# boundedPolyMutation: Bounded Polynomial Mutation Operator In nsga2R: Elitist Non-dominated Sorting Genetic Algorithm based on R

## Description

The bounded polynomial mutation operator is a real-parameter genetic operator. Like in the simulated binary crossover operator, the probability distribution is also a polynomial function instead of a normal distribution.

## Usage

 `1` ```boundedPolyMutation(parent_chromosome, lowerBounds, upperBounds, mprob, mum) ```

## Arguments

 `parent_chromosome` Mating pool with decision variables `lowerBounds` Lower bounds of each decision variable `upperBounds` Upper bounds of each decision variable `mprob` Mutation probability `mum` Mutation distribution index, it can be any nonnegative real number

## Value

Return the offspring population with decision variables

## Author(s)

Ching-Shih (Vince) Tsou [email protected]

## References

Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. (2002), " A fast and elitist multiobjective genetic algorithm: NSGA-II", IEEE Transactions on Evolutionary Computation, 6(2), 182-197.

## Examples

 ```1 2 3 4 5 6 7 8``` ```set.seed(1234) lowerBounds <- rep(0,30) upperBounds <- rep(1,30) mprob <- 0.2 MutDistIdx <- 20 matingPool <- matrix(runif(1200, 0, 1), nrow=40, ncol=30) childAfterM <- boundedPolyMutation(matingPool,lowerBounds,upperBounds,mprob,MutDistIdx) childAfterM ```

### Example output

