# NSGA3: Elitist Non-dominated Sorting Genetic Algorithm version III In MaOEA: Many Objective Evolutionary Algorithm

## 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` ```NSGA3(population, fun, nObjective, control = list(), ...) ```

## 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
\$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
[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
[,68]      [,69]      [,70]       [,71]      [,72]      [,73]
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[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
[5,] 0.19005658 0.06398252 0.06398252 0.789197587 0.51865086 0.65940395
[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
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[10,] 0.29284772 0.92770900 0.92770900 0.012301408 0.27939939 0.27995141
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[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
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[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.