Using R version 3.6.3 and library(lpSolve) I am unable to solve a linear programming problem. I would like to find the 7 best solutions that maximize:
f.obj <- sampleDB$ob1
given the constraints:
f.con <- with(sampleDB, matrix(c(con1, con2, con3, con4, con5, con6, con7, con8, con9, con10, con11, con12, con13), nrow = 13, byrow = TRUE))
f.dir <- c("<=", ">=", ">=", ">=", ">=", ">=", ">=", ">=", "<=", "<=", ">=", "<=", "=")
f.rhs <- c(50000, 1, 1, 1, 1, 1, 3, 3, 2, 3, 4, 4, 8)
sampleDB$OptSc1 <- lp("max", f.obj, f.con, f.dir, f.rhs, all.bin = TRUE)$solution
On the 7th $solution, however, R runs indefinitely, without providing an answer. Is there simply not a 7th solution to be found? I haven’t worked out the calculus on paper, but I find that hard to believe. And if that is the case, how can I determine the number of solutions that exist before I run the code? When I use $num.bin.solns it tells me there’s only 1.
Perhaps my approach is flawed, but here is how I’ve set it up. It is the very last line, where I run into trouble.
f.con <- with(sampleDB, matrix(c(con1, con2, con3, con4, con5, con6, con7, con8, con9, con10, con11, con12, con13), nrow = 13, byrow = TRUE))
f.dir <- c("<=", ">=", ">=", ">=", ">=", ">=", ">=", ">=", "<=", "<=", ">=", "<=", "=")
f.rhs <- c(50000, 1, 1, 1, 1, 1, 3, 3, 2, 3, 4, 4, 8)
f.obj <- sampleDB$ob1
sampleDB$OptSc1 <- lp("max", f.obj, f.con, f.dir, f.rhs, all.bin = TRUE)$solution
Sc1 <- sum(sampleDB$OptSc1*sampleDB$ob1) - 0.00005
f.con <- with(sampleDB, matrix(c(con1, con2, con3, con4, con5, con6, con7, con8, con9, con10, con11, con12, con13, ob1), nrow = 14, byrow = TRUE))
f.dir <- c("<=", ">=", ">=", ">=", ">=", ">=", ">=", ">=", "<=", "<=", ">=", "<=", "=", "<")
f.rhs <- c(50000, 1, 1, 1, 1, 1, 3, 3, 2, 3, 4, 4, 8, Sc1)
sampleDB$OptSc2 <- lp("max", f.obj, f.con, f.dir, f.rhs, all.bin = TRUE)$solution
Sc2 <- sum(sampleDB$OptSc2*sampleDB$ob1) - 0.00005
f.con <- with(sampleDB, matrix(c(con1, con2, con3, con4, con5, con6, con7, con8, con9, con10, con11, con12, con13, ob1), nrow = 14, byrow = TRUE))
f.dir <- c("<=", ">=", ">=", ">=", ">=", ">=", ">=", ">=", "<=", "<=", ">=", "<=", "=", "<")
f.rhs <- c(50000, 1, 1, 1, 1, 1, 3, 3, 2, 3, 4, 4, 8, Sc2)
sampleDB$OptSc3 <- lp("max", f.obj, f.con, f.dir, f.rhs, all.bin = TRUE)$solution
Sc3 <- sum(sampleDB$OptSc3*sampleDB$ob1) - 0.00005
f.con <- with(sampleDB, matrix(c(con1, con2, con3, con4, con5, con6, con7, con8, con9, con10, con11, con12, con13, ob1), nrow = 14, byrow = TRUE))
f.dir <- c("<=", ">=", ">=", ">=", ">=", ">=", ">=", ">=", "<=", "<=", ">=", "<=", "=", "<")
f.rhs <- c(50000, 1, 1, 1, 1, 1, 3, 3, 2, 3, 4, 4, 8, Sc3)
sampleDB$OptSc4 <- lp("max", f.obj, f.con, f.dir, f.rhs, all.bin = TRUE)$solution
Sc4 <- sum(sampleDB$OptSc4*sampleDB$ob1) - 0.00005
f.con <- with(sampleDB, matrix(c(con1, con2, con3, con4, con5, con6, con7, con8, con9, con10, con11, con12, con13, ob1), nrow = 14, byrow = TRUE))
f.dir <- c("<=", ">=", ">=", ">=", ">=", ">=", ">=", ">=", "<=", "<=", ">=", "<=", "=", "<")
f.rhs <- c(50000, 1, 1, 1, 1, 1, 3, 3, 2, 3, 4, 4, 8, Sc4)
sampleDB$OptSc5 <- lp("max", f.obj, f.con, f.dir, f.rhs, all.bin = TRUE)$solution
Sc5 <- sum(sampleDB$OptSc5*sampleDB$ob1) - 0.00005
f.con <- with(sampleDB, matrix(c(con1, con2, con3, con4, con5, con6, con7, con8, con9, con10, con11, con12, con13, ob1), nrow = 14, byrow = TRUE))
f.dir <- c("<=", ">=", ">=", ">=", ">=", ">=", ">=", ">=", "<=", "<=", ">=", "<=", "=", "<")
f.rhs <- c(50000, 1, 1, 1, 1, 1, 3, 3, 2, 3, 4, 4, 8, Sc5)
sampleDB$OptSc6 <- lp("max", f.obj, f.con, f.dir, f.rhs, all.bin = TRUE)$solution
Sc6 <- sum(sampleDB$OptSc6*sampleDB$ob1) - 0.00005