```Loading required package: mco
[,1]       [,2]       [,3]       [,4]       [,5]       [,6]
[1,] 0.113703411 0.55333359 0.92640048 0.74427722 0.55538428 0.66075463
[2,] 0.622299405 0.64640609 0.47190972 0.95837082 0.59079840 0.52835938
[3,] 0.609274733 0.31182431 0.14261534 0.99459825 0.43250740 0.31749382
[4,] 0.623379442 0.62181920 0.54426976 0.94236072 0.22484576 0.76785547
[5,] 0.909471080 0.32977018 0.19617465 0.48613541 0.08498474 0.52630849
[6,] 0.640310605 0.50199747 0.89858049 0.28345954 0.72892226 0.73744155
[7,] 0.009495756 0.67709453 0.38949978 0.25154570 0.43101637 0.30766574
[8,] 0.232550506 0.48499124 0.31087078 0.50325517 0.05261028 0.40417325
[9,] 0.620120687 0.28921297 0.16002866 0.61181551 0.80240202 0.20440245
[10,] 0.514251141 0.72768975 0.89618585 0.31844581 0.32527830 0.98563309
[11,] 0.690388562 0.07377988 0.16639378 0.95180876 0.66038202 0.58884792
[12,] 0.568150725 0.41120421 0.89117645 0.65197637 0.58427152 0.39867708
[13,] 0.282733584 0.71727174 0.13407820 0.12743340 0.76920698 0.12106922
[14,] 0.923433484 0.50454591 0.13161413 0.42304699 0.42697577 0.75806140
[15,] 0.292315840 0.15299896 0.05910709 0.91431691 0.34357270 0.56678128
[16,] 0.837295628 0.44974172 0.51158358 0.46779233 0.75911999 0.93217357
[17,] 0.286223285 0.49396092 0.30019905 0.90816915 0.42403021 0.68138210
[18,] 0.266820780 0.75120020 0.02671690 0.59774328 0.56088725 0.69741122
[19,] 0.195772458 0.14303453 0.30964743 0.63174282 0.11613577 0.47922247
[20,] 0.179916862 0.84839241 0.74211966 0.84054803 0.30302180 0.83584114
[21,] 0.316612455 0.86483383 0.03545673 0.46847401 0.47880269 0.42288150
[22,] 0.313173512 0.04185728 0.56507611 0.98363511 0.34483055 0.03139212
[23,] 0.080407160 0.31718216 0.30563725 0.32438603 0.60071414 0.25814665
[24,] 0.039995918 0.01374994 0.20419632 0.48394655 0.07608332 0.33484473
[25,] 0.218799541 0.23902573 0.10061649 0.47081676 0.95599261 0.13354967
[26,] 0.810598552 0.70649462 0.32568192 0.62747768 0.02220682 0.49954639
[27,] 0.525697547 0.30809476 0.15506197 0.74160019 0.84171063 0.80213563
[28,] 0.914658166 0.50854757 0.12996214 0.56596682 0.61281545 0.27115326
[29,] 0.831345047 0.05164662 0.43553106 0.98078651 0.31009417 0.44896835
[30,] 0.045770263 0.56456984 0.03864265 0.57681274 0.74256937 0.57653493
[31,] 0.456091482 0.12148019 0.71330156 0.43904205 0.67182230 0.79705290
[32,] 0.265186672 0.89283638 0.10076904 0.22859970 0.99251599 0.56695890
[33,] 0.304672203 0.01462726 0.95030494 0.08215807 0.12048445 0.10669682
[34,] 0.507306870 0.82098599 0.12181776 0.85026492 0.88323958 0.80764845
[35,] 0.181096208 0.08996133 0.21965662 0.23466126 0.81582339 0.56711207
[36,] 0.759670635 0.51918998 0.91308777 0.99700795 0.82185118 0.21224093
[37,] 0.201248038 0.38426669 0.94585312 0.60189755 0.83470266 0.74239766
[38,] 0.258809819 0.07005250 0.27915622 0.99874081 0.73273222 0.30721835
[39,] 0.992150418 0.25680118 0.12347109 0.37559938 0.97623320 0.52850453
[40,] 0.901669637 0.66849540 0.79716046 0.55512663 0.63920458 0.98970989
[,7]      [,8]       [,9]       [,10]      [,11]        [,12]
[1,] 0.424109178 0.3691760 0.19840001 0.003145462 0.74692294 0.8146524148
[2,] 0.147106397 0.4292521 0.86180531 0.557941298 0.41662872 0.8824088296
[3,] 0.217134715 0.9185144 0.36480033 0.465007336 0.73361900 0.7454413087
[4,] 0.689117507 0.7843448 0.15325377 0.329715145 0.77579487 0.5017915608
[5,] 0.980212709 0.7378315 0.33928338 0.835475627 0.57358702 0.9885014733
[6,] 0.477033039 0.2807726 0.36718044 0.977701663 0.17600232 0.5552680509
[7,] 0.773523622 0.4568266 0.42737908 0.660514947 0.75826533 0.9193874028
[8,] 0.574312945 0.2875376 0.18633690 0.233574860 0.09268309 0.6304392638
[9,] 0.965939701 0.6962911 0.65801660 0.819200420 0.62235853 0.6132155319
[10,] 0.879867546 0.8207563 0.92041138 0.724684895 0.41591320 0.0336092997
