examples: Unconstrained and Constrained Optimization Examples
In mopsocd: MOPSOCD: Multi-objective Particle Swarm Optimization with Crowding Distance
Description
Examples on how to use the MOPSOCD solver for unconstrained and constrained optimization.
See Also
mopsocd pareto
Examples
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## Typical MOPSOCD usage:
## 1) Define Objectives
## Format:
## fn <- function(x) {
## ## User-Defined Objective Functions
## f1 <- Objective Function 1
## f2 <- Objective Function 2
## ...
## fn <- Objective Function n
## ## End of User-Defined Objective Functions
## return(c(f1,f2, ...,fn))
## }
##
## 2) Define Constraints
## Format:
## gn <- function(x) {
## ## User-Defined Constraints
## g1 <- Constraint 1
## g2 <- Constraint 2
## ...
## gn <- Constraint n
## ## End of User-Defined Constraints
## return(c(g1,g2, ...,gn))
## }
##
## 3) Set Arguments
## 4) Run Solver
## 5) Print Pareto Object Fields
## 6) Plot Non-Dominated Points
#####################
## Example 1: Viennet Test Function (Unconstrained Optimization)
#####################
## Define Objectives
viennet <- function(x){
f1 <- 0.5*(x[1]^2+x[2]^2)+sin(x[1]^2+x[2]^2)
f2 <- 0.125*(3*x[1]-2*x[2]+4)^2+(1.0/27.0)*(x[1]-x[2]+1)^2+15
f3 <- 1.0/(x[1]^2+x[2]^2+1)-1.1*exp(-(x[1]^2+x[2]^2))
return(c(f1,f2,f3))
}
## Set Arguments
varcount <- 2
fncount <- 3
lbound <- c(-3,-3)
ubound <- c(3,3)
optmin <- 0
## Run Solver (gn omitted)
ex1 <- mopsocd(viennet,varcnt=varcount,fncnt=fncount,
lowerbound=lbound,upperbound=ubound,opt=optmin)
## Access Pareto Object Fields
print(ex1$numsols)
print(ex1$objfnvalues)
print(ex1$paramvalues)
## Plot
#library(scatterplot3d)
#scatterplot3d(ex1$objfnvalues[,1],ex1$objfnvalues[,2],ex1$objfnvalues[,3])
#####################
## Example 2: Kita Test Function (Constrained Optimization)
#####################
## Define Objectives
kita <- function(x) {
f1 <- -(x[1] * x[1]) + x[2]
f2 <- (x[1]/2)+x[2]+1
return(c(f1,f2))
}
## Define Constraints
gn <- function(x) {
g1 <- x[1]/6.0 + x[2] - 13.0/2.0 <= 0.0
g2 <- x[1]/2.0 + x[2] - 15.0/2.0 <= 0.0
g3 <- 5.0*x[1]+x[2] - 30.0 <= 0.0
return(c(g1,g2,g3))
}
## Set Arguments
varcount <- 2
fncount <- 2
lbound <- c(0,0)
ubound <- c(7,7)
optmax <- 1
## Run Solver
ex2 <- mopsocd(kita,gn,varcnt=varcount,fncnt=fncount,
lowerbound=lbound,upperbound=ubound,opt=optmax)
## Access Pareto Object Fields
print(ex2$numsols)
print(ex2$objfnvalues)
print(ex2$paramvalues)
## Plot
plot(ex2$objfnvalues[,1],ex2$objfnvalues[,2])
#####################
## Example 3: Osyczka-Kundu Test Function (Constrained Optimization)
#####################
## Define Objectives
osyczka <- function(x){
f1 <- -(25.0*(x[1]-2.0)^2+(x[2]-2.0)^2+(x[3]-1.0)^2+(x[4]-4.0)^2+(x[5]-1.0)^2)
f2 <- 0.0
for (i in 1:6) {
f2 <- f2+x[i]^2
}
return(c(f1,f2))
}
## Define Constraints
gn <- function(x) {
## User-Defined Constraints
g1 <- x[1] + x[2] - 2.0 >= 0.0
g2 <- 6.0 - x[1] - x[2] >= 0.0
g3 <- 2.0 - x[2] + x[1] >= 0.0
g4 <- 2.0 - x[1] + 3.0*x[2] >= 0.0
g5 <- 4.0 - (x[3] - 3.0)^2 - x[4] >= 0.0
g6 <- (x[5] - 3.0)^2 + x[6] - 4.0 >= 0.0
## End of User-Defined Constraints
return(c(g1,g2,g3,g4,g5,g6))
}
## Set Arguments
varcount <- 6
fncount <- 2
lbound <- c(0,0,1,0,1,0)
ubound <- c(10,10,5,6,5,10)
optmin <- 0
## Run Solver
ex3 <- mopsocd(osyczka,gn,varcnt=varcount,fncnt=fncount,
lowerbound=lbound,upperbound=ubound,opt=optmin,
popsize=100,maxgen=25,archivesize=500)
