问题

I want to solve an optimization problem in R; The dummy data for the same is given below.

# Input Data
DTM <- sample(1:30,10,replace=T)
DIM <- rep(30,10)
Price <- 100 - seq(0.4,1,length.out=10)

# Variables that shall be changed to find optimal solution
Hike <- sample(0:1,10,replace=T)
Position <- sample(-2:2,10,replace=T)

# Objective function
hikes_till_now <- cumsum(Hike) - Hike
PostHike <- numeric(10)
for (i in seq_along(Hike)){
  PostHike[i] <- 99.60 - 0.25*(Hike[i]*(1-DTM[i]/DIM[i]))
  if(i>1) {
    PostHike[i] <- PostHike[i] - 0.25*hikes_till_now[i]
  }
}
Pnl <- Position*(PostHike-Price)

# Snapshot of data
all.data <- data.frame(DTM,DIM,Price,Hike,Position,Pnl)
all.data

#    DTM DIM    Price Hike Position        Pnl
# 1    3  30 99.60000    1        2 -0.4500000
# 2   11  30 99.53333    1        2 -0.6833333
# 3   29  30 99.46667    1        2 -0.7500000
# 4   16  30 99.40000    1       -2  1.3333333
# 5   25  30 99.33333    0        2 -1.4666667
# 6    5  30 99.26667    1        1 -0.8750000
# 7    3  30 99.20000    0       -1  0.8500000
# 8    8  30 99.13333    0        0  0.0000000
# 9   22  30 99.06667    0       -2  1.4333333
# 10  11  30 99.00000    0       -2  1.3000000

Variable description

So, the first section of the code contains the inputs to my system - DTM, DIM & Price.

The second section consists of the variables I'd like to modify to find the optimal solution - Hike & Position. The values have been initiated as above.

The final section consists of the calculations I'll have to do to arrive at my objective function, which is to maximize Pnl.

Constraints

I also have a couple of constraints -

The sum of Hike should be less than 4
The sum of Position should be 0, and each Position value should be between -2 & +2

I have previously worked in GAMS and MATLAB, but I am just unable to get optimization to work here. I have gone through examples in the Rsymphony package and this answer but I was unable to get them to work for multiple variable inputs.

Help appreciated.

来源：https://stackoverflow.com/questions/39787940/optimization-in-r-for-multiple-variables

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