LPsolve Hybrid constraints - r

Question

I use the following R code to optimize Soccer lineups for my fantasy sports league. It has been working great up until now, but a new wrinkle has been added into the list of constraints that I would like to resolve.
A lineup consists of 8 players. 1GK, 2D, 2M, 2F, & 1 Util.
When creating the model Matrix, I now have to account for hybrid player positions such as M/F or D/M
In R what is the correct way to add a 1 in the column for M and a 1 in the column for F if a players position is M/F? Is this the correct approach to resolve this or should I be looking at other ideas.
Working Solver code with GK D M F positions accounted for but not D/M or M/F
df <- read.csv("players.csv",encoding = "UTF-8")
mm <- cbind(model.matrix(as.formula("FP~Pos+0"), df))
mm <- cbind(mm, mm, 1, df$Salary, df$Salary, df$FP)
colnames(mm) <- c("D", "F", "GK", "M", "D", "F", "GK", "M", "tot", "salary", "minSal", "FP")
mm <- t(mm)
obj <- df$FP
dir <- c("<=", "<=", "<=", "<=", ">=", ">=", ">=", ">=", "==", "<=", ">=", "<=")
x <- 20000
vals <- c()
ptm <- proc.time()
for(i in 1:5){
rhs <- c(3, 3, 1, 3, 2, 2, 1, 2, 8, 50000, 49500, x)
lp <- lp(direction = 'max',
objective.in = obj,
all.bin = T,
const.rhs = rhs,
const.dir = dir,
const.mat = mm)
vals <- c(vals, lp$objval)
x <- lp$objval - 0.00001
df$selected <- lp$solution
lineup <- df[df$selected == 1, ]
lineup = subset(lineup, select = -c(selected))
lineup <- lineup %>%
arrange(Pos)
print("---- Start ----")
print(i)
print(lineup)
print(sum(lineup$FP))
print(mean(lineup$own, na.rm = TRUE))
print(sum(lineup$Salary))
print(sum(lineup$S))
print("---- END ----")
}
proc.time() - ptm
Here is a sample pool of approx 100 players with a few hybrid players included.
structure(list(Name = structure(c(104L, 105L, 92L, 16L, 84L,
53L, 85L, 37L, 21L, 34L, 100L, 101L, 83L, 31L, 14L, 35L, 98L,
59L, 60L, 5L, 6L, 78L, 57L, 89L, 26L, 17L, 74L, 63L, 33L, 71L,
75L, 41L, 9L, 39L, 12L, 1L, 29L, 7L, 2L, 68L, 73L, 90L, 46L,
72L, 79L, 50L, 88L, 20L, 97L, 64L, 67L, 3L, 94L, 4L, 22L, 103L,
52L, 47L, 30L, 58L, 10L, 44L, 28L, 38L, 23L, 15L, 49L, 69L, 81L,
43L, 99L, 93L, 32L, 56L, 82L, 91L, 62L, 36L, 70L, 48L, 11L, 77L,
27L, 51L, 25L, 24L, 65L, 96L, 42L, 18L, 102L, 86L, 76L, 87L,
45L, 61L, 40L, 95L, 8L, 55L, 13L, 66L, 80L, 19L, 54L), .Label = c(" Bojan",
" Oscar", " Willian", "Aaron Ramsey", "Abel Hernandez", "Adam Smith",
"Adama Diomande", "Adlene Guedioura", "Adnan Januzaj", "Ahmed Elmohamady",
"Alex Iwobi", "Alex Oxlade-Chamberlain", "Alexis Sanchez", "Andre Gray",
"Andrew Robertson", "Andros Townsend", "Anthony Martial", "Antonio Valencia",
"Ben Mee", "Branislav Ivanovic", "Calum Chambers", "Cedric Soares",
"Cesc Fabregas", "Charlie Daniels", "Christian Fuchs", "Curtis Davies",