# For better results, use the following settings:
# popsize=1000,maxgen=1000.
## Access Pareto Object Fields
print(ex3$numsols)
print(ex3$objfnvalues)
print(ex3$paramvalues)
## Plot
plot(ex3$objfnvalues[,1],ex3$objfnvalues[,2])
Example output
[1] 250
[,1] [,2] [,3]
[1,] 1.228796018 15.00025 0.176684852
[2,] 0.000596315 16.98180 -0.099960175
[3,] 1.448129546 15.00001 0.161894056
[4,] 7.482665747 15.02963 0.069267246
[5,] 8.191314820 15.00793 0.064294255
[6,] 0.593862552 15.39900 -0.022355697
[7,] 2.240430901 15.00420 0.146404287
[8,] 3.173933248 15.00068 0.134886914
[9,] 7.409818573 15.06034 0.069567664
[10,] 3.329774203 15.00121 0.133161940
[11,] 4.277449194 15.00110 0.122567561
[12,] 3.486110372 15.00044 0.131450410
[13,] 3.085414785 15.00683 0.135879774
[14,] 0.651934286 15.32032 -0.013030093
[15,] 8.107792697 15.00870 0.061956194
[16,] 5.631281415 15.01644 0.076201205
[17,] 0.535489021 15.42275 -0.031641888
[18,] 1.894962462 15.00293 0.151841440
[19,] 5.688042098 15.04500 0.075968588
[20,] 2.324519461 15.00047 0.145223867
[21,] 0.997344552 15.12165 0.042486325
[22,] 3.767731604 15.00347 0.128374787
[23,] 5.192231149 15.01884 0.078188187
[24,] 5.132555667 15.00482 0.078494455
[25,] 6.531184685 15.00714 0.072818243
[26,] 4.207610521 15.00107 0.123402530
[27,] 5.764988260 15.01452 0.075659483
[28,] 3.617083839 15.00044 0.130022092
[29,] 1.837472739 15.00030 0.152873604
[30,] 0.367563263 15.62257 -0.057393803
[31,] 6.594140486 15.01149 0.072593873
[32,] 3.542967870 15.00202 0.130830234
[33,] 3.841647441 15.00284 0.127561055
[34,] 2.900268138 15.00369 0.137999362
[35,] 3.255673899 15.00197 0.133979045
[36,] 7.546145543 15.01519 0.068997113
[37,] 5.386307120 15.00660 0.077261131
[38,] 7.704605826 15.02667 0.058766527
[39,] 2.745398890 15.00307 0.139830957
[40,] 4.781094416 15.04469 0.080629774
[41,] 3.702907365 15.00332 0.129084948
[42,] 6.829395081 15.01129 0.071753501
[43,] 0.068567438 16.32286 -0.094561119
[44,] 2.620564257 15.00650 0.141357743
[45,] 5.560947994 15.01349 0.076495531
[46,] 3.020596140 15.00196 0.136614519
[47,] 4.731120400 15.00416 0.081005536
[48,] 7.630317268 15.02920 0.068624184
[49,] 2.974729250 15.00064 0.137138966
[50,] 7.013744377 15.02183 0.071085060
[51,] 0.265937816 15.79042 -0.071756902
[52,] 0.173999195 15.97147 -0.083434740
[53,] 7.575175782 15.08837 0.055164696
[54,] 3.676921893 15.00346 0.129368973
[55,] 3.895238273 15.00263 0.126967479
[56,] 6.137777297 15.00542 0.074238513
[57,] 7.290132129 15.03892 0.070043487
[58,] 0.403501599 15.57591 -0.052050034
[59,] 6.718892320 15.01322 0.072149125
[60,] 8.189423303 15.00791 0.064369480
[61,] 0.880744700 15.17756 0.023893997
[62,] 5.968161249 15.02550 0.074871834
[63,] 4.434130160 15.00634 0.084395963
[64,] 4.485075514 15.00308 0.091527625
[65,] 5.855959421 15.05538 0.075302185
[66,] 7.220075791 15.05530 0.070313834
[67,] 7.754429151 15.00695 0.068033615
[68,] 0.439036384 15.52645 -0.046662192
[69,] 5.231635913 15.00732 0.077992003
[70,] 7.824993199 15.01496 0.067668071
[71,] 6.939320202 15.06164 0.071356613
[72,] 4.821995919 15.00454 0.080340454
[73,] 2.037602177 15.00055 0.149459712
[74,] 6.672903032 15.03265 0.072313200
[75,] 2.679421660 15.00080 0.140631601
[76,] 2.441483921 15.00025 0.143648234
[77,] 5.272818987 15.00589 0.077791625
[78,] 0.213135461 15.89074 -0.078649519
[79,] 0.752747862 15.24946 0.003254016
[80,] 5.093712816 15.04197 0.078700366
[81,] 0.958171045 15.15466 0.036270653
[82,] 5.347533212 15.00502 0.077439061
[83,] 2.198098263 15.00031 0.147015837
[84,] 7.954189265 15.01249 0.060588390
[85,] 0.146922358 16.05179 -0.086558096
[86,] 4.949497438 15.00200 0.100818300
[87,] 0.826250330 15.20616 0.015125628
[88,] 6.896475258 15.00604 0.071511817
[89,] 4.145082676 15.00723 0.124135531
[90,] 4.988919136 15.00185 0.102008633
[91,] 5.898426192 15.02016 0.075138067
[92,] 5.309535545 15.00514 0.077616689
