NSGA3: Elitist Non-dominated Sorting Genetic Algorithm version III
In MaOEA: Many Objective Evolutionary Algorithm
Description
Usage
Arguments
Value
References
Examples
Description
Do an iteration of Elitist Non-dominated Sorting Genetic Algorithm version III (NSGA-III). THe variation is using SBX and polynomial mutation.
Usage
1
Arguments
population
The parent generation. One individual per column. nrow = number of variable, ncol = number of individuals in the population.
fun
Objective function being solved. Currently available in the package DTLZ1-DTLZ4, WFG4-WFG9.
nObjective
The number of objective functions. A scalar value. Needed to generate weight vectors.
control
A list, containing the following:
weightVector NSGA-III require a set of reference points defined a priori. The reference can be any point. If not supplied, 5*nObjective points are generated from a sobol sequence. Column major: nrow = nObjective, ncol = number of reference points
crossoverProbability The probability of doing crossover. Should be between 0-1. Negative value will behave like a zero, and values larger than 1 will behave like 1. Default to 1.
mutationProbability The probability of doing mutation. Should be between 0-1. Negative value will behave like a zero, and values larger than 1 will behave like 1. Default to 1
mutationDistribution The distribution index for polynomial mutation. Larger index makes the distribution sharper around the parent.
crossoverDistribution The distribution index for SBX. Larger index makes the distribution sharper around each parent.
...
Further arguments to be passed to fun
Value
#' @return Returns a list for the next generation
population The new generation design points. Column major.
populationObjective The new generation's objective values. Column major.
References
Deb, K., Jain, H.: An evolutionary many-objective optimization algorithm using
reference-point-based nondominated sorting approach, part I: Solving problems with box constraints.
Trans. Evol. Comp. 18 (4), 577–601 (2014)
Examples
1
2
3
4
5
6
7
8
9
10
11
nVar <- 14
nObjective <- 5
nIndividual <- 100
#control for NSGA3
ctrl <- list(crossoverProbability = 1,
mutationProbability = 1/nVar)
#Initial population
population <- matrix(runif(nIndividual*nVar), nrow = nVar)
# run a generation of NSGA-III with standard WFG8 test function.
NSGA3(population, WFG8,nObjective,ctrl,nObjective)
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().
$population
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.79238276 0.59517508 0.41522434 0.59517508 0.7977519 0.418387513
[2,] 0.98909722 0.15316826 0.90012160 0.15316826 0.8706306 0.882064418
[3,] 0.46818967 0.45475677 0.87212504 0.45475677 0.7052827 0.722193975
[4,] 0.59653217 0.32583912 0.08772934 0.32583912 0.9162719 0.088069222
[5,] 0.61192184 0.06398252 0.92286934 0.06398252 0.9187914 0.656968106
[6,] 0.06485533 0.07912143 0.45062678 0.07912143 0.7458760 0.864753943
[7,] 0.46855987 0.15065082 0.40996732 0.15065082 0.5962809 0.802962790
[8,] 0.93356924 0.05946864 0.53063452 0.05946864 0.3292424 0.693153681
[9,] 0.52235712 0.75640562 0.40670491 0.75640562 0.2298100 0.006375945
[10,] 0.15873548 0.92770900 0.61532273 0.92770900 0.9375008 0.435648699
[11,] 0.38676540 0.27034175 0.96748722 0.27034175 0.6070034 0.574339144
[12,] 0.44246320 0.37305418 0.81694383 0.37305418 0.8571831 0.618334848
[13,] 0.74872144 0.81003144 0.88773189 0.81003144 0.5660571 0.340853403
[14,] 0.57422842 0.34657259 0.60327129 0.34657259 0.5083197 0.794556550
[,7] [,8] [,9] [,10] [,11] [,12]
[1,] 0.80557317 0.59517508 0.42530499 0.59517508 0.80907629 0.44807301
[2,] 0.81139911 0.15316826 0.87178085 0.15316826 0.79751035 0.70738404
[3,] 0.91712924 0.45475677 0.14874226 0.45475677 0.92465270 0.99724883
[4,] 0.02427151 0.32583912 0.90853402 0.32583912 0.21973600 0.13049579
[5,] 0.05011832 0.06398252 0.40234126 0.06398252 0.05011832 0.56999455
