问题
I used excel solver to solve an optimization problem, and I am trying to replicate it in R.
I found many packages like optim, ROI etc., but it seems all of them only take a vector as the object to optimize and allow the variables to take any continuous value. In my case, I have a constraint matrix that also needs to be satisfied and my variables can only take binary values.
Here is problem I want to solve:
A-D are machines, 1-3 are tasks and the number in the first matrix is the value generated by using X machine to do Y task. The constraints are: A-D can do and only can do one task (cannot split); each task can be worked and only be worked by one machine.
Here is the code I am using:
par = rep(c(0,1),6)
mat <- matrix(c(9,10,11,4,5,10,1,3,5,7,5,4), nrow = 3)
fr <- function(x) {
y= matrix(x,nrow = 4)
sum(mat %*% y)
}
a = optim(par, fr)
Some questions: How can I optimize maximum, seems this function default optimize minimum? How can I add constraints into it? How can I limit to binary variables?
回答1:
You need to construct a vector for the objective function and a constraint matrix, finally solving with one of the R LP solvers:
library(lpSolve)
costs <- matrix(c(9, 10, 11, 4, 5, 10, 1, 3, 5, 7, 5, 4), nrow=3)
nr <- nrow(costs)
nc <- ncol(costs)
columns <- t(sapply(1:nc, function(x) rep(c(0, 1, 0), c(nr*(x-1), nr, nr*(nc-x)))))
rows <- t(sapply(1:nr, function(x) rep(rep(c(0, 1, 0), c(x-1, 1, nr-x)), nc)))
mod <- lp("max", as.vector(costs), rbind(columns, rows), "<=", rep(1, nr+nc), binary.vec=rep(TRUE, nr*nc))
Now you can grab the solution and the objective function:
mod$objval
# [1] 27
matrix(mod$solution, nrow=nr)
# [,1] [,2] [,3] [,4]
# [1,] 0 0 0 1
# [2,] 1 0 0 0
# [3,] 0 1 0 0
Note that functions like optim are not well suited for this problem both because they don't consider matrices of constraints and also because they cannot limit to binary variable values.
来源：https://stackoverflow.com/questions/30225830/how-to-replicate-excel-solver-in-r