[93,] 7.662996854 15.03610 0.068473984
[94,] 0.323784023 15.69148 -0.063732690
[95,] 6.974857005 15.02722 0.071227286
[96,] 2.933156433 15.00031 0.137617890
[97,] 3.579469134 15.00763 0.130432267
[98,] 3.802366082 15.00234 0.127994121
[99,] 6.773156568 15.00876 0.071955155
[100,] 0.117330606 16.16372 -0.089774113
[101,] 6.405726954 15.02246 0.073266599
[102,] 0.715164825 15.27392 -0.002822626
[103,] 0.500483357 15.45791 -0.037149062
[104,] 1.123709661 15.08182 0.062278625
[105,] 7.915018904 15.01406 0.060294266
[106,] 1.512931239 15.01153 0.160004457
[107,] 3.430644873 15.00477 0.132056234
[108,] 0.472424878 15.48458 -0.041520325
[109,] 7.785683943 15.02404 0.059363159
[110,] 0.304838628 15.71365 -0.066408719
[111,] 5.817054729 15.02013 0.075453986
[112,] 2.840521756 15.00616 0.138698709
[113,] 7.258561981 15.01349 0.070165969
[114,] 4.025143990 15.00120 0.125511063
[115,] 4.692814463 15.02908 0.081313388
[116,] 0.687406894 15.29297 -0.007307805
[117,] 5.930663112 15.01693 0.075014511
[118,] 5.056223443 15.03772 0.078904546
[119,] 5.024200424 15.00168 0.103416808
[120,] 2.164409360 15.00016 0.147511604
[121,] 1.668047777 15.00631 0.142878948
[122,] 6.013767323 15.01407 0.074699714
[123,] 4.603181324 15.00481 0.082123797
[124,] 4.860227257 15.04848 0.080082624
[125,] 7.342933904 15.03495 0.069835973
[126,] 2.128758544 15.00334 0.148045628
[127,] 6.863918954 15.05292 0.071629295
[128,] 6.495690822 15.01736 0.072944865
[129,] 7.358067152 15.00664 0.069775830
[130,] 3.992396524 15.00573 0.125880980
[131,] 1.049613475 15.10043 0.050723478
[132,] 6.187797287 15.01860 0.074054900
[133,] 1.728886554 15.00109 0.154969582
[134,] 6.102103969 15.01043 0.074370254
[135,] 0.236513724 15.85594 -0.075654748
[136,] 1.092490939 15.08643 0.057428306
[137,] 3.958676637 15.00078 0.126259794
[138,] 6.072165269 15.01139 0.074481373
[139,] 3.063404783 15.00293 0.136128475
[140,] 1.629085232 15.00729 0.137239109
[141,] 3.374918472 15.00054 0.132666306
[142,] 7.177296594 15.01816 0.070476497
[143,] 6.315980948 15.01521 0.073589319
[144,] 5.439553572 15.00538 0.077021839
[145,] 7.061230619 15.01626 0.070910243
[146,] 3.927332201 15.00823 0.126610211
[147,] 0.785426385 15.22828 0.008536058
[148,] 3.211469389 15.00103 0.134469057
[149,] 4.179700165 15.00932 0.123731266
[150,] 5.542302070 15.00501 0.076574787
[151,] 1.161389053 15.06795 0.068096176
[152,] 2.462121319 15.00039 0.143377306
[153,] 1.698072886 15.00604 0.147253036
[154,] 1.999755850 15.00008 0.150069708
[155,] 4.320567524 15.01924 0.122041974
[156,] 6.239664454 15.00548 0.073865730
[157,] 2.383973378 15.00502 0.144414072
[158,] 4.914267576 15.01122 0.079736029
[159,] 4.514559089 15.00696 0.083121044
[160,] 2.667225526 15.00244 0.140781109
[161,] 2.078484496 15.00585 0.148816381
[162,] 1.799681084 15.00126 0.153579448
[163,] 2.577937490 15.00237 0.141891289
[164,] 6.440007715 15.01247 0.073143836
[165,] 6.037135196 15.01533 0.074612081
[166,] 0.040505636 16.48046 -0.096986802
[167,] 4.566357584 15.00498 0.082506929
[168,] 7.866031923 15.01633 0.059938005
[169,] 4.635008533 15.01187 0.081818959
[170,] 4.661259477 15.03342 0.081582503
[171,] 5.664644966 15.04421 0.076063974
[172,] 0.926664693 15.16266 0.031247834
[173,] 2.340610544 15.00149 0.145002782
[174,] 5.499092717 15.05095 0.076760583
[175,] 4.370355617 15.00399 0.087367112
[176,] 1.409504376 15.00288 0.163163243
[177,] 6.464178612 15.02429 0.073057409
[178,] 1.268828869 15.00328 0.169866439
[179,] 6.756666780 15.02255 0.072014152
[180,] 0.022952129 16.61104 -0.098367327
[181,] 4.889529916 15.00741 0.079892279
[182,] 7.106340993 15.01499 0.070742848
[183,] 1.183056247 15.05863 0.071423044
[184,] 8.035290641 15.00828 0.066336315
[185,] 1.977023621 15.00023 0.150443260
[186,] 1.938732086 15.00448 0.151085547
[187,] 6.367503680 15.03215 0.073403785
[188,] 5.785529387 15.00516 0.075578077
[189,] 4.544884199 15.03801 0.082749059