"Daley Blind", "Daniel Drinkwater", "David de Gea", "Demarai Gray",
"Diego Costa", "Donald Love", "Dusan Tadic", "Eden Hazard", "Eldin Jakupovic",
"Erik Pieters", "Etienne Capoue", "Fernando Llorente", "Gareth Barry",
"Glenn Whelan", "Gylfi Sigurdsson", "Hector Bellerin", "Idrissa Gueye",
"Jack Cork", "Jack Rodwell", "Jason Puncheon", "Jefferson Montero",
"Jeremain Lens", "Jeremy Pied", "Jermain Defoe", "Joe Allen",
"Joel Ward", "John Obi Mikel", "Jordi Amat", "Jordon Ibe", "Joshua King",
"Juan Mata", "Kasper Schmeichel", "Kevin Mirallas", "Kyle Naughton",
"Laurent Koscielny", "Leighton Baines", "Leroy Fer", "Lukasz Fabianski",
"Maarten Stekelenburg", "Marc Albrighton", "Mason Holgate", "Matt Targett",
"Matthew Lowton", "Max Gradel", "Michy Batshuayi", "Modou Barrow",
"Nacho Monreal", "Nathan Redmond", "Nordin Amrabat", "Pape Souare",
"Papy Djilobodji", "Patrick van Aanholt", "Paul Pogba", "Phil Bardsley",
"Pierre-Emile Højbjerg", "Ramiro Funes Mori", "Riyad Mahrez",
"Robert Snodgrass", "Ross Barkley", "Ryan Fraser", "Sam Clucas",
"Sam Vokes", "Santiago Cazorla", "Serge Gnabry", "Shane Long",
"Shaun Maloney", "Simon Francis", "Stephen Kingsley", "Stephen Ward",
"Steven Davis", "Steven Defour", "Theo Walcott", "Thibaut Courtois",
"Tom Heaton", "Wayne Rooney", "Wayne Routledge", "Wilfried Zaha",
"Xherdan Shaqiri", "Zlatan Ibrahimovic"), class = "factor"),
Salary = c(7000L, 9600L, 5700L, 7100L, 6500L, 3200L, 7800L,
4200L, 3300L, 8600L, 4200L, 7900L, 9900L, 8700L, 7700L, 4300L,
6700L, 5600L, 3700L, 6600L, 4700L, 5700L, 6600L, 7200L, 3500L,
7300L, 5900L, 4300L, 7700L, 7100L, 4000L, 9100L, 7400L, 4000L,
5800L, 5700L, 5600L, 6300L, 6800L, 4500L, 5100L, 3400L, 5700L,
5100L, 8000L, 7800L, 7000L, 5100L, 4900L, 4500L, 3300L, 8300L,
3200L, 6600L, 4900L, 6300L, 4400L, 4200L, 4800L, 5200L, 5200L,
4500L, 4300L, 7100L, 6500L, 4100L, 3000L, 3800L, 4700L, 4600L,
5800L, 4600L, 4200L, 6100L, 3500L, 6800L, 5800L, 4800L, 7300L,
5000L, 5000L, 3300L, 4200L, 3900L, 6100L, 5500L, 5400L, 4700L,
4700L, 4600L, 4400L, 3400L, 4300L, 4900L, 4600L, 4000L, 3500L,
3600L, 3300L, 4800L, 9300L, 7900L, 3700L, 3400L, 2800L),
Position = structure(c(5L, 3L, 2L, 5L, 5L, 5L, 5L, 5L, 1L,
6L, 4L, 3L, 6L, 3L, 3L, 4L, 6L, 6L, 1L, 3L, 1L, 1L, 5L, 5L,
1L, 6L, 6L, 5L, 5L, 3L, 6L, 5L, 5L, 5L, 6L, 6L, 4L, 3L, 5L,
1L, 2L, 5L, 5L, 6L, 5L, 3L, 3L, 2L, 5L, 4L, 1L, 5L, 1L, 5L,
1L, 6L, 1L, 6L, 6L, 4L, 1L, 5L, 5L, 3L, 5L, 1L, 1L, 1L, 5L,
5L, 4L, 1L, 1L, 3L, 1L, 3L, 2L, 1L, 6L, 3L, 6L, 1L, 1L, 5L,
1L, 2L, 4L, 5L, 1L, 1L, 5L, 5L, 1L, 5L, 5L, 1L, 5L, 1L, 5L,
6L, 6L, 5L, 1L, 1L, 1L), .Label = c("D", "D/M", "F", "GK",
"M", "M/F"), class = "factor"), FP = c(23.5, 21.75, 21, 19.75,
17.5, 17.333, 16.625, 16.5, 16.5, 16.25, 16, 15.25, 14.875,
14.25, 13.75, 13.5, 13.375, 13.25, 12.875, 12.75, 12.75,
