260 0.03237073
[3,] 0.02594029 0.03911230 0.014782319 0.005445430 0.06854795 0.29459297
[4,] 0.27575601 0.11115928 0.028186626 0.016714553 0.01512257 0.85551935
[5,] 0.93979158 0.96371862 0.985352040 0.980404003 0.96637484 0.18917055
[,55] [,56] [,57] [,58] [,59] [,60]
[1,] 0.02635589 0.009815330 0.04525532 0.01891099 0.02519304 0.0431832
[2,] 0.02190955 0.008987052 0.03202343 0.01256386 0.01485276 0.0280299
[3,] 0.07225297 0.008487375 0.03622733 0.01870100 0.03144580 0.1126746
[4,] 0.68356107 0.032838010 0.68088871 0.04773532 0.04530276 0.1815596
[5,] 0.70498937 0.980418255 0.69056461 0.98819507 0.99026806 0.9545110
[,61] [,62] [,63] [,64] [,65] [,66]
[1,] 0.02124385 0.045768887 0.01720460 0.006130202 0.01760184 0.044111264
[2,] 0.01888967 0.025415722 0.01006394 0.005288618 0.01370191 0.007234155
[3,] 0.01164942 0.159387358 0.01621772 0.008608555 0.02099823 0.063238338
[4,] 0.06787048 0.008260895 0.01673265 0.054937199 0.02523185 0.366528351
[5,] 0.97929795 0.947488769 0.98485546 0.977143008 0.98603308 0.896641239
[,67] [,68] [,69] [,70] [,71] [,72]
[1,] 0.012026707 0.008465319 0.08087501 0.11590024 0.05704484 0.02620690
[2,] 0.006855235 0.005839232 0.07174809 0.07703916 0.03432513 0.01757277
[3,] 0.026476631 0.004884047 0.22939221 0.18738540 0.05738241 0.06134119
[4,] 0.044356748 0.056549814 0.17508435 0.42180673 0.70791688 0.06794099
[5,] 0.979255259 0.975699282 0.84893909 0.71515377 0.65140760 0.97738976
[,73] [,74] [,75] [,76] [,77] [,78]
[1,] 0.02313666 0.02541980 0.04438008 0.0000000 0.1352397 0.011423401
[2,] 0.01445994 0.01614678 0.01911396 0.0000000 0.1385223 0.009777136
[3,] 0.03042705 0.02659889 0.02814720 0.0000000 0.3108743 0.016293567
[4,] 0.02447916 0.02459913 0.06526616 0.0125858 0.4827396 0.004554735
[5,] 0.98863166 0.98649795 0.97489267 0.9718209 0.3692117 0.982491498
[,79] [,80] [,81] [,82] [,83] [,84]
[1,] 0.01742173 0.05334461 0.001782884 0.01446258 0.01923808 0.14040111
[2,] 0.01254827 0.02130175 0.003524532 0.01042242 0.01197066 0.14278550
[3,] 0.02631592 0.13943735 0.012584387 0.01906726 0.01691258 0.14736112
[4,] 0.02917878 0.70363598 0.096787291 0.08070066 0.09829455 0.06798636
[5,] 0.98523684 0.61292470 0.969850001 0.98232483 0.98363360 0.75475005
[,85] [,86] [,87] [,88] [,89] [,90]
[1,] 0.009145151 0.020896615 0.01743710 0.03929354 0.1097200 0.02336824
[2,] 0.015901846 0.008504363 0.01476515 0.04646023 0.0545494 0.01693236
[3,] 0.035585921 0.061782541 0.01322467 0.12677960 0.2068573 0.05026018
[4,] 0.346173617 0.136511632 0.03249445 0.20088258 0.2378666 0.08314403
[5,] 0.904516285 0.971310198 0.97779115 0.93155073 0.7882024 0.97794231
[,91] [,92] [,93] [,94] [,95] [,96]
[1,] 0.01433764 0.28143108 0.026141944 0.02197990 0.02530400 0.04001719
[2,] 0.01671278 0.03831532 0.009211723 0.01792000 0.02529331 0.01546301
[3,] 0.08541266 0.28282231 0.026714367 0.07634812 0.02089869 0.09726278
[4,] 0.05038729 0.13552417 0.014958293 0.06122696 0.33598842 0.98091523
[5,] 0.96582875 0.09561000 0.979189748 0.96756861 0.92712475 0.00000000
[,97] [,98] [,99] [,100]
[1,] 0.13866695 0.06644982 0.03499156 0.02954007
[2,] 0.06253262 0.05069866 0.01912316 0.03085476
[3,] 0.16591766 0.33981404 0.02967760 0.15525240
[4,] 0.09300336 0.62941298 0.01736101 0.47863055
[5,] 0.81359747 0.56959566 0.98300103 0.83263443
$idealPoint
[1] 0.7532505 0.7247962 0.7501569 0.8090407 1.1394237
$nadirPoint
[1] 0.2814311 0.1782149 0.5748508 0.9809152 0.9910007
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