[190,] 6.204029765 15.00985 0.073995570
[191,] 4.337714097 15.00479 0.121830555
[192,] 6.289276223 15.01908 0.073685805
[193,] 6.353618763 15.02347 0.073453711
[194,] 1.596846125 15.00024 0.157867768
[195,] 8.082648750 15.00900 0.061690159
[196,] 2.538082022 15.00308 0.142396405
[197,] 2.096375495 15.00174 0.148539618
[198,] 7.990944220 15.01183 0.066663400
[199,] 1.763603638 15.00117 0.154276017
[200,] 6.264322840 15.02804 0.073776187
[201,] 7.130758920 15.00933 0.070651636
[202,] 2.503102500 15.00484 0.142845022
[203,] 7.883128049 15.01550 0.060061312
[204,] 5.486293766 15.02584 0.076816214
[205,] 2.792164962 15.00282 0.139271237
[206,] 1.311343263 15.01845 0.167248409
[207,] 0.904695440 15.17616 0.027734137
[208,] 2.829895665 15.00175 0.138824000
[209,] 6.640437096 15.03145 0.072428920
[210,] 8.056933831 15.00959 0.061442486
[211,] 0.054791467 16.39093 -0.095784277
[212,] 5.450340820 15.01385 0.076974029
[213,] 0.017436502 16.73927 -0.098778007
[214,] 7.155714195 15.03147 0.070557942
[215,] 6.625250202 15.03343 0.072483035
[216,] 1.213845877 15.05108 0.076127127
[217,] 0.004610167 16.84790 -0.099688428
[218,] 1.552094292 15.00837 0.126129786
[219,] 7.077240088 15.01068 0.070850992
[220,] 1.059631560 15.09666 0.052294381
[221,] 8.004323527 15.01081 0.060985287
[222,] 3.237174781 15.00279 0.134183853
[223,] 0.811049139 15.21523 0.012673553
[224,] 2.381254215 15.00118 0.144450694
[225,] 0.117760552 16.13102 -0.089728968
[226,] 4.103270212 15.00176 0.124619170
[227,] 4.104730772 15.01429 0.124602356
[228,] 6.823725984 15.02694 0.071773864
[229,] 4.943877364 15.00533 0.079553912
[230,] 7.087203477 15.02817 0.070814032
[231,] 8.147506810 15.00781 0.065216469
[232,] 4.389027444 15.00352 0.088793024
[233,] 6.239060433 15.03332 0.073867927
[234,] 3.452518557 15.00045 0.131817183
[235,] 2.282369377 15.00038 0.145810125
[236,] 3.582040625 15.00174 0.130404231
[237,] 4.963718642 15.04436 0.079434658
[238,] 5.227113458 15.03942 0.078014290
[239,] 6.824239742 15.00656 0.071772019
[240,] 4.728752468 15.00229 0.096135780
[241,] 4.755143932 15.00841 0.080821565
[242,] 4.622598348 15.03903 0.081935269
[243,] 4.377635727 15.00719 0.086153320
[244,] 7.774310231 15.02107 0.067933217
[245,] 7.881197653 15.00704 0.067355483
[246,] 6.115379770 15.02509 0.074321146
[247,] 8.144363085 15.00772 0.065259623
[248,] 3.975297943 15.03705 0.126073319
[249,] 5.410236969 15.02010 0.077152893
[250,] 4.913682139 15.04895 0.079739682
[,1] [,2]
[1,] -1.867185389 -0.81910606
[2,] -0.005087548 0.01927849
[3,] -1.981983333 -0.97100945
[4,] -2.944903567 -2.18266945
[5,] -2.957077204 -2.41019839
[6,] -0.599611642 0.20879323
[7,] -2.116731744 -1.08393330
[8,] -2.165388449 -1.27115683
[9,] -2.746158180 -2.41510999
[10,] -2.174040132 -1.29707731
[11,] -2.278891835 -1.38035121
[12,] -2.195635194 -1.30131342
[13,] -2.131665255 -1.30450404
[14,] -0.573293655 0.34000689
[15,] -3.000000000 -2.47797498
[16,] -2.708197126 -2.18810199
[17,] -0.524979984 0.29433910
[18,] -2.030138175 -1.11795068
[19,] -2.861195997 -1.99396521
[20,] -2.090961823 -1.16046997
[21,] -0.723456993 0.42318279
[22,] -2.199253127 -1.36835862
[23,] -2.673668972 -2.15401579
[24,] -2.736059257 -2.06211258
[25,] -2.793791458 -2.21967090
[26,] -2.252967149 -1.40176864
[27,] -2.721122824 -2.19354811
[28,] -2.207567849 -1.31547237
[29,] -2.038230639 -1.07898205
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[68,] 1.71521871 6.206836
[69,] 2.19089217 6.133134
[70,] 2.06627619 6.151793
[71,] 0.91911792 6.327384
[72,] 2.00386314 6.159259
[73,] 0.48535565 6.411852
[74,] 1.84567149 6.177024
[75,] 2.26588206 6.121279
[76,] 2.70691512 6.048088
[77,] 1.22936398 6.291042
[78,] 0.08049306 6.486568
[79,] 0.80654162 6.362600
[80,] 2.02415982 6.160056
[81,] 1.06727125 6.321249
[82,] 2.57428712 6.066354
[83,] 2.85430445 6.020066
[84,] 0.76696113 6.360597
[85,] 0.61294045 6.396857