f.con <- with(sampleDB, matrix(c(con1, con2, con3, con4, con5, con6, con7, con8, con9, con10, con11, con12, con13, ob1), nrow = 14, byrow = TRUE))
f.dir <- c("<=", ">=", ">=", ">=", ">=", ">=", ">=", ">=", "<=", "<=", ">=", "<=", "=", "<")
f.rhs <- c(50000, 1, 1, 1, 1, 1, 3, 3, 2, 3, 4, 4, 8, Sc6)
sampleDB$OptPTS7 <- lp("max", f.obj, f.con, f.dir, f.rhs, all.bin = TRUE)$solution
With each successive solution, I’ve added the value of the objective function to the next set of constraints. I’ve had to subtract a constant from that value because just using $objval results in the same solution every time. I think that has something to do with the number of digits R rounds to when it provides $objval versus the number of digits it solves to when it finds the $solution. Could something similar be going on here? I’ve tried adjusting the constant, but with no success.
Here is my data:
> dput(sampleDB)
structure(list(ob1 = c(3.76390594863582, 0.761939836551001, 29.2816194322234,
25.6047156208718, 46.515648347798, 0.000775902255483371, 1.7383258322208,
0.860421775707736, 36.119549083882, 10.8264421015821, 17.644563116085,
48.2681849744957, 0.0584569560341531, 3.84854719993989, 24.521642473583,
0.618624719605915, 3.21696699627368, 0.822385557362038, 13.2627797942269,
1.16888158165636, 50.3890677507142, 45.6227945060737, 23.3781201716661,
9.58355716685232, 18.4360445501486, 0.866566734404375, 0.935399012727439,
31.2122220781987, 30.293989476655, 13.5739646407219, 5.57008973760041,
3.61618759223241, 1.00615527571242, 25.6420493131819, 1.6474300975448,
24.6706762652845, 9.27194306443524, 24.6387678541115, 11.5123618884146,
11.3407582281099, 16.0255967486797, 21.1480496069011, 5.74789240344409,
3.14241492068053, 38.3331153154964, 3.83583328824607, 11.8030518948405,
8.23167774687087, 0.118852807837664, 0.00851398132035089, 35.2165914308258,
16.759966944604, 0.380100182318346, 35.8845200546817, 27.5194772098823,
14.6776249377007, 23.1061187216053, 47.4149591424868, 31.4855232971828,
8.8615632266222, 29.6644975905997, 17.2460363725348, 2.22926277783991,
9.81478187329139, 3.12321137200172, 5.03215748446557, 30.1925503759452,
14.8211664403754, 29.6543255569287, 3.69994390962281, 1.16471854437625,
2.15551731934886, 3.61151750499129, 1.05665700637375e-10, 22.7906474629311,
9.40962778322496, 25.4798767018317, 50.6011616967978, 0.231149829684813,
0.248627324982034, 0.503272593590455, 27.5892643878618, 36.4464019337861,
16.9871054101199, 5.64127640058401, 12.4496926631512, 23.9660578409599,
21.2389971857764, 17.5726088561276, 0.635729431188716, 13.5027248387733,
0.0160651908985738, 0.912007831942838, 26.354703609983, 0.511024185054345,
6.84778020648871, 16.5507310768833, 7.25136585492291, 30.1191633710188,
20.3468655455802, 34.862749806773, 5.66676128646327, 14.5244230484807,
40.5878566545177, 17.8080850499182, 0.0700904613405446, 3.61149734086541,
16.9447749516927, 14.6790497896104, 31.4734829876786, 32.8468645210727,
8.31928047505007, 19.4871570005619, 10.3478182830777, 31.6494117269382,
1.68128013423518, 9.59756770552769, 9.24165679092327, 10.8669284256663,
12.9515512672302, 41.2176730754142, 45.1669401812466, 19.3049166345003,
6.32107305031539, 5.63133803706955, 3.98428873426775, 53.3399624408037,
24.7365539578648, 0.255625130043758, 0.67073060246001, 22.041816061752,
6.00533376388743, 1.52414935244212, 37.7496147181442, 16.2687669787792,
6.84442158221665, 0.117539826717849, 11.0310962514469, 12.8601298456175,
1.42921140612006, 36.4708142560788, 29.3186871190892, 14.9679845357087,
0.0788070686815829, 38.9998866099898, 0.587574212636836, 19.1401868171519,
24.1120839856018, 8.54476359053375, 56.1959339053684, 17.87539243789,
14.9540689353385, 5.55794057811982, 36.9626800151774, 0.395280644044746,