[6,] 0.67496233 0.07912143 0.62543818 0.07912143 0.69111955 0.09688489
[7,] 0.44176660 0.15065082 0.87786511 0.15065082 0.44213835 0.24608580
[8,] 0.66490996 0.05946864 0.11669171 0.05946864 0.94798137 0.82185666
[9,] 0.70067776 0.75640562 0.14276472 0.75640562 0.85431560 0.58577796
[10,] 0.42850292 0.92770900 0.29987078 0.92770900 0.46878043 0.97399862
[11,] 0.90802817 0.27034175 0.79536819 0.27034175 0.90367948 0.43339770
[12,] 0.34215319 0.37305418 0.99510647 0.37305418 0.34215319 0.64008575
[13,] 0.09344907 0.81003144 0.07260505 0.81003144 0.09344907 0.92344191
[14,] 0.55497833 0.34657259 0.16937969 0.34657259 0.56881861 0.88443336
[,13] [,14] [,15] [,16] [,17] [,18]
[1,] 0.59517508 0.77165604 0.40770269 0.41041392 0.59517508 0.8202399
[2,] 0.15316826 0.97710039 0.97710039 0.70708767 0.15316826 0.7736050
[3,] 0.45475677 0.03731832 0.04889067 0.18919295 0.45475677 0.5171435
[4,] 0.32583912 0.36237396 0.36322173 0.70710644 0.32583912 0.7977451
[5,] 0.06398252 0.14818204 0.14818204 0.01033697 0.06398252 0.6944135
[6,] 0.07912143 0.12482182 0.12482182 0.52397433 0.07912143 0.2579115
[7,] 0.15065082 0.61727189 0.57733367 0.52397642 0.15065082 0.3546327
[8,] 0.05946864 0.34720182 0.20147516 0.73257562 0.05946864 0.2460770
[9,] 0.75640562 0.30562863 0.18505131 0.03274999 0.75640562 0.4848095
[10,] 0.92770900 0.91303292 0.91303292 0.08036027 0.92770900 0.6433276
[11,] 0.27034175 0.26786261 0.26442111 0.59611114 0.27034175 0.8130203
[12,] 0.37305418 0.81084104 0.81078496 0.08510854 0.37305418 0.9598869
[13,] 0.81003144 0.84380362 0.84380362 0.90192337 0.81003144 0.5914286
[14,] 0.34657259 0.40004273 0.52007225 0.11267624 0.34657259 0.1100577
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[1,] 0.832343994 0.59517508 0.4797500 0.4557857 0.8717994 0.59517508
[2,] 0.844601330 0.15316826 0.8910517 0.6035466 0.9869252 0.15316826
[3,] 0.132518489 0.45475677 0.0388335 0.2184373 0.4602665 0.45475677
[4,] 0.416371072 0.32583912 0.3852310 0.9711844 0.5954854 0.32583912
[5,] 0.566840647 0.06398252 0.9709074 0.6144317 0.6109143 0.06398252
[6,] 0.713298337 0.07912143 0.1797093 0.7927401 0.6446914 0.07912143
[7,] 0.278312425 0.15065082 0.4373645 0.7591118 0.7957335 0.15065082
[8,] 0.572392972 0.05946864 0.3157601 0.2892671 0.9324969 0.05946864
[9,] 0.330320968 0.75640562 0.2473747 0.9697201 0.9218709 0.75640562
[10,] 0.002269806 0.92770900 0.3238595 0.3915642 0.7180246 0.92770900
[11,] 0.383306508 0.27034175 0.9437239 0.4998578 0.2263646 0.27034175
[12,] 0.947206178 0.37305418 0.9088778 0.1609090 0.5105898 0.37305418
[13,] 0.039554944 0.81003144 0.2930647 0.9521970 0.1769900 0.81003144
[14,] 0.335652850 0.34657259 0.9286837 0.2597021 0.5741009 0.34657259
[,25] [,26] [,27] [,28] [,29] [,30]
[1,] 0.82023040 0.59517508 0.4976155 0.59517508 0.40323563 0.8741795
[2,] 0.77886527 0.15316826 0.8793166 0.15316826 0.39154835 0.9047138
[3,] 0.23204755 0.45475677 0.5683276 0.45475677 0.54513171 0.7439585
[4,] 0.89362236 0.32583912 0.5438822 0.32583912 0.11412575 0.6014357
[5,] 0.08001872 0.06398252 0.5645093 0.06398252 0.28314098 0.5035641
[6,] 0.25796762 0.07912143 0.6961125 0.07912143 0.45725577 0.9805103
[7,] 0.35424722 0.15065082 0.0758175 0.15065082 0.78074297 0.9673634
[8,] 0.34654390 0.05946864 0.9272011 0.05946864 0.02871647 0.1123244
[9,] 0.48247962 0.75640562 0.3578377 0.75640562 0.27111072 0.4006124
[10,] 0.39733574 0.92770900 0.3523341 0.92770900 0.33044209 0.7655287
[11,] 0.09331368 0.27034175 0.8517971 0.27034175 0.57607909 0.9301504
[12,] 0.66320787 0.37305418 0.3430249 0.37305418 0.99464698 0.3627463
[13,] 0.30656208 0.81003144 0.5121207 0.81003144 0.15406396 0.3529311
[14,] 0.89006617 0.34657259 0.8389594 0.34657259 0.77305121 0.3274318
[,31] [,32] [,33] [,34] [,35] [,36]
[1,] 0.59517508 0.88234246 0.38888187 0.464683361 0.7445066 0.59517508
[2,] 0.15316826 0.90578656 0.38939441 0.496128432 0.9283678 0.15316826
