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

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.