Optimization of budget allocation in R (formerly Excel Solver)

Question

i translated a Problem I had in Excel into R. I want to allocate a fixed Budget in a form that \"Gesamt\" (which is returned by the function) is maximized.

NrwGe         


        

Answer 1

Try optim with the L-BFGS-U method (which allows for bounds) and a lower bound of 0. Then project the input components onto a vector which sums to 5000 passing that to NrwGes. fscale = -1 says to maximize rather than minimize. The final allocation will be proj(res$par) as shown at the bottom. No packages are used.

proj <- function(x) 5000 * x / sum(x)
st <- proj(rep(1, 5))
f <- function(x) NrwGes(proj(x))
res <- optim(st, f, lower = 0 * st, method = "L-BFGS-B", control = list(fnscale = -1))

giving:

> res
$`par`
[1] 2107.8438  482.5702  468.9409  268.0808  142.4305

$value
[1] 86.64285

$counts
function gradient 
      14       14 

$convergence
[1] 0

$message
[1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"

> proj(res$par)  # final allocation
[1] 3037.3561  695.3729  675.7334  386.2984  205.2391

Answer 2

An option is nloptr package :

library(nloptr)

# we use NLOPT_LN_COBYLA algorithm because it doesn't need gradient functions
opts <- list(algorithm="NLOPT_LN_COBYLA",
             xtol_rel=1.0e-8,
             maxeval=10000)
# objective function (negative because nloptr always minimize)
objFun <- function(x){ -NrwGes(x) }

# sum of budget <= 5000 (in the form g(x) <= 0)
g <- function(x){ sum(x) - 5000 }


res <- nloptr(x0=rep.int(0,5), # initial solution (all zeros)
              eval_f=objFun, 
              lb=rep.int(0,5), # lowerbounds = 0
              ub=rep.int(5000,5), # upperbounds = 5000
              eval_g_ineq=g,
              opts=opts)

Result :

> res
Call:
nloptr(x0 = rep.int(0, 5), eval_f = objFun, lb = rep.int(0, 5), 
    ub = rep.int(5000, 5), eval_g_ineq = g, opts = opts)


Minimization using NLopt version 2.4.2 

NLopt solver status: 4 ( NLOPT_XTOL_REACHED: Optimization stopped because xtol_rel 
or xtol_abs (above) was reached. )

Number of Iterations....: 261 
Termination conditions:  xtol_rel: 1e-08    maxeval: 10000 
Number of inequality constraints:  1 
Number of equality constraints:    0 
Optimal value of objective function:  -86.6428477187536 
Optimal value of controls: 3037.382 695.3725 675.7232 386.2929 205.2291

N.B. you can access to solution, objective of res using res$solution, res$objective etc.