[3,] 0.45475677 0.74589470 0.63294631 0.564191404 0.4320800 0.45475677
[4,] 0.32583912 0.39756643 0.25537028 0.869397948 0.7012537 0.32583912
[5,] 0.06398252 0.05178989 0.01997915 0.940494177 0.2656189 0.06398252
[6,] 0.07912143 0.73620536 0.09260675 0.211606521 0.6634334 0.07912143
[7,] 0.15065082 0.94330968 0.56305435 0.511736533 0.5618730 0.15065082
[8,] 0.05946864 0.25653553 0.61263472 0.893394516 0.9853941 0.05946864
[9,] 0.75640562 0.56103140 0.19355710 0.239528591 0.8143439 0.75640562
[10,] 0.92770900 0.97536253 0.91148666 0.138349557 0.7404577 0.92770900
[11,] 0.27034175 0.46992404 0.29462935 0.465838156 0.6048598 0.27034175
[12,] 0.37305418 0.17331994 0.31813905 0.004503186 0.3544867 0.37305418
[13,] 0.81003144 0.04343326 0.41773745 0.368373419 0.8438718 0.81003144
[14,] 0.34657259 0.84358549 0.48487047 0.529152489 0.8584848 0.34657259
[,37] [,38] [,39] [,40] [,41] [,42]
[1,] 0.87644821 0.59517508 0.38888187 0.59517508 0.49854233 0.7819627
[2,] 0.90746599 0.15316826 0.38727364 0.15316826 0.87931658 0.6421169
[3,] 0.40159561 0.45475677 0.63294631 0.45475677 0.32998887 0.3366353
[4,] 0.60079491 0.32583912 0.25836317 0.32583912 0.54242937 0.6222317
[5,] 0.50654621 0.06398252 0.01631622 0.06398252 0.56313820 0.5161231
[6,] 0.87629910 0.07912143 0.09260675 0.07912143 0.22614003 0.6884779
[7,] 0.96120737 0.15065082 0.56222583 0.15065082 0.04469146 0.5366336
[8,] 0.09887265 0.05946864 0.61263472 0.05946864 0.92771167 0.2668231
[9,] 0.20572340 0.75640562 0.19355710 0.75640562 0.43189482 0.4395090
[10,] 0.09999855 0.92770900 0.91148666 0.92770900 0.35233414 0.9115233
[11,] 0.93044824 0.27034175 0.29563212 0.27034175 0.85179709 0.7709925
[12,] 0.40992427 0.37305418 0.31813905 0.37305418 0.34302486 0.8566138
[13,] 0.98609177 0.81003144 0.39855664 0.81003144 0.49714862 0.9277300
[14,] 0.33438849 0.34657259 0.48487047 0.34657259 0.83895941 0.8328267
[,43] [,44] [,45] [,46] [,47] [,48] [,49]
[1,] 0.4225043 0.8847341 0.59517508 0.59517508 0.79028519 0.36509715 0.4153973
[2,] 0.2694762 0.8878383 0.15316826 0.15316826 0.47461812 0.73181740 0.1653083
[3,] 0.9528958 0.1202421 0.45475677 0.45475677 0.46818967 0.61244571 0.1601495
[4,] 0.1198220 0.6390294 0.32583912 0.32583912 0.07449544 0.10466183 0.2239881
[5,] 0.5377732 0.5911932 0.06398252 0.06398252 0.47967969 0.06567777 0.4782603
[6,] 0.2940219 0.5941919 0.07912143 0.07912143 0.06485533 0.09793958 0.3223502
[7,] 0.8768432 0.7289550 0.15065082 0.15065082 0.46855987 0.10696846 0.2975268
[8,] 0.1125586 0.2505878 0.05946864 0.05946864 0.79913446 0.83916831 0.9616176
[9,] 0.7040808 0.2189984 0.75640562 0.75640562 0.52951635 0.04145517 0.8521074
[10,] 0.3004683 0.4778068 0.92770900 0.92770900 0.14925857 0.20057534 0.4689986
[11,] 0.3864409 0.3287891 0.27034175 0.27034175 0.38676540 0.43329525 0.3200617
[12,] 0.6988727 0.7325115 0.37305418 0.37305418 0.44246320 0.31121473 0.6514525
[13,] 0.6328157 0.1125145 0.81003144 0.81003144 0.74872144 0.77474863 0.9020246
[14,] 0.1217727 0.7486564 0.34657259 0.34657259 0.23599757 0.92075378 0.5696888
[,50] [,51] [,52] [,53] [,54] [,55]
[1,] 0.77094023 0.59517508 0.39861765 0.7860266 0.59517508 0.59517508
[2,] 0.49808484 0.15316826 0.06609779 0.4111952 0.15316826 0.15316826
[3,] 0.04392775 0.45475677 0.84342928 0.5248244 0.45475677 0.45475677
[4,] 0.49141013 0.32583912 0.21856584 0.5308352 0.32583912 0.32583912
[5,] 0.22237206 0.06398252 0.28171751 0.0537161 0.06398252 0.06398252
[6,] 0.56796834 0.07912143 0.35509305 0.4964901 0.07912143 0.07912143
[7,] 0.48190625 0.15065082 0.81351559 0.6173291 0.15065082 0.15065082
[8,] 0.20344257 0.05946864 0.03397890 0.3495703 0.05946864 0.05946864
[9,] 0.71388624 0.75640562 0.06180130 0.3069872 0.75640562 0.75640562
[10,] 0.41027346 0.92770900 0.14329040 0.3122301 0.92770900 0.92770900
[11,] 0.67043810 0.27034175 0.12158280 0.7658955 0.27034175 0.27034175