[86,] 1.93509368 6.174081
[87,] 2.83131988 6.021962
[88,] 2.71142458 6.047506
[89,] 1.73025487 6.206971
[90,] 1.69495785 6.200560
[91,] 1.91153422 6.179486
[92,] 0.44170016 6.424629
[93,] 1.42622695 6.249585
[94,] 1.59007917 6.223211
[95,] 2.84399794 6.024610
[96,] 0.53222893 6.394477
[97,] 2.14196474 6.136040
[98,] 2.62190651 6.054949
[99,] 0.93516187 6.332578
[100,] 2.33092439 6.108020
[101,] 1.04164550 6.317520
[102,] 1.46977276 6.249947
[103,] 2.58298308 6.063663
[104,] 1.13279720 6.296874
[105,] 2.31897592 6.110538
[106,] 1.89677723 6.182611
[107,] 1.76713073 6.202644
[108,] 2.07848514 6.152823
[109,] 2.13115692 6.138037
[110,] 0.55261293 6.390054
[111,] 2.33888842 6.109008
[112,] 1.60009147 6.229010
[113,] 1.92304792 6.178135
[114,] 2.59528274 6.063677
[115,] 2.63998491 6.056952
[116,] 1.14392348 6.297527
[117,] 2.38574229 6.099642
[118,] 1.61420337 6.226515
[119,] 0.33363311 6.439296
[120,] 1.67624063 6.208643
[121,] 2.64575580 6.055751
[122,] 0.58574614 6.398588
[123,] 2.60803686 6.058533
[124,] 0.35244781 6.430526
[125,] 1.49808176 6.246057
[126,] 2.83674852 6.023804
[127,] 2.60936152 6.060590
[128,] 1.76142906 6.202131
[129,] 1.48708572 6.243390
[130,] 1.85178906 6.189106
[131,] 0.39784045 6.414818
[132,] 2.86423059 6.021267
[133,] 2.63025652 6.057617
[134,] 2.87029637 6.021594
[135,] 1.68670996 6.203944
[136,] 2.26230540 6.120397
[137,] 2.97543201 5.999785
[138,] 1.05958760 6.322832
[139,] 2.59188930 6.065309
[140,] 1.74409953 6.203533
[141,] 1.74770590 6.205568
[142,] 0.40944430 6.423143
[143,] 0.74854330 6.368281
[144,] 2.98467744 5.997101
[145,] 1.45831844 6.247152
[146,] 0.70496185 6.372344
[147,] 0.72423471 6.378766
[148,] 2.07484379 6.153133
[149,] 1.45168591 6.249232
[150,] 2.43497514 6.089447
[151,] 2.01439841 6.162564
[152,] 1.21682316 6.291523
[153,] 0.69491766 6.374599
[154,] 1.43876288 6.246693
[155,] 1.62323738 6.223655
[156,] 1.93274935 6.174006
[157,] 2.62746950 6.058682
[158,] 0.73330286 6.374247
[159,] 1.44184506 6.246689
[160,] 2.01580348 6.162048
[161,] 0.59612950 6.399761
[162,] 1.49264412 6.241165
[163,] 2.86605644 6.022132
[164,] 2.43643387 6.090660
[165,] 0.61039103 6.394368
[166,] 2.98569596 5.997497
[167,] 2.26273854 6.120704
[168,] 2.41422397 6.093970
[169,] 2.75360142 6.030979
[170,] 2.72228222 6.042245
[1] 17
[,1] [,2]
[1,] -247.419689 79.95877
[2,] -7.533948 19.76004
[3,] -84.840024 28.49016
[4,] -234.577137 63.76414
[5,] -221.739903 55.24450
[6,] -143.006855 38.95729
[7,] -205.889181 50.33242
[8,] -243.750250 75.18362
[9,] -187.597785 45.40006
[10,] -44.842185 24.19731
[11,] -236.989269 69.84034
[12,] -239.863196 70.02122
[13,] -180.013093 41.53024
[14,] -43.708194 20.59682
[15,] -145.885931 40.45811
[16,] -20.728511 20.55802
[17,] -233.353329 62.34427
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 4.9814888 1.007788 4.286634 1.354881 3.530752 4.631496
[2,] 1.9405007 1.251101 1.855396 1.524593 1.158906 2.705422
[3,] 0.2225743 2.007886 2.039009 1.960054 1.786125 3.635850
[4,] 4.9628185 1.008914 2.862058 1.418172 3.001112 4.348264
[5,] 4.8998220 1.028415 2.877270 1.402797 1.549656 4.186962
[6,] 4.3300415 1.260928 1.747249 1.554395 1.440376 3.327820
[7,] 4.8000628 1.089468 2.204252 1.387483 1.880826 3.972849
[8,] 4.9724169 1.024630 4.043095 1.350351 3.374083 4.455818
[9,] 4.6620830 1.012683 2.477085 1.372816 1.609894 3.468024
[10,] 0.7894782 1.246152 2.014517 1.470641 1.461432 3.696524
[11,] 4.9582435 1.017446 3.307765 1.538003 3.420027 4.383790
[12,] 4.9740183 1.014676 3.693622 1.367230 2.893576 4.512854
[13,] 4.6123130 1.203751 2.537542 1.468092 1.000000 3.035356
[14,] 0.8080591 1.302018 1.535087 1.476371 2.023679 3.101157
[15,] 4.3438468 1.095084 1.785145 1.496066 1.916773 3.360197
[16,] 1.2653724 1.304092 1.933474 1.589038 1.261089 3.066348
[17,] 4.9538598 1.004875 1.702959 1.374690 3.616193 4.350526
mopsocd documentation built on May 2, 2019, 2:38 p.m.
