LPsolve 混合约束
LPsolve Hybrid constraints
我使用以下 R 代码为我的梦幻体育联盟优化足球阵容。到目前为止它一直运行良好，但是我想解决的约束列表中添加了一个新问题。
一个阵容由8名球员组成。 1GK、2D、2M、2F 和 1 个实用程序。
创建模型矩阵时，我现在必须考虑混合玩家位置，例如 M/F 或 D/M
在 R 中，如果玩家位置为 M/F，在 M 列中添加 1 并在 F 列中添加 1 的正确方法是什么？这是解决此问题的正确方法还是我应该考虑其他想法。
包含 GK D M F 位置但不包含 D/M 或 M/F
的工作求解器代码
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
这里是大约 100 名玩家的样本池，其中包括一些混合玩家。
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))
通过使用空矩阵并为每个位置的行填充正确的值，我能够让它工作。
#### 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 ----")
}
我使用以下 R 代码为我的梦幻体育联盟优化足球阵容。到目前为止它一直运行良好，但是我想解决的约束列表中添加了一个新问题。
一个阵容由8名球员组成。 1GK、2D、2M、2F 和 1 个实用程序。
创建模型矩阵时，我现在必须考虑混合玩家位置，例如 M/F 或 D/M
在 R 中，如果玩家位置为 M/F，在 M 列中添加 1 并在 F 列中添加 1 的正确方法是什么？这是解决此问题的正确方法还是我应该考虑其他想法。
包含 GK D M F 位置但不包含 D/M 或 M/F
的工作求解器代码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
这里是大约 100 名玩家的样本池，其中包括一些混合玩家。
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))
通过使用空矩阵并为每个位置的行填充正确的值，我能够让它工作。
#### 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 ----")
}