[12,] 0.52269218 0.37305418 0.56323615 0.8453037 0.37305418 0.37305418
[13,] 0.61811778 0.81003144 0.30770204 0.9086645 0.81003144 0.81003144
[14,] 0.90251026 0.34657259 0.34415315 0.8200778 0.34657259 0.34657259
[,56] [,57] [,58] [,59] [,60] [,61]
[1,] 0.42571102 0.91417719 0.72914851 0.59517508 0.498036971 0.59517508
[2,] 0.03739189 0.85955135 0.54196152 0.15316826 0.498102476 0.15316826
[3,] 0.17444149 0.47962332 0.97853766 0.45475677 0.564191404 0.45475677
[4,] 0.44914594 0.48775501 0.76239397 0.32583912 0.869397948 0.32583912
[5,] 0.52946136 0.68813961 0.06826338 0.06398252 0.940494177 0.06398252
[6,] 0.06557241 0.46490273 0.39395244 0.07912143 0.565449024 0.07912143
[7,] 0.67989580 0.38585475 0.44165768 0.15065082 0.511736533 0.15065082
[8,] 0.57625225 0.06747851 0.02224909 0.05946864 0.893394516 0.05946864
[9,] 0.11710836 0.25118863 0.79188381 0.75640562 0.707606523 0.75640562
[10,] 0.58019206 0.42305799 0.79446901 0.92770900 0.138349557 0.92770900
[11,] 0.16800936 0.20883115 0.23369572 0.27034175 0.672250203 0.27034175
[12,] 0.78405080 0.53104340 0.27190639 0.37305418 0.004503186 0.37305418
[13,] 0.02224496 0.94591672 0.23661861 0.81003144 0.617552940 0.81003144
[14,] 0.93455314 0.90450487 0.96091211 0.34657259 0.906472131 0.34657259
[,62] [,63] [,64] [,65] [,66] [,67]
[1,] 0.33787008 0.78041040 0.832343994 0.3408371 0.59517508 0.32701643
[2,] 0.58713451 0.36673955 0.406597472 0.1454008 0.15316826 0.53595666
[3,] 0.14770046 0.70348071 0.150625645 0.4114491 0.45475677 0.13247433
[4,] 0.02991679 0.65069623 0.416371072 0.7339594 0.32583912 0.02171283
[5,] 0.12558699 0.14736613 0.566865323 0.7950932 0.06398252 0.84339515
[6,] 0.71995717 0.74877174 0.713298337 0.2293277 0.07912143 0.45780687
[7,] 0.61353211 0.10863935 0.278312425 0.1826018 0.15065082 0.56974895
[8,] 0.35296303 0.32886142 0.539073124 0.7279907 0.05946864 0.34535090
[9,] 0.14267012 0.85182338 0.330320968 0.3526670 0.75640562 0.13928775
[10,] 0.74621636 0.06897737 0.002269806 0.9029031 0.92770900 0.48403364
[11,] 0.86170532 0.67577032 0.348751486 0.1998537 0.27034175 0.30649723
[12,] 0.36245698 0.85774238 0.617737921 0.8914124 0.37305418 0.05201470
[13,] 0.51507934 0.39826137 0.039554944 0.9879641 0.81003144 0.48811389
[14,] 0.79192399 0.17425810 0.168095117 0.4064225 0.34657259 0.11185414
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[1,] 0.70583318 0.59517508 0.59517508 0.713262499 0.47374939 0.47374939
[2,] 0.65860622 0.15316826 0.15316826 0.651886103 0.05252428 0.04261931
[3,] 0.65905426 0.45475677 0.45475677 0.143893007 0.82053171 0.82053171
[4,] 0.97603862 0.32583912 0.32583912 0.008067586 0.03863682 0.03863682
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[6,] 0.44280514 0.07912143 0.07912143 0.088299450 0.09549886 0.09207376
[7,] 0.83083536 0.15065082 0.15065082 0.344271593 0.58487855 0.59010663
[8,] 0.12126500 0.05946864 0.05946864 0.914584855 0.74687729 0.44579087
[9,] 0.57401162 0.75640562 0.75640562 0.595040215 0.45540027 0.45540027
[10,] 0.29284772 0.92770900 0.92770900 0.012301408 0.27939939 0.27995141
[11,] 0.26328922 0.27034175 0.27034175 0.454557283 0.64776261 0.65311366
[12,] 0.07733234 0.37305418 0.37305418 0.547032596 0.93983939 0.93983939
[13,] 0.65850468 0.81003144 0.81003144 0.655737108 0.61130100 0.61130100
[14,] 0.96636540 0.34657259 0.34657259 0.063938660 0.02847064 0.02847064
[,74] [,75] [,76] [,77] [,78] [,79] [,80]
[1,] 0.7140598 0.59517508 0.59517508 0.7448637 0.33829042 0.81972804 0.5545401
[2,] 0.5871345 0.15316826 0.15316826 0.3915483 0.05219401 0.31629169 0.8513716
[3,] 0.1477005 0.45475677 0.45475677 0.5451317 0.96715211 0.39437522 0.5128820
[4,] 0.7199228 0.32583912 0.32583912 0.1141257 0.52348683 0.21121787 0.6300638
[5,] 0.1255870 0.06398252 0.06398252 0.4591349 0.40555634 0.94331209 0.7452795
[6,] 0.7223787 0.07912143 0.07912143 0.4596623 0.40513157 0.39776431 0.7503845
