[R] Penalty function constrained optimization

[Simon Knapp]

perhaps:

obj<-function(f){
    f <- array(f, dim=c(nfleets, nareas)) # just for clarity
    F <- q*f
    Z <- M+sum(F)
    S <- exp(-Z)
    Catch<- N*F/Z*(1-S)
    Tot.Catch <- sum(Catch)
    NR<-array(0,dim=c(nfleets,nareas))
    NR<-Price*Catch - f*cost
    d.NR<-array(0,dim=c(nfleets,nareas))
    f <- apply(f, 1, sum) ##### sum effort for each fleet
    d.NR<- N*q/Z*(1-S-F/Z+F/Z*S+F*S)*Price - cost + 1000*max(0,(f-9))^2
    return(sum(d.NR*d.NR))
}

On Wed, Oct 17, 2012 at 5:06 AM, hayduke <cusackc at onid.orst.edu> wrote:
> Hi All,
> I am trying to use optim() to minimize a function with a penalty function
> term. This is a simple model bioeconomic model of a fishery. The penalty
> function constrains the amount of effort (f) at 9. This works fine. The code
> is:
> **********
> nfleets<-2
> M<-1
> M<-array(M,dim=c(nfleets))
> N<-1000
> cost<-c(30,30)
> cost<-array(cost,dim=c(nfleets))
> Price<-2
> Price<-array(Price,dim=c(nfleets))
> q<-array(0.1,dim=c(nfleets))
> f<-1
> f<-array(f,dim=c(nfleets))
> f1<-f[1]
> f2<-f[2]
> init.eff<-array(8,dim=c(nfleets))
> OF<-c(q*f)
> F<- sum(q*f)
> Z<-M+F
> Catch<-array(0,dim=c(nfleets))
>
> obj<-function(f){
> F <- q*f
> Z <- M+sum(F)
> S <- exp(-Z)
> Catch<- N*F/Z*(1-S)
> Tot.Catch <- sum(Catch)
> NR<-array(0,dim=c(nfleets))
> NR<-Price*Catch - f*cost
> d.NR<-array(0,dim=c(nfleets))
> d.NR<- N*q/Z*(1-S-F/Z+F/Z*S+F*S)*Price-cost +1000*(max(0,f-9))^2
> return(sum(d.NR*d.NR))}
> zero.bnd <-  rep.int(0, length(f))
> opt.eff  <- optim( init.eff, obj, method="L-BFGS-B", lower=zero.bnd )
> ***
>
> However, now I am trying to add another dimension to the problem: areas.
> Does anybody have any suggestions regarding how to implement the penalty
> function so it works over all areas? i.e. that the sum of each fleet's
> effort is 9 across all areas?
> The code with areas is below. In the obj function, the ??? denote the start
> of the penalty function and the place where I need help....
> ***
> nfleets<-2
> nareas<-2
> M<-1
> M<-array(M,dim=c(nfleets,nareas))
> N<-1000
> cost<-c(30,30)
> cost<-array(cost,dim=c(nfleets,nareas))
> Price<-2
> Price<-array(Price,dim=c(nfleets,nareas))
> q<-array(0.1,dim=c(nfleets,nareas))
> f<-1
> f<-array(f,dim=c(nfleets,nareas))
> init.eff<-array(3,dim=c(nfleets,nareas))
> OF<-array(c(q*f), dim=c(nfleets, nareas))
> F<- sum(q*f)
> Z<-M+F
> Catch<-array(0,dim=c(nfleets, nareas))
>
> obj<-function(f){
> F <- q*f
> Z <- M+sum(F)
> S <- exp(-Z)
> Catch<- N*F/Z*(1-S)
> Tot.Catch <- sum(Catch)
> NR<-array(0,dim=c(nfleets,nareas))
> NR<-Price*Catch - f*cost
> d.NR<-array(0,dim=c(nfleets,nareas))
> d.NR<- N*q/Z*(1-S-F/Z+F/Z*S+F*S)*Price-cost +???????1000*sum(max(0,(f-9))^2
> return(sum(d.NR*d.NR))}
>
> zero.bnd <-  rep.int(0, length(f))
> opt.eff  <- optim( init.eff, obj, method="Nelder-Mead" )
>
> Thanks very much!
>
>
>
> --
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