[11,] 0.527468964 0.6551535 0.73389406 0.976357153 0.77651087 0.0367674298
[12,] 0.592698951 0.4135047 0.88231927 0.265113029 0.78131515 0.7759688012
[13,] 0.263886474 0.9518294 0.98225909 0.878820043 0.96729632 0.9982450008
[14,] 0.279542709 0.2431095 0.09627905 0.487889212 0.21590325 0.9601184016
[15,] 0.065103244 0.6086850 0.47261674 0.269851289 0.86700891 0.7269823240
[16,] 0.588345463 0.7579515 0.38605066 0.395096999 0.41691803 0.6805038610
[17,] 0.262355682 0.6936674 0.37416586 0.759339716 0.51302872 0.2302903324
[18,] 0.003282331 0.1154278 0.02785566 0.100801642 0.77493732 0.5777834911
[19,] 0.622680347 0.6359117 0.86422859 0.421359690 0.13254332 0.5739705635
[20,] 0.520051165 0.3090254 0.41052928 0.684910234 0.43321728 0.0495949083
[21,] 0.891717930 0.3529985 0.95584022 0.083669889 0.66204757 0.3728201450
[22,] 0.029556814 0.9809583 0.27215284 0.205986500 0.90771977 0.8947680488
[23,] 0.599769349 0.5388828 0.51724649 0.002146712 0.29999742 0.3917717456
[24,] 0.268419770 0.4374826 0.97830984 0.107842679 0.11479113 0.5169452706
[25,] 0.036306334 0.9135507 0.36969649 0.210695599 0.93234592 0.1752800765
[26,] 0.100705462 0.4524834 0.31043044 0.115153674 0.19993327 0.1926054636
[27,] 0.748161140 0.2164755 0.03420963 0.687159432 0.02546308 0.5747260568
[28,] 0.015031884 0.9916091 0.66756585 0.193272230 0.42584008 0.3931208388
[29,] 0.049461146 0.5484554 0.92091638 0.984921893 0.31239038 0.6251974967
[30,] 0.747623786 0.7688158 0.04498960 0.914382618 0.27560130 0.5711683798
[31,] 0.357237664 0.9134217 0.20113263 0.694714032 0.66349054 0.1406190705
[32,] 0.758958196 0.6821120 0.74351488 0.739891944 0.78389610 0.2892716692
[33,] 0.375956343 0.4072514 0.12216882 0.732440298 0.43969737 0.0006121558
[34,] 0.799462709 0.3110266 0.70888359 0.652598444 0.89755365 0.9553637172
[35,] 0.025692766 0.1460828 0.99883359 0.167046307 0.27220721 0.4729048298
[36,] 0.506358550 0.1966677 0.94391305 0.923180858 0.65902903 0.9770535454
[37,] 0.821228646 0.1922093 0.59290390 0.548162914 0.38028929 0.5202592486
[38,] 0.433751752 0.4084144 0.73129564 0.536495635 0.93539078 0.4671611886
[39,] 0.335111782 0.4176035 0.48673418 0.018843747 0.73550093 0.8044374597
[40,] 0.344637322 0.8345428 0.76815200 0.366399628 0.59009045 0.1420735531
[,13]      [,14]      [,15]      [,16]      [,17]      [,18]
[1,] 0.52357778 0.83541903 0.19132825 0.28097181 0.52689513 0.47845845
[2,] 0.56042112 0.29500818 0.99020375 0.17418816 0.18787605 0.11027702
[3,] 0.66034281 0.29989024 0.68088234 0.17022444 0.50964893 0.62935352
[4,] 0.40715179 0.92464863 0.86469794 0.56054363 0.92707328 0.11342334
[5,] 0.13615199 0.55653936 0.24166076 0.42880059 0.23981486 0.83029322
[6,] 0.07388093 0.85447573 0.86257910 0.38918677 0.35628694 0.32796644
[7,] 0.71320600 0.03892874 0.79077361 0.84370641 0.05689367 0.77065987
[8,] 0.70279491 0.03982544 0.61232477 0.20879071 0.88473156 0.02763326
[9,] 0.76389526 0.63254297 0.20855917 0.50942478 0.51199296 0.54003520
[10,] 0.15705626 0.23908677 0.05941213 0.39496533 0.80471187 0.47894014
[11,] 0.59934461 0.25252500 0.61911355 0.25816006 0.23681766 0.87790452
[12,] 0.76334179 0.62462450 0.80393136 0.80296144 0.68683534 0.48682885
[13,] 0.96046435 0.40568980 0.19863062 0.30699922 0.86050943 0.22235618
[14,] 0.30802085 0.79847307 0.66565012 0.07813034 0.45015293 0.50914490
[15,] 0.65706588 0.11746294 0.40293278 0.94677874 0.17037473 0.01213047
[16,] 0.33780463 0.99449728 0.38696269 0.37866848 0.50869632 0.08849086
[17,] 0.60425038 0.64985733 0.06022841 0.32745204 0.87001938 0.31857639
[18,] 0.08395502 0.65561093 0.42028041 0.66482686 0.03330662 0.54530642
[19,] 0.60566724 0.74747962 0.55109725 0.77732101 0.25815528 0.28196300
[20,] 0.59591103 0.51427321 0.81607572 0.48412162 0.93708628 0.73440098
[21,] 0.66891915 0.38033012 0.83779684 0.87354719 0.61503638 0.01069213
