CODEWITHSUNDEEP
roptimizationconstraintslinear-programming
itpetersen
itpetersen

Reputation: 1515

Optimize value with linear (or non-linear?) constraints in R

I am trying to pick the best possible fantasy football team given different constraints. My goal is to pick the players that maximize the sum of their projected points.

The constraints are:

1) The team must include:

-1 QB

-2 RBs

-2 WRs

-1 TE

2) A player's risk must not exceed 6

3) The sum of the players' costs must not exceed 300.

How can I do this? What is the best package/function in R to optimize these constraints? What would the function call look like to maximize the projected points given these constraints? FYI, I'll be searching through 100-300 players.

Thanks in advance! Here is a small example data set:

name <- c("Aaron Rodgers","Tom Brady","Arian Foster","Ray Rice","LeSean McCoy","Calvin Johnson","Larry Fitzgerald","Wes Welker","Rob Gronkowski","Jimmy Graham")

pos <- c("QB","QB","RB","RB","RB","WR","WR","WR","TE","TE")

pts <- c(167, 136, 195, 174, 144, 135, 89, 81, 114, 111) 

risk <- c(2.9, 3.4, 0.7, 1.1, 3.5, 5.0, 6.7, 4.7, 3.7, 8.8) 

cost <- c(60, 47, 63, 62, 40, 60, 50, 35, 40, 40) 

mydata <- data.frame(name, pos, pts, risk, cost)

Upvotes: 3

Views: 2388

Answers (1)

flodel
flodel

Reputation: 89057

Your constraints and objective are linear, but your variables are binaries: whether each player should be picked or not. So your problem is a little more general than a Linear Programming (LP), it is a Mixed-Integer Programming (MIP). On CRAN's Optimization Task View, look for their MIP section.

CPLEX is a commercial solver you probably not have access to, but GLPK is free. If I were you, I would probably go with the high level interface Rglpk.

It will require you put your problem in matrix form, I suggest you look at the documentation and examples.

Edit: Here is an implementation:

# We are going to solve:
# maximize f'x subject to A*x <dir> b
# where:
#   x is the variable to solve for: a vector of 0 or 1:
#     1 when the player is selected, 0 otherwise,
#   f is your objective vector,
#   A is a matrix, b a vector, and <dir> a vector of "<=", "==", or ">=",
#   defining your linear constraints.

# number of variables
num.players <- length(name)
# objective:
f <- pts
# the variable are booleans
var.types <- rep("B", num.players)
# the constraints
A <- rbind(as.numeric(pos == "QB"), # num QB
           as.numeric(pos == "RB"), # num RB
           as.numeric(pos == "WR"), # num WR
           as.numeric(pos == "TE"), # num TE
           diag(risk),              # player's risk
           cost)                    # total cost

dir <- c("==",
         "==",
         "==",
         "==",
         rep("<=", num.players),
         "<=")

b <- c(1,
       2,
       2,
       1,
       rep(6, num.players),
       300)

library(Rglpk)
sol <- Rglpk_solve_LP(obj = f, mat = A, dir = dir, rhs = b,
                      types = var.types, max = TRUE)
sol
# $optimum
# [1] 836                      ### <- the optimal total points

# $solution
#  [1] 1 0 1 0 1 1 0 1 1 0     ### <- a `1` for the selected players

# $status
# [1] 0                        ### <- an optimal solution has been found

# your dream team
name[sol$solution == 1]
# [1] "Aaron Rodgers"  "Arian Foster"   "LeSean McCoy"
# [4] "Calvin Johnson" "Wes Welker"     "Rob Gronkowski

Upvotes: 8

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