1.07674554879846, 4.87595384871698, 0.730790455643416, 4.77938961343802,
36.5930225603752, 6.3156631883412, 2.05167371659919, 31.6929424430418,
17.6305139543803, 16.9398903995792, 9.75698970116204, 43.4336993813029,
0.588743075979379, 6.09789512987062, 36.4954751452142, 7.69262016459491,
2.87597095799429, 12.1681415252796, 4.58191560848135, 23.7538049036987,
25.1427517344264, 20.0519184025836, 29.4927328850699, 1.33748961169543,
39.4479182035543, 0.441370123452924, 23.7498897163996, 15.7616609235736,
36.8549436431343, 0.0663852722160569, 0.0918124030705618, 1.25242751000894,
18.0739991702356, 7.06553825435209, 12.4796413738869, 27.8552789159797,
26.6259855804049, 0.311795849359767, 14.4732740319035, 39.9536545066622,
6.3980851966008, 15.0089771683311, 34.4200642580808, 8.13027793300107,
14.7493990298081, 0.3951907625925, 9.75657890439648, 0.256024732233337,
46.0046651298316, 51.5680095016789, 1.72725130053754, 5.03766583469193,
15.0436426367201, 1.17684799481056, 1.93112320683624, 29.6889243456999,
29.7211195911729, 31.7941379629697, 45.9248408765764, 17.7605207537162,
2.95611831176694, 0.151488301728442, 30.3914109853713, 31.9978301250799,
15.3205065678634, 35.9335447191147, 7.19484758961864, 8.89621140755178,
8.6754114215515, 11.0115966437219, 1.23963532658536, 13.8604427436658,
33.7987381362404, 19.1582258005406, 24.6416326081839, 14.2876103449465,
1.48612540520681, 38.554568328169, 0.452760949146604, 25.6825917815542,
15.7382000365344, 14.946317880251, 3.01535182710049, 0.607979104438032,
36.7743845247456, 30.9121383956393, 1.16723929498915, 0.0332154435244338,
2.40692683054348, 0.997253439938718, 27.0033372777404, 49.0444152380632,
22.9170526863693, 31.0952750653481, 2.11025411621386, 16.4575354173225,
23.929528911132, 31.7758022000095, 23.6042504638421, 31.5507652711827,
0.852297922051439, 14.383476605355, 31.229730529653, 1.6397757344741,
0.0457480405286347, 9.43726268513148, 5.05059874819956, 13.9407963360925,
10.7318187572402), con1 = c(3500L, 3000L, 5500L, 5400L, 9800L,
3000L, 3000L, 3000L, 6800L, 3600L, 4000L, 9700L, 3000L, 3000L,
6500L, 3200L, 3800L, 3000L, 4900L, 3000L, 10000L, 9300L, 6000L,
4200L, 4800L, 3000L, 3000L, 6000L, 6500L, 4700L, 3400L, 3000L,
3000L, 6200L, 3000L, 5200L, 4800L, 6400L, 3200L, 4100L, 4400L,
5200L, 3600L, 3000L, 8900L, 3200L, 3500L, 3500L, 3000L, 3000L,
7900L, 3700L, 3000L, 7700L, 6200L, 4800L, 3600L, 9500L, 6300L,
3400L, 7300L, 4900L, 3000L, 3000L, 3300L, 3500L, 6500L, 3900L,
4500L, 3300L, 3000L, 3800L, 3000L, 3000L, 6700L, 4000L, 5000L,
10900L, 3000L, 3000L, 3000L, 5400L, 7900L, 3300L, 3200L, 3100L,
5400L, 7000L, 4800L, 3000L, 3600L, 3000L, 3000L, 5900L, 3000L,
3100L, 4400L, 3000L, 6500L, 4600L, 6600L, 3200L, 4500L, 7600L,
4700L, 3000L, 4000L, 3500L, 3400L, 6200L, 5800L, 4300L, 4000L,
4600L, 5700L, 3000L, 6100L, 3000L, 3700L, 3600L, 8300L, 9200L,
3300L, 3000L, 3100L, 3500L, 9900L, 4700L, 3000L, 3000L, 4500L,
3400L, 3000L, 7200L, 4400L, 3500L, 3000L, 3400L, 4000L, 3000L,
8600L, 5600L, 4800L, 3000L, 6900L, 3100L, 5600L, 5300L, 3800L,
11200L, 4800L, 3300L, 4100L, 8500L, 3000L, 3000L, 3400L, 3000L,
3500L, 8000L, 3000L, 3000L, 7400L, 4900L, 4600L, 3100L, 9000L,
3000L, 3200L, 8700L, 3400L, 3000L, 4000L, 3800L, 4700L, 4300L,
5000L, 6600L, 3000L, 8200L, 3000L, 5300L, 4100L, 6700L, 3000L,
3000L, 3000L, 4700L, 3000L, 3800L, 6100L, 6100L, 3100L, 3600L,
7500L, 3800L, 5200L, 6900L, 3200L, 3900L, 3000L, 3300L, 3000L,
9600L, 10400L, 3000L, 4000L, 3800L, 3000L, 3000L, 6000L, 5800L,
6400L, 9400L, 3500L, 3000L, 3000L, 5900L, 5800L, 4100L, 6700L,
3000L, 3300L, 3400L, 3700L, 3100L, 3300L, 6400L, 4100L, 3900L,
4000L, 3000L, 6800L, 3000L, 5500L, 3800L, 4700L, 3300L, 3100L,
8400L, 6000L, 3300L, 3000L, 3000L, 3200L, 6000L, 8800L, 5400L,