[22,] 0.80104330 0.61130827 0.01209806 0.04988784 0.94951899 0.59863873
[23,] 0.85545589 0.97691111 0.57269810 0.70549387 0.81559449 0.80714860
[24,] 0.05013991 0.21585867 0.30164086 0.82551193 0.04931545 0.46599317
[25,] 0.67443409 0.74874936 0.03867870 0.33661402 0.23297481 0.21658603
[26,] 0.84589330 0.43237563 0.33932484 0.93152059 0.51204261 0.08006783
[27,] 0.74639832 0.82859624 0.26745324 0.48404591 0.71036062 0.41057972
[28,] 0.82956440 0.88334052 0.97402374 0.94604700 0.28465309 0.63918557
[29,] 0.12790013 0.97978864 0.95114345 0.31126072 0.46494880 0.05624466
[30,] 0.79410844 0.91400073 0.61606061 0.59905187 0.76090803 0.56831566
[31,] 0.35550591 0.25748658 0.96483701 0.89022341 0.12814305 0.70799067
[32,] 0.94808167 0.22344782 0.87803452 0.60736355 0.93429535 0.97579369
[33,] 0.96809441 0.79063292 0.11999000 0.37579248 0.39354950 0.97070298
[34,] 0.58617930 0.16509481 0.59625786 0.56005963 0.32127160 0.11691571
[35,] 0.11049426 0.83807586 0.35692019 0.93942724 0.94736129 0.21385867
[36,] 0.78383547 0.97192044 0.67488646 0.68233145 0.84165254 0.18008459
[37,] 0.60182294 0.49753823 0.63819020 0.28719002 0.52265474 0.45519014
[38,] 0.08827442 0.03980805 0.69686702 0.77512980 0.89169600 0.20389975
[39,] 0.65726228 0.62515660 0.62519597 0.25877803 0.20674070 0.97433515
[40,] 0.33208094 0.83038591 0.12222209 0.33933783 0.95019871 0.09940844
[,19]        [,20]      [,21]      [,22]      [,23]      [,24]
[1,] 0.8248006778 0.0332543079 0.10994604 0.10806949 0.68691379 0.54173620
[2,] 0.1010262312 0.6476548435 0.87143679 0.58484017 0.25156730 0.45577571
[3,] 0.9721297773 0.0040038908 0.51441977 0.64585140 0.44550453 0.21103420
[4,] 0.0043137661 0.5773450769 0.28569882 0.16716337 0.52916309 0.23063895
[5,] 0.4610729334 0.2195595172 0.33673402 0.45775700 0.56818118 0.59109980
[6,] 0.9856622049 0.6105293497 0.56965201 0.90846708 0.93042103 0.23303186
[7,] 0.4394909204 0.9270527456 0.18422929 0.56594591 0.17238205 0.75740365
[8,] 0.3435957879 0.5732149626 0.43937147 0.94494588 0.04801750 0.55154607
[9,] 0.3051547669 0.7990209830 0.66182218 0.74474213 0.09893908 0.12249631
[10,] 0.9876470899 0.3004978194 0.42033862 0.71676715 0.01920277 0.15050640
[11,] 0.9242956992 0.8878271687 0.61849242 0.54536640 0.92039977 0.14578579
[12,] 0.0122110262 0.8550552714 0.19562365 0.97673628 0.74644589 0.99056821
[13,] 0.1748932553 0.8370745510 0.92830503 0.94353491 0.60540889 0.02609232
[14,] 0.4689253644 0.0721003956 0.67357420 0.19624488 0.37769609 0.60673435
[15,] 0.6206978902 0.6239091882 0.13103702 0.54599676 0.34149088 0.10212060
[16,] 0.7414696360 0.5107358950 0.37688659 0.64486106 0.32753956 0.50942560
[17,] 0.4815281834 0.0658973011 0.30230307 0.10492118 0.39729129 0.18742135
[18,] 0.8071745096 0.2241470253 0.80525769 0.03820773 0.65010612 0.50722189
[19,] 0.9878338575 0.5814365137 0.47012840 0.77091537 0.98059174 0.38517551
[20,] 0.9275750027 0.3622224077 0.44144600 0.95731114 0.86942494 0.53582062
[21,] 0.2715825546 0.9448925692 0.07959662 0.11068343 0.64157316 0.92186830
[22,] 0.0987931858 0.0565309483 0.37353533 0.40224748 0.40952429 0.58355793
[23,] 0.0656125834 0.0002812684 0.38793475 0.02749887 0.92093733 0.81290209
[24,] 0.1873251994 0.2899808860 0.39029461 0.41438876 0.45142194 0.76753305
[25,] 0.5919763285 0.2172976583 0.23941948 0.33575474 0.91427262 0.60756352
[26,] 0.0008630857 0.6885741784 0.78958566 0.91807567 0.02635509 0.53378231
[27,] 0.5363056090 0.8648701455 0.01587122 0.19694351 0.34193931 0.28547890
[28,] 0.6553977022 0.0298377264 0.39876005 0.98193083 0.25607750 0.12418847
[29,] 0.1947120593 0.7015088277 0.38826759 0.27175760 0.77713162 0.48396407
[30,] 0.6218706350 0.1667423935 0.45778016 0.53153673 0.29605462 0.36735679
[31,] 0.5526229665 0.7850592399 0.29664580 0.94594644 0.25745843 0.65711640
[32,] 0.7111809149 0.1458532037 0.80323753 0.90491402 0.47133590 0.95156857