12.5, 12.375, 12, 11.75, 11.625, 11.375, 11, 10.875, 10.625,
10.5, 10.375, 10.125, 10, 9.625, 9.625, 9.5, 9.25, 9.125,
9.125, 9, 9, 8.875, 8.875, 8.75, 8.75, 8.5, 8.5, 8.5, 8.5,
8.5, 8.25, 8.25, 8, 8, 7.875, 7.875, 7.875, 7.75, 7.5, 7.5,
7.5, 7.5, 7.25, 7.25, 7.125, 7, 6.875, 6.625, 6.625, 6.5,
6.5, 6.5, 6.25, 6.25, 6.125, 6.125, 6.125, 6, 6, 6, 6, 5.875,
5.875, 5.75, 5.75, 5.75, 5.75, 5.75, 5.75, 5.75, 5.75, 5.625,
5.5, 5.5, 5.5, 5.5, 5.375, 5.375, 5.25, 5.125, 5, 5, 5, 5
), teamAbbrev = structure(c(11L, 9L, 7L, 5L, 7L, 4L, 6L,
14L, 1L, 4L, 3L, 9L, 8L, 4L, 3L, 7L, 1L, 6L, 13L, 7L, 2L,
12L, 9L, 1L, 7L, 9L, 10L, 13L, 10L, 4L, 14L, 13L, 12L, 6L,
1L, 11L, 9L, 7L, 4L, 10L, 1L, 1L, 5L, 13L, 9L, 12L, 3L, 4L,
3L, 13L, 6L, 4L, 13L, 1L, 10L, 5L, 5L, 13L, 8L, 8L, 7L, 13L,
8L, 13L, 4L, 7L, 10L, 3L, 10L, 6L, 4L, 2L, 12L, 2L, 6L, 10L,
6L, 11L, 2L, 12L, 1L, 12L, 9L, 11L, 8L, 2L, 6L, 10L, 1L,
9L, 13L, 2L, 5L, 7L, 12L, 1L, 11L, 3L, 14L, 2L, 1L, 8L, 11L,
3L, 13L), .Label = c("ARS", "BOU", "BUR", "CHE", "CRY", "EVE",
"HUL", "LEI", "MU", "SOU", "STK", "SUN", "SWA", "WAT"), class = "factor")), .Names = c("Name",
"Salary", "Position", "FP", "teamAbbrev"), class = "data.frame", row.names = c(NA,
-105L))

Answer 1

By using an empty matrix and filling the rows with the correct values for each position I was able to get this to work.
#### SOLVER ##### ----
mm <- matrix(0, nrow = 8, ncol = nrow(df))
# Goal Keeper
j<-1
i<-1
for (i in 1:nrow(df)){
if (df$Pos[i]=="GK")
mm[j,i]<-1
}
# Defender
j<-2
i<-1
for (i in 1:nrow(df)){
if (df$Pos[i]=="D")
mm[j,i]<-1
}
# Midfielder
j<-3
i<-1
for (i in 1:nrow(df)){
if (df$Pos[i]=="M" ||
df$Pos[i]=="M/F")
mm[j,i]<-1
}
# Forward
j<-4
i<-1
for (i in 1:nrow(df)){
if (df$Pos[i]=="F" ||
df$Pos[i]=="M/F")
mm[j,i]<-1
}
# Utility
j<-5
i<-1
for (i in 1:nrow(df)){
if (!df$Pos[i]=="GK")
mm[j,i]<-1
}
# Salary
mm[6, ] <- df$Salary
mm[7, ] <- df$FP
mm[8, ] <- 1
# rbind existing matrix to itself to set minimum constraints
mm <- rbind(mm, mm[1:5,])
i<-1
objective.in <- df$FP
const.mat <- mm
const.dir <- c("<=", "<=", "<=", "<=", "<=", "<=", "<=", "==",
">=", ">=", ">=", ">=", ">=")
x <- 20000
vals <- c()
for(i in 1:5){
const.rhs <- c(1, 4, 4, 4, 7, 50000, x, 8, # max for each contraint
1, 2, 2, 2, 7) # min for each constraint
sol <- lp(direction = "max", objective.in, # maximize objective function
const.mat, const.dir, const.rhs, # constraints
all.bin = TRUE)
vals <- c(vals, sol$objval)
x <- sol$objval - 0.00001
inds <- which(sol$solution == 1)
sum(df$salary[inds])
solution<-df[inds, ]
solution <- solution[,-c(8)]
solution <- solution %>%
arrange(Pos)
print("---- Start ----")
print(i)
print(solution)
print(sum(solution$FP))
print(sum(solution$Salary))
print(sum(solution$S))
print("---- END ----")
}