[7,] 0.6144361 0.15065082 0.15065082 0.7807430 0.57358427 0.08028215 0.4396948
[8,] 0.7453969 0.05946864 0.05946864 0.6255913 0.69467889 0.11513587 0.8005333
[9,] 0.5919728 0.75640562 0.75640562 0.2155930 0.91491889 0.85880682 0.4769061
[10,] 0.7462164 0.92770900 0.92770900 0.3281697 0.43595273 0.14060035 0.7318948
[11,] 0.8617053 0.27034175 0.27034175 0.5760791 0.35834293 0.49304786 0.8522164
[12,] 0.3624570 0.37305418 0.37305418 0.9946470 0.83731380 0.79358438 0.4190260
[13,] 0.9094690 0.81003144 0.81003144 0.1540640 0.62034087 0.95811439 0.3534494
[14,] 0.7919240 0.34657259 0.34657259 0.7730512 0.79673642 0.34816247 0.1892424
[,81] [,82] [,83] [,84] [,85] [,86]
[1,] 0.59517508 0.59517508 0.30002309 0.86970185 0.59517508 0.56004421
[2,] 0.15316826 0.15316826 0.20968910 0.47244609 0.15316826 0.74665735
[3,] 0.45475677 0.45475677 0.79743804 0.46026652 0.45475677 0.81863785
[4,] 0.32583912 0.32583912 0.90799711 0.07344868 0.32583912 0.83187858
[5,] 0.06398252 0.06398252 0.77878226 0.47867215 0.06398252 0.68043001
[6,] 0.07912143 0.07912143 0.40031494 0.64469145 0.07912143 0.84522108
[7,] 0.15065082 0.15065082 0.51743729 0.79573349 0.15065082 0.98920844
[8,] 0.05946864 0.05946864 0.33917577 0.79806212 0.05946864 0.61160096
[9,] 0.75640562 0.75640562 0.85426703 0.92903010 0.75640562 0.75602637
[10,] 0.92770900 0.92770900 0.64531908 0.70854767 0.92770900 0.92726450
[11,] 0.27034175 0.27034175 0.15511044 0.22636459 0.27034175 0.07918622
[12,] 0.37305418 0.37305418 0.01301471 0.49147367 0.37305418 0.92350583
[13,] 0.81003144 0.81003144 0.08887104 0.17699003 0.81003144 0.80699483
[14,] 0.34657259 0.34657259 0.42443765 0.23587008 0.34657259 0.99830189
[,87] [,88] [,89] [,90] [,91] [,92]
[1,] 0.7145169 0.68024156 0.59517508 0.29845232 0.5354198 0.59517508
[2,] 0.5359567 0.86459908 0.15316826 0.11770482 0.3797508 0.15316826
[3,] 0.1324743 0.14874226 0.45475677 0.92346929 0.2251338 0.45475677
[4,] 0.7117189 0.97266935 0.32583912 0.32973688 0.6322833 0.32583912
[5,] 0.8433952 0.40585310 0.06398252 0.12255860 0.6817068 0.06398252
[6,] 0.4602284 0.62543818 0.07912143 0.18540048 0.2811619 0.07912143
[7,] 0.5706530 0.91886939 0.15065082 0.29779510 0.4402233 0.15065082
[8,] 0.7377848 0.99712766 0.05946864 0.36454789 0.5951695 0.05946864
[9,] 0.5885904 0.14276472 0.75640562 0.08712979 0.1375457 0.75640562
[10,] 0.4840336 0.79375726 0.92770900 0.42838371 0.8381862 0.92770900
[11,] 0.3064972 0.80297270 0.27034175 0.47640473 0.2409479 0.27034175
[12,] 0.0520147 0.99471577 0.37305418 0.19651806 0.4176269 0.37305418
[13,] 0.8825036 0.07260505 0.81003144 0.74352076 0.6381812 0.81003144
[14,] 0.1118541 0.16937969 0.34657259 0.64703716 0.1180869 0.34657259
[,93] [,94] [,95] [,96] [,97] [,98] [,99]
[1,] 0.93181335 0.2792192 0.59517508 0.8640301 0.27797573 0.9280825 0.59517508
[2,] 0.84015527 0.6807378 0.15316826 0.3362882 0.86491644 0.7878583 0.15316826
[3,] 0.93631719 0.9748485 0.45475677 0.9746601 0.57624939 0.1934971 0.45475677
[4,] 0.39756643 0.2266207 0.32583912 0.9422129 0.70393511 0.3843627 0.32583912
[5,] 0.05178989 0.9508044 0.06398252 0.9046138 0.91316064 0.7022408 0.06398252
[6,] 0.73620536 0.8369664 0.07912143 0.8379521 0.73189894 0.5355291 0.07912143
[7,] 0.94330968 0.6440461 0.15065082 0.4139745 0.70098162 0.7619649 0.15065082
[8,] 0.62089991 0.6957562 0.05946864 0.6319005 0.95157921 0.5449926 0.05946864
[9,] 0.73250929 0.7771597 0.75640562 0.4535915 0.02599233 0.2040860 0.75640562
[10,] 0.97602662 0.7350707 0.92770900 0.7362903 0.94598694 0.8088901 0.92770900
[11,] 0.46992404 0.8579083 0.27034175 0.2686987 0.62749580 0.8748411 0.27034175
[12,] 0.66836642 0.9017007 0.37305418 0.6321234 0.29771277 0.1706296 0.37305418
[13,] 0.71952978 0.9020666 0.81003144 0.9055757 0.98623518 0.6288843 0.81003144
[14,] 0.83474344 0.8775972 0.34657259 0.8736318 0.93325600 0.7307826 0.34657259
[,100]
[1,] 0.2700174
[2,] 0.8706306
[3,] 0.3749928