[33,] 0.3914565546 0.6762002339 0.87139501 0.91496000 0.07028715 0.30711898
[34,] 0.8356535558 0.5202723837 0.90347605 0.30102181 0.22659552 0.82072507
[35,] 0.3349178364 0.7049989968 0.27289891 0.76610854 0.11474652 0.85521609
[36,] 0.8860823966 0.2645380092 0.67543921 0.18938981 0.07997872 0.04594012
[37,] 0.6917566981 0.5106579767 0.71141103 0.10136097 0.48388064 0.86377842
[38,] 0.9165655458 0.7922364022 0.20165717 0.08598643 0.98242556 0.47614039
[39,] 0.3700721294 0.1797051979 0.55670852 0.50923331 0.96716870 0.12170523
[40,] 0.6150684627 0.8646464990 0.62351335 0.42179987 0.79386561 0.65589569
[,25]        [,26]      [,27]       [,28]      [,29]       [,30]
[1,] 0.332793031 8.376339e-01 0.98311488 0.667999492 0.24169185 0.167994908
[2,] 0.458144111 4.874663e-01 0.26107766 0.995813008 0.72417416 0.920245474
[3,] 0.886233608 1.103370e-01 0.43474285 0.903794139 0.14148725 0.682476294
[4,] 0.793329014 3.360893e-01 0.70764482 0.340299979 0.82244663 0.012365578
[5,] 0.045780544 9.416317e-01 0.90294457 0.257298679 0.39410591 0.637488722
[6,] 0.067791622 3.896648e-01 0.51312311 0.535483958 0.43621682 0.766650478
[7,] 0.662651305 4.565140e-01 0.50052403 0.493265830 0.54304442 0.457386415
[8,] 0.228873497 1.073443e-01 0.04979171 0.018923723 0.10087204 0.476240053
[9,] 0.566012896 9.626749e-01 0.24939016 0.225062550 0.76522173 0.704544815
[10,] 0.330171705 9.880969e-01 0.82148793 0.658708520 0.36094052 0.466410293
[11,] 0.999303025 4.038305e-01 0.19816424 0.129843158 0.89784999 0.273552161
[12,] 0.880583881 8.675411e-01 0.88109284 0.115849975 0.72183160 0.008326433
[13,] 0.003169789 6.336720e-02 0.36431779 0.032231048 0.23229847 0.035968955
[14,] 0.640476994 6.840599e-01 0.26994998 0.288598927 0.09242703 0.233275756
[15,] 0.200231169 6.885818e-01 0.61206776 0.577510604 0.61436836 0.875836252
[16,] 0.689499255 3.139780e-01 0.16545058 0.038555500 0.20184154 0.929886921
[17,] 0.749853460 6.385193e-01 0.43529441 0.726268208 0.89235846 0.408776656
[18,] 0.238327119 6.412363e-01 0.95148622 0.880390306 0.31380989 0.151565895
[19,] 0.952966778 4.929685e-01 0.57960293 0.756422072 0.18370321 0.357522574
[20,] 0.584783275 8.560004e-01 0.79079790 0.405224441 0.92132083 0.374593878
[21,] 0.799458068 1.453584e-01 0.57884620 0.082265533 0.41185982 0.562581659
[22,] 0.934602503 2.995514e-01 0.54187464 0.423766234 0.61353494 0.308272849
[23,] 0.076592922 2.007586e-01 0.76257168 0.129306000 0.01178739 0.778141683
[24,] 0.663601630 9.788740e-01 0.14225535 0.030568625 0.85459831 0.925971020
[25,] 0.987434667 4.949632e-01 0.39185771 0.036700484 0.61310549 0.664977765
[26,] 0.252331066 4.033863e-01 0.80370827 0.357248281 0.43489836 0.305246623
[27,] 0.039436219 8.625999e-01 0.94901189 0.245515005 0.26069906 0.823105626
[28,] 0.985621971 6.944009e-01 0.03845219 0.516365171 0.25347783 0.612483564
[29,] 0.132850762 3.577581e-01 0.66919590 0.567572717 0.17749917 0.518398514
[30,] 0.176190732 3.736045e-01 0.16308326 0.446571097 0.64681045 0.596523283
[31,] 0.482794811 1.917544e-01 0.11632979 0.723905587 0.16618141 0.307030329
[32,] 0.636085044 9.300941e-01 0.13242307 0.336218068 0.02518213 0.730599530
[33,] 0.986979070 5.106329e-05 0.42851495 0.207526805 0.67166066 0.381917193
[34,] 0.099534687 9.310219e-01 0.26464756 0.991406904 0.07938249 0.592990426
[35,] 0.693682792 6.894351e-01 0.69703196 0.002089346 0.01529103 0.814812751
[36,] 0.001308702 2.527522e-01 0.15712685 0.934506335 0.22248065 0.300281578
[37,] 0.767425936 6.736818e-01 0.36728343 0.829913499 0.42801609 0.197865871
[38,] 0.319979546 4.768093e-01 0.33312497 0.331518768 0.01244971 0.507930327
[39,] 0.941597028 9.047651e-01 0.63495096 0.730816669 0.15535875 0.170140526
[40,] 0.195397579 3.055097e-01 0.40570821 0.138862453 0.12828180 0.272492176
```

nsga2R documentation built on May 29, 2017, 8:02 p.m.