R Package Documentation
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Description
Examples on how to use the MOPSOCD solver for unconstrained and constrained optimization.
See Also
mopsocd pareto
Examples
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 | ## Typical MOPSOCD usage:
## 1) Define Objectives
## Format:
## fn <- function(x) {
## ## User-Defined Objective Functions
## f1 <- Objective Function 1
## f2 <- Objective Function 2
## ...
## fn <- Objective Function n
## ## End of User-Defined Objective Functions
## return(c(f1,f2, ...,fn))
## }
##
## 2) Define Constraints
## Format:
## gn <- function(x) {
## ## User-Defined Constraints
## g1 <- Constraint 1
## g2 <- Constraint 2
## ...
## gn <- Constraint n
## ## End of User-Defined Constraints
## return(c(g1,g2, ...,gn))
## }
##
## 3) Set Arguments
## 4) Run Solver
## 5) Print Pareto Object Fields
## 6) Plot Non-Dominated Points
#####################
## Example 1: Viennet Test Function (Unconstrained Optimization)
#####################
## Define Objectives
viennet <- function(x){
f1 <- 0.5*(x[1]^2+x[2]^2)+sin(x[1]^2+x[2]^2)
f2 <- 0.125*(3*x[1]-2*x[2]+4)^2+(1.0/27.0)*(x[1]-x[2]+1)^2+15
f3 <- 1.0/(x[1]^2+x[2]^2+1)-1.1*exp(-(x[1]^2+x[2]^2))
return(c(f1,f2,f3))
}
## Set Arguments
varcount <- 2
fncount <- 3
lbound <- c(-3,-3)
ubound <- c(3,3)
optmin <- 0
## Run Solver (gn omitted)
ex1 <- mopsocd(viennet,varcnt=varcount,fncnt=fncount,
lowerbound=lbound,upperbound=ubound,opt=optmin)
## Access Pareto Object Fields
print(ex1$numsols)
print(ex1$objfnvalues)
print(ex1$paramvalues)
## Plot
#library(scatterplot3d)
#scatterplot3d(ex1$objfnvalues[,1],ex1$objfnvalues[,2],ex1$objfnvalues[,3])
#####################
## Example 2: Kita Test Function (Constrained Optimization)
#####################
## Define Objectives
kita <- function(x) {
f1 <- -(x[1] * x[1]) + x[2]
f2 <- (x[1]/2)+x[2]+1
return(c(f1,f2))
}
## Define Constraints
gn <- function(x) {
g1 <- x[1]/6.0 + x[2] - 13.0/2.0 <= 0.0
g2 <- x[1]/2.0 + x[2] - 15.0/2.0 <= 0.0
g3 <- 5.0*x[1]+x[2] - 30.0 <= 0.0
return(c(g1,g2,g3))
}
## Set Arguments
varcount <- 2
fncount <- 2
lbound <- c(0,0)
ubound <- c(7,7)
optmax <- 1
## Run Solver
ex2 <- mopsocd(kita,gn,varcnt=varcount,fncnt=fncount,
lowerbound=lbound,upperbound=ubound,opt=optmax)
## Access Pareto Object Fields
print(ex2$numsols)
print(ex2$objfnvalues)
print(ex2$paramvalues)
## Plot
plot(ex2$objfnvalues[,1],ex2$objfnvalues[,2])
#####################
## Example 3: Osyczka-Kundu Test Function (Constrained Optimization)
#####################
## Define Objectives
osyczka <- function(x){
f1 <- -(25.0*(x[1]-2.0)^2+(x[2]-2.0)^2+(x[3]-1.0)^2+(x[4]-4.0)^2+(x[5]-1.0)^2)
f2 <- 0.0
for (i in 1:6) {
f2 <- f2+x[i]^2
}
return(c(f1,f2))
}
## Define Constraints
gn <- function(x) {
## User-Defined Constraints
g1 <- x[1] + x[2] - 2.0 >= 0.0
g2 <- 6.0 - x[1] - x[2] >= 0.0
g3 <- 2.0 - x[2] + x[1] >= 0.0
g4 <- 2.0 - x[1] + 3.0*x[2] >= 0.0
g5 <- 4.0 - (x[3] - 3.0)^2 - x[4] >= 0.0
g6 <- (x[5] - 3.0)^2 + x[6] - 4.0 >= 0.0
## End of User-Defined Constraints
return(c(g1,g2,g3,g4,g5,g6))
}
## Set Arguments
varcount <- 6
fncount <- 2
lbound <- c(0,0,1,0,1,0)
ubound <- c(10,10,5,6,5,10)
optmin <- 0
## Run Solver
ex3 <- mopsocd(osyczka,gn,varcnt=varcount,fncnt=fncount,
lowerbound=lbound,upperbound=ubound,opt=optmin,
popsize=100,maxgen=25,archivesize=500)