[4,] 0.9230296
[5,] 0.8337879
[6,] 0.1712796
[7,] 0.5962809
[8,] 0.2654144
[9,] 0.2518880
[10,] 0.9375008
[11,] 0.6070034
[12,] 0.5862591
[13,] 0.5660571
[14,] 0.5165901
$objective
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.9261112 0.9469137 0.8924781 0.9469137 0.9043228 0.8995893 0.9222292
[2,] 1.0270333 0.9593451 0.9920032 0.9593451 1.0334474 0.9812326 1.0980139
[3,] 2.2344939 1.1078766 1.5397371 1.1078766 2.0508946 1.5445420 2.0013878
[4,] 5.2358959 4.5448695 3.2960922 4.5448695 5.3107503 3.3272881 5.4142566
[5,] 9.0449921 9.8737074 10.3645499 9.8737074 8.9919413 10.3638254 8.9861736
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] 0.9469137 0.9238822 0.9469137 0.9170447 0.9073262 0.9469137 0.9299123
[2,] 0.9593451 0.9392287 0.9593451 1.0884393 1.0036417 0.9593451 0.9379285
[3,] 1.1078766 1.5822282 1.1078766 1.9784402 1.4540136 1.1078766 2.2090379
[4,] 4.5448695 3.3930073 4.5448695 5.4305963 3.5579359 4.5448695 5.1552938
[5,] 9.8737074 10.3696370 9.8737074 8.9613279 10.2932169 9.8737074 9.1486193
[,15] [,16] [,17] [,18] [,19] [,20] [,21]
[1,] 0.9339828 0.9431602 0.9469137 0.9234588 0.9266524 0.9469137 0.9092843
[2,] 0.9397853 0.9590020 0.9593451 1.0117020 0.9529142 0.9593451 0.9142053
[3,] 1.6407222 1.4623510 1.1078766 1.9839671 2.1129836 1.1078766 1.6658745
[4,] 3.2687781 3.3791797 4.5448695 5.5004515 5.5255305 4.5448695 3.6742533
[5,] 10.4254646 10.4269428 9.8737074 8.9116086 8.8637918 9.8737074 10.2075780
[,22] [,23] [,24] [,25] [,26] [,27] [,28]
[1,] 0.9021878 0.8992962 0.9469137 0.9470940 0.9469137 0.9132197 0.9469137
[2,] 0.9188728 1.0067365 0.9593451 0.9865031 0.9593451 0.9851693 0.9593451
[3,] 1.3932079 2.3163384 1.1078766 2.0262870 1.1078766 1.6742780 1.1078766
[4,] 3.6250575 5.5769195 4.5448695 5.5247951 4.5448695 3.7768689 4.5448695
[5,] 10.2664940 8.6386196 9.8737074 8.9390209 9.8737074 10.1550909 9.8737074
[,29] [,30] [,31] [,32] [,33] [,34] [,35]
[1,] 0.9269531 0.9096621 0.9469137 0.9238016 0.9423053 0.9238189 0.9000372
[2,] 0.9537786 1.0691204 0.9593451 1.0892157 0.9717301 0.9604489 0.9819575
[3,] 1.2099255 2.1976057 1.1078766 2.2265490 1.2125991 1.3304379 2.0672274
[4,] 3.3887180 5.6540674 4.5448695 5.7078736 3.3190820 3.7216500 5.0195413
[5,] 10.4293306 8.6337974 9.8737074 8.6104611 10.4787340 10.2617391 9.2325278
[,36] [,37] [,38] [,39] [,40] [,41] [,42]
[1,] 0.9469137 0.9128495 0.9469137 0.9426293 0.9469137 0.9223586 0.8973275
[2,] 0.9593451 0.9997610 0.9593451 0.9718854 0.9593451 0.9643189 0.9444844
[3,] 1.1078766 2.2297821 1.1078766 1.2114536 1.1078766 1.6921464 1.7535476
[4,] 4.5448695 5.6702514 4.5448695 3.3197056 4.5448695 3.7927790 5.3585789
[5,] 9.8737074 8.6302587 9.8737074 10.4790534 9.8737074 10.1631594 9.0668667
[,43] [,44] [,45] [,46] [,47] [,48] [,49]
[1,] 0.921126 0.9191650 0.9469137 0.9469137 0.9298400 0.9483847 0.9076303
[2,] 0.954699 0.9447641 0.9593451 0.9593451 0.9821561 0.9990435 0.9110361
[3,] 1.120798 2.2292433 1.1078766 1.1078766 1.5712379 1.4226941 1.0321888
[4,] 3.512368 5.7315290 4.5448695 4.5448695 5.5016369 3.1177293 3.4661153
[5,] 10.375191 8.5988205 9.8737074 9.8737074 9.0642365 10.5395498 10.3800548
[,50] [,51] [,52] [,53] [,54] [,55] [,56]
[1,] 0.9187770 0.9469137 0.9482321 0.9227591 0.9469137 0.9469137 0.9277405
[2,] 0.9235967 0.9593451 0.9550782 0.9708189 0.9593451 0.9593451 0.9285782
[3,] 1.5822051 1.1078766 0.9948773 1.4732528 1.1078766 1.1078766 0.9565821
[4,] 5.3850607 4.5448695 3.4111260 5.4908331 4.5448695 4.5448695 3.5526806
[5,] 9.1407362 9.8737074 10.4619965 9.0742958 9.8737074 9.8737074 10.3739311
[,57] [,58] [,59] [,60] [,61] [,62] [,63]
[1,] 0.9267192 0.9453132 0.9469137 0.8989453 0.9469137 0.9183014 0.9340765
[2,] 1.0301407 1.0513745 0.9593451 0.9382276 0.9593451 0.9275418 0.9902102
[3,] 2.2184258 1.6010005 1.1078766 1.3350062 1.1078766 1.2776094 1.4172247
[4,] 5.8875092 5.1738901 4.5448695 3.8871452 4.5448695 2.9608258 5.4847302