6600L, 3700L, 4900L, 5100L, 6300L, 5600L, 6500L, 3000L, 4200L,
6200L, 3000L, 3400L, 3500L, 3300L, 3600L, 4300L), con2 = c(1,
0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1,
0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1,
0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0,
0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0,
1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0,
0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0,
1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1,
0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0), con3 = c(0, 1, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1,
0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1,
1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0,
0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0,
0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0,
1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0,
0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0,
0, 1, 0, 0, 0, 0), con4 = c(0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0,
0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0,
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0,
0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0,
0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0,
1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0,
1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0,
1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0,
1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1,
0), con5 = c(0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0,
1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0,
0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0,
1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0,
1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0,
0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0,
0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0), con6 = c(0,
0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0,
0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0,
0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1,
0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1,
1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0,
0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0,
0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1), con7 = c(1, 1, 0, 0, 1, 0,
0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1,
1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0,
0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1,
1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0,
1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0,
1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0,
0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0,
1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1,
1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0,
1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0,
0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0,
0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1,
1, 1, 0, 0, 0, 0), con8 = c(0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0,
0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1,
0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0,
0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1,
0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0,
0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1,
0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0,
1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1,
1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1,
1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0,
1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0,
1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1,
1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1,
0), con13 = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1), con9 = c(0,
0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1,
0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0,
0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0,
0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1), con10 = c(1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1,
1, 0, 0, 0, 0, 0), con11 = c(0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1,
1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1,
0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1,
0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1,
1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0,
1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1,
1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1,
1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0,
1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1,
1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1,
1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1,
1), con12 = c(1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0,
1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1,
0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0,
0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1,
0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1,
0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0,
1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1,
0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1,
0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1,
1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1), ID = c("id103",
"id84", "id39", "id110", "id171", "id129", "id118", "id51", "id48",
"id105", "id186", "id264", "id152", "id135", "id220", "id238",
"id217", "id234", "id89", "id67", "id63", "id113", "id47", "id166",
"id189", "id256", "id162", "id224", "id96", "id159", "id28",
"id239", "id124", "id191", "id260", "id192", "id206", "id255",
"id146", "id42", "id61", "id59", "id258", "id237", "id55", "id123",
"id60", "id81", "id102", "id222", "id250", "id261", "id29", "id137",
"id138", "id190", "id251", "id168", "id169", "id187", "id6",
"id144", "id231", "id56", "id176", "id143", "id78", "id111",
"id32", "id30", "id202", "id126", "id226", "id259", "id172",
"id83", "id37", "id121", "id257", "id38", "id179", "id24", "id52",
"id127", "id57", "id141", "id232", "id114", "id64", "id132",
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"id228", "id235", "id82", "id44", "id151", "id194", "id65", "id109",
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"id40", "id184", "id104", "id19", "id147", "id112", "id8", "id155",
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"id243", "id131", "id204", "id77", "id197", "id170", "id201",
"id211", "id73", "id198", "id92", "id35", "id223", "id199", "id157",
"id209", "id241", "id16", "id11", "id173", "id215", "id25", "id108",
"id185", "id9", "id252", "id90", "id12", "id13", "id86", "id212",
"id41", "id107", "id165", "id134", "id177", "id230", "id87",
"id68", "id240", "id88", "id245", "id203", "id167", "id91", "id156",
"id221", "id139", "id69", "id33", "id253", "id80", "id93", "id262",
"id183", "id120", "id140", "id218", "id161", "id58", "id210",
"id193", "id229", "id205", "id196", "id17", "id119", "id136",
"id125", "id49", "id27", "id133", "id14", "id248", "id244", "id97",
"id43", "id22", "id70", "id10", "id219", "id1", "id15", "id263",
"id216", "id247", "id46", "id188", "id149", "id26", "id18", "id50",
"id4", "id3", "id76", "id71", "id106", "id130")), row.names = c(NA,
264L), class = "data.frame")
1