# For better results, use the following settings:
# popsize=1000,maxgen=1000.
## Access Pareto Object Fields
print(ex3$numsols)
print(ex3$objfnvalues)
print(ex3$paramvalues)
## Plot
plot(ex3$objfnvalues[,1],ex3$objfnvalues[,2])
|
Example output
[1] 250
[,1] [,2] [,3]
[1,] 1.228796018 15.00025 0.176684852
[2,] 0.000596315 16.98180 -0.099960175
[3,] 1.448129546 15.00001 0.161894056
[4,] 7.482665747 15.02963 0.069267246
[5,] 8.191314820 15.00793 0.064294255
[6,] 0.593862552 15.39900 -0.022355697
[7,] 2.240430901 15.00420 0.146404287
[8,] 3.173933248 15.00068 0.134886914
[9,] 7.409818573 15.06034 0.069567664
[10,] 3.329774203 15.00121 0.133161940
[11,] 4.277449194 15.00110 0.122567561
[12,] 3.486110372 15.00044 0.131450410
[13,] 3.085414785 15.00683 0.135879774
[14,] 0.651934286 15.32032 -0.013030093
[15,] 8.107792697 15.00870 0.061956194
[16,] 5.631281415 15.01644 0.076201205
[17,] 0.535489021 15.42275 -0.031641888
[18,] 1.894962462 15.00293 0.151841440
[19,] 5.688042098 15.04500 0.075968588
[20,] 2.324519461 15.00047 0.145223867
[21,] 0.997344552 15.12165 0.042486325
[22,] 3.767731604 15.00347 0.128374787
[23,] 5.192231149 15.01884 0.078188187
[24,] 5.132555667 15.00482 0.078494455
[25,] 6.531184685 15.00714 0.072818243
[26,] 4.207610521 15.00107 0.123402530
[27,] 5.764988260 15.01452 0.075659483
[28,] 3.617083839 15.00044 0.130022092
[29,] 1.837472739 15.00030 0.152873604
[30,] 0.367563263 15.62257 -0.057393803
[31,] 6.594140486 15.01149 0.072593873
[32,] 3.542967870 15.00202 0.130830234
[33,] 3.841647441 15.00284 0.127561055
[34,] 2.900268138 15.00369 0.137999362
[35,] 3.255673899 15.00197 0.133979045
[36,] 7.546145543 15.01519 0.068997113
[37,] 5.386307120 15.00660 0.077261131
[38,] 7.704605826 15.02667 0.058766527
[39,] 2.745398890 15.00307 0.139830957
[40,] 4.781094416 15.04469 0.080629774
[41,] 3.702907365 15.00332 0.129084948
[42,] 6.829395081 15.01129 0.071753501
[43,] 0.068567438 16.32286 -0.094561119
[44,] 2.620564257 15.00650 0.141357743
[45,] 5.560947994 15.01349 0.076495531
[46,] 3.020596140 15.00196 0.136614519
[47,] 4.731120400 15.00416 0.081005536
[48,] 7.630317268 15.02920 0.068624184
[49,] 2.974729250 15.00064 0.137138966
[50,] 7.013744377 15.02183 0.071085060
[51,] 0.265937816 15.79042 -0.071756902
[52,] 0.173999195 15.97147 -0.083434740
[53,] 7.575175782 15.08837 0.055164696
[54,] 3.676921893 15.00346 0.129368973
[55,] 3.895238273 15.00263 0.126967479
[56,] 6.137777297 15.00542 0.074238513
[57,] 7.290132129 15.03892 0.070043487
[58,] 0.403501599 15.57591 -0.052050034
[59,] 6.718892320 15.01322 0.072149125
[60,] 8.189423303 15.00791 0.064369480
[61,] 0.880744700 15.17756 0.023893997
[62,] 5.968161249 15.02550 0.074871834
[63,] 4.434130160 15.00634 0.084395963
[64,] 4.485075514 15.00308 0.091527625
[65,] 5.855959421 15.05538 0.075302185
[66,] 7.220075791 15.05530 0.070313834
[67,] 7.754429151 15.00695 0.068033615
[68,] 0.439036384 15.52645 -0.046662192
[69,] 5.231635913 15.00732 0.077992003
[70,] 7.824993199 15.01496 0.067668071
[71,] 6.939320202 15.06164 0.071356613
[72,] 4.821995919 15.00454 0.080340454
[73,] 2.037602177 15.00055 0.149459712
[74,] 6.672903032 15.03265 0.072313200
[75,] 2.679421660 15.00080 0.140631601
[76,] 2.441483921 15.00025 0.143648234
[77,] 5.272818987 15.00589 0.077791625
[78,] 0.213135461 15.89074 -0.078649519
[79,] 0.752747862 15.24946 0.003254016
[80,] 5.093712816 15.04197 0.078700366
[81,] 0.958171045 15.15466 0.036270653
[82,] 5.347533212 15.00502 0.077439061
[83,] 2.198098263 15.00031 0.147015837
[84,] 7.954189265 15.01249 0.060588390
[85,] 0.146922358 16.05179 -0.086558096
[86,] 4.949497438 15.00200 0.100818300
[87,] 0.826250330 15.20616 0.015125628
[88,] 6.896475258 15.00604 0.071511817