[5,] 8.4527764 9.3412238 9.8737074 10.1399246 9.8737074 10.5682490 9.1098668
[,64] [,65] [,66] [,67] [,68] [,69] [,70]
[1,] 0.9328282 0.9088546 0.9469137 0.9269934 0.9389789 0.9469137 0.9469137
[2,] 0.9474022 0.9148125 0.9593451 0.9343384 1.0209382 0.9593451 0.9593451
[3,] 1.5118987 0.9984325 1.1078766 1.2452088 1.7259716 1.1078766 1.1078766
[4,] 5.7354778 3.0209972 4.5448695 2.9143223 5.0013048 4.5448695 4.5448695
[5,] 8.8704668 10.5522257 9.8737074 10.5989577 9.4325482 9.8737074 9.8737074
[,71] [,72] [,73] [,74] [,75] [,76] [,77]
[1,] 0.9221126 0.9198293 0.9210772 0.9010486 0.9469137 0.9469137 0.9123577
[2,] 0.9423652 0.9261984 0.9262454 0.9183328 0.9593451 0.9593451 0.9599229
[3,] 1.7287790 0.9637605 0.9567248 1.6284843 1.1078766 1.1078766 1.4141051
[4,] 5.0343819 3.8276317 3.8290955 5.0421775 4.5448695 4.5448695 5.2773913
[5,] 9.3936114 10.2355298 10.2367823 9.3679103 9.8737074 9.8737074 9.2488590
[,78] [,79] [,80] [,81] [,82] [,83] [,84]
[1,] 0.9046134 0.9149463 0.9022484 0.9469137 0.9469137 0.9227571 0.9028759
[2,] 0.9097007 0.9449413 0.9712395 0.9593451 0.9593451 0.9370127 0.9584488
[3,] 0.9355966 1.3581181 1.7208400 1.1078766 1.1078766 1.0340602 1.5959869
[4,] 3.0045171 5.6793122 4.0859527 4.5448695 4.5448695 2.7827210 5.8651883
[5,] 10.5534453 8.9124396 9.9641199 9.8737074 9.8737074 10.6450024 8.6589079
[,85] [,86] [,87] [,88] [,89] [,90] [,91]
[1,] 0.9469137 0.8815139 0.9095021 0.9010592 0.9469137 0.9490269 0.9246248
[2,] 0.9593451 0.9763077 0.9236988 0.9244811 0.9593451 0.9589505 0.9379213
[3,] 1.1078766 1.5945350 1.5751301 1.9152988 1.1078766 1.0112137 1.2870290
[4,] 4.5448695 4.1340998 5.0719642 4.7396354 4.5448695 2.8048157 4.1533570
[5,] 9.8737074 9.9211237 9.3747039 9.5050071 9.8737074 10.6752241 10.0525171
[,92] [,93] [,94] [,95] [,96] [,97] [,98]
[1,] 0.9469137 0.9027924 0.8650480 0.9469137 0.8945464 0.8821927 0.9008958
[2,] 0.9593451 1.1041131 0.9217288 0.9593451 0.9688970 0.9221700 0.9403063
[3,] 1.1078766 2.1547320 1.1973792 1.1078766 1.3667417 1.3072429 2.1145937
[4,] 4.5448695 5.9522116 2.5422991 4.5448695 5.8648242 2.5129458 5.9748279
[5,] 9.8737074 8.3340292 10.6242610 9.8737074 8.6713457 10.6418278 8.3583270
[,99] [,100]
[1,] 0.9469137 0.9139391
[2,] 0.9593451 0.9386603
[3,] 1.1078766 1.3328277
[4,] 4.5448695 2.4978648
[5,] 9.8737074 10.6874162
MaOEA documentation built on Aug. 31, 2020, 5:07 p.m.
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Description Usage Arguments Value References Examples
Description
Do an iteration of Elitist Non-dominated Sorting Genetic Algorithm version III (NSGA-III). THe variation is using SBX and polynomial mutation.
Usage
1 |
Arguments
population |
The parent generation. One individual per column. nrow = number of variable, ncol = number of individuals in the population. |
fun |
Objective function being solved. Currently available in the package DTLZ1-DTLZ4, WFG4-WFG9. |
nObjective |
The number of objective functions. A scalar value. Needed to generate weight vectors. |
control |
A list, containing the following:
|
... |
Further arguments to be passed to |
Value
#' @return Returns a list for the next generation
population The new generation design points. Column major.
populationObjective The new generation's objective values. Column major.
References
Deb, K., Jain, H.: An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: Solving problems with box constraints. Trans. Evol. Comp. 18 (4), 577–601 (2014)
Examples
1 2 3 4 5 6 7 8 9 10 11 | nVar <- 14
nObjective <- 5
nIndividual <- 100
#control for NSGA3
ctrl <- list(crossoverProbability = 1,
mutationProbability = 1/nVar)
#Initial population
population <- matrix(runif(nIndividual*nVar), nrow = nVar)
# run a generation of NSGA-III with standard WFG8 test function.
NSGA3(population, WFG8,nObjective,ctrl,nObjective)
|
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().
