LPsolve Гибридные ограничения

Question

Я использую следующий код R, чтобы оптимизировать составные части Soccer для моей спортивной лиги фэнтези. До настоящего времени он работал отлично, но в список ограничений, которые я бы хотел решить, добавлена ​​новая морщина.

Линейка состоит из 8 игроков. 1GK, 2D, 2M, 2F, & 1 Util.

При создании матричной модели, я теперь должен учитывать гибридную игроков позиций, такие как M/F или D/M

В R, что является правильным способом для добавления 1 в колонке для М и 1 в столбце F, если позиция игрока равна M/F? Является ли это правильным подходом к решению этого вопроса или я должен смотреть на другие идеи.

Рабочий Solver код с GK D M F позиции составляли, но не D/M или 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 

Вот образец бассейн около 100 игроков с несколькими гибридными игроков включены.

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

Используя пустую матрицу и заполняя строки правильными значениями для каждой позиции, я смог заставить ее работать.

#### 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 ----") 
}