[89,] 4.145082676 15.00723 0.124135531
[90,] 4.988919136 15.00185 0.102008633
[91,] 5.898426192 15.02016 0.075138067
[92,] 5.309535545 15.00514 0.077616689
[93,] 7.662996854 15.03610 0.068473984
[94,] 0.323784023 15.69148 -0.063732690
[95,] 6.974857005 15.02722 0.071227286
[96,] 2.933156433 15.00031 0.137617890
[97,] 3.579469134 15.00763 0.130432267
[98,] 3.802366082 15.00234 0.127994121
[99,] 6.773156568 15.00876 0.071955155
[100,] 0.117330606 16.16372 -0.089774113
[101,] 6.405726954 15.02246 0.073266599
[102,] 0.715164825 15.27392 -0.002822626
[103,] 0.500483357 15.45791 -0.037149062
[104,] 1.123709661 15.08182 0.062278625
[105,] 7.915018904 15.01406 0.060294266
[106,] 1.512931239 15.01153 0.160004457
[107,] 3.430644873 15.00477 0.132056234
[108,] 0.472424878 15.48458 -0.041520325
[109,] 7.785683943 15.02404 0.059363159
[110,] 0.304838628 15.71365 -0.066408719
[111,] 5.817054729 15.02013 0.075453986
[112,] 2.840521756 15.00616 0.138698709
[113,] 7.258561981 15.01349 0.070165969
[114,] 4.025143990 15.00120 0.125511063
[115,] 4.692814463 15.02908 0.081313388
[116,] 0.687406894 15.29297 -0.007307805
[117,] 5.930663112 15.01693 0.075014511
[118,] 5.056223443 15.03772 0.078904546
[119,] 5.024200424 15.00168 0.103416808
[120,] 2.164409360 15.00016 0.147511604
[121,] 1.668047777 15.00631 0.142878948
[122,] 6.013767323 15.01407 0.074699714
[123,] 4.603181324 15.00481 0.082123797
[124,] 4.860227257 15.04848 0.080082624
[125,] 7.342933904 15.03495 0.069835973
[126,] 2.128758544 15.00334 0.148045628
[127,] 6.863918954 15.05292 0.071629295
[128,] 6.495690822 15.01736 0.072944865
[129,] 7.358067152 15.00664 0.069775830
[130,] 3.992396524 15.00573 0.125880980
[131,] 1.049613475 15.10043 0.050723478
[132,] 6.187797287 15.01860 0.074054900
[133,] 1.728886554 15.00109 0.154969582
[134,] 6.102103969 15.01043 0.074370254
[135,] 0.236513724 15.85594 -0.075654748
[136,] 1.092490939 15.08643 0.057428306
[137,] 3.958676637 15.00078 0.126259794
[138,] 6.072165269 15.01139 0.074481373
[139,] 3.063404783 15.00293 0.136128475
[140,] 1.629085232 15.00729 0.137239109
[141,] 3.374918472 15.00054 0.132666306
[142,] 7.177296594 15.01816 0.070476497
[143,] 6.315980948 15.01521 0.073589319
[144,] 5.439553572 15.00538 0.077021839
[145,] 7.061230619 15.01626 0.070910243
[146,] 3.927332201 15.00823 0.126610211
[147,] 0.785426385 15.22828 0.008536058
[148,] 3.211469389 15.00103 0.134469057
[149,] 4.179700165 15.00932 0.123731266
[150,] 5.542302070 15.00501 0.076574787
[151,] 1.161389053 15.06795 0.068096176
[152,] 2.462121319 15.00039 0.143377306
[153,] 1.698072886 15.00604 0.147253036
[154,] 1.999755850 15.00008 0.150069708
[155,] 4.320567524 15.01924 0.122041974
[156,] 6.239664454 15.00548 0.073865730
[157,] 2.383973378 15.00502 0.144414072
[158,] 4.914267576 15.01122 0.079736029
[159,] 4.514559089 15.00696 0.083121044
[160,] 2.667225526 15.00244 0.140781109
[161,] 2.078484496 15.00585 0.148816381
[162,] 1.799681084 15.00126 0.153579448
[163,] 2.577937490 15.00237 0.141891289
[164,] 6.440007715 15.01247 0.073143836
[165,] 6.037135196 15.01533 0.074612081
[166,] 0.040505636 16.48046 -0.096986802
[167,] 4.566357584 15.00498 0.082506929
[168,] 7.866031923 15.01633 0.059938005
[169,] 4.635008533 15.01187 0.081818959
[170,] 4.661259477 15.03342 0.081582503
[171,] 5.664644966 15.04421 0.076063974
[172,] 0.926664693 15.16266 0.031247834
[173,] 2.340610544 15.00149 0.145002782
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[1] 17
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[,1] [,2] [,3] [,4] [,5] [,6]
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[17,] 4.9538598 1.004875 1.702959 1.374690 3.616193 4.350526
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