$population
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.79238276 0.59517508 0.41522434 0.59517508 0.7977519 0.418387513
[2,] 0.98909722 0.15316826 0.90012160 0.15316826 0.8706306 0.882064418
[3,] 0.46818967 0.45475677 0.87212504 0.45475677 0.7052827 0.722193975
[4,] 0.59653217 0.32583912 0.08772934 0.32583912 0.9162719 0.088069222
[5,] 0.61192184 0.06398252 0.92286934 0.06398252 0.9187914 0.656968106
[6,] 0.06485533 0.07912143 0.45062678 0.07912143 0.7458760 0.864753943
[7,] 0.46855987 0.15065082 0.40996732 0.15065082 0.5962809 0.802962790
[8,] 0.93356924 0.05946864 0.53063452 0.05946864 0.3292424 0.693153681
[9,] 0.52235712 0.75640562 0.40670491 0.75640562 0.2298100 0.006375945
[10,] 0.15873548 0.92770900 0.61532273 0.92770900 0.9375008 0.435648699
[11,] 0.38676540 0.27034175 0.96748722 0.27034175 0.6070034 0.574339144
[12,] 0.44246320 0.37305418 0.81694383 0.37305418 0.8571831 0.618334848
[13,] 0.74872144 0.81003144 0.88773189 0.81003144 0.5660571 0.340853403
[14,] 0.57422842 0.34657259 0.60327129 0.34657259 0.5083197 0.794556550
[,7] [,8] [,9] [,10] [,11] [,12]
[1,] 0.80557317 0.59517508 0.42530499 0.59517508 0.80907629 0.44807301
[2,] 0.81139911 0.15316826 0.87178085 0.15316826 0.79751035 0.70738404
[3,] 0.91712924 0.45475677 0.14874226 0.45475677 0.92465270 0.99724883
[4,] 0.02427151 0.32583912 0.90853402 0.32583912 0.21973600 0.13049579
[5,] 0.05011832 0.06398252 0.40234126 0.06398252 0.05011832 0.56999455
[6,] 0.67496233 0.07912143 0.62543818 0.07912143 0.69111955 0.09688489
[7,] 0.44176660 0.15065082 0.87786511 0.15065082 0.44213835 0.24608580
[8,] 0.66490996 0.05946864 0.11669171 0.05946864 0.94798137 0.82185666
[9,] 0.70067776 0.75640562 0.14276472 0.75640562 0.85431560 0.58577796
[10,] 0.42850292 0.92770900 0.29987078 0.92770900 0.46878043 0.97399862
[11,] 0.90802817 0.27034175 0.79536819 0.27034175 0.90367948 0.43339770
[12,] 0.34215319 0.37305418 0.99510647 0.37305418 0.34215319 0.64008575
[13,] 0.09344907 0.81003144 0.07260505 0.81003144 0.09344907 0.92344191
[14,] 0.55497833 0.34657259 0.16937969 0.34657259 0.56881861 0.88443336
[,13] [,14] [,15] [,16] [,17] [,18]
[1,] 0.59517508 0.77165604 0.40770269 0.41041392 0.59517508 0.8202399
[2,] 0.15316826 0.97710039 0.97710039 0.70708767 0.15316826 0.7736050
[3,] 0.45475677 0.03731832 0.04889067 0.18919295 0.45475677 0.5171435
[4,] 0.32583912 0.36237396 0.36322173 0.70710644 0.32583912 0.7977451
[5,] 0.06398252 0.14818204 0.14818204 0.01033697 0.06398252 0.6944135
[6,] 0.07912143 0.12482182 0.12482182 0.52397433 0.07912143 0.2579115
[7,] 0.15065082 0.61727189 0.57733367 0.52397642 0.15065082 0.3546327
[8,] 0.05946864 0.34720182 0.20147516 0.73257562 0.05946864 0.2460770
[9,] 0.75640562 0.30562863 0.18505131 0.03274999 0.75640562 0.4848095
[10,] 0.92770900 0.91303292 0.91303292 0.08036027 0.92770900 0.6433276
[11,] 0.27034175 0.26786261 0.26442111 0.59611114 0.27034175 0.8130203
[12,] 0.37305418 0.81084104 0.81078496 0.08510854 0.37305418 0.9598869
[13,] 0.81003144 0.84380362 0.84380362 0.90192337 0.81003144 0.5914286
[14,] 0.34657259 0.40004273 0.52007225 0.11267624 0.34657259 0.1100577
[,19] [,20] [,21] [,22] [,23] [,24]
[1,] 0.832343994 0.59517508 0.4797500 0.4557857 0.8717994 0.59517508
[2,] 0.844601330 0.15316826 0.8910517 0.6035466 0.9869252 0.15316826
[3,] 0.132518489 0.45475677 0.0388335 0.2184373 0.4602665 0.45475677
[4,] 0.416371072 0.32583912 0.3852310 0.9711844 0.5954854 0.32583912
[5,] 0.566840647 0.06398252 0.9709074 0.6144317 0.6109143 0.06398252
[6,] 0.713298337 0.07912143 0.1797093 0.7927401 0.6446914 0.07912143
[7,] 0.278312425 0.15065082 0.4373645 0.7591118 0.7957335 0.15065082
[8,] 0.572392972 0.05946864 0.3157601 0.2892671 0.9324969 0.05946864
[9,] 0.330320968 0.75640562 0.2473747 0.9697201 0.9218709 0.75640562
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