[R] optim() not finding optimal values

[Nikhil Kaza]

Your function is very irregular, so the optim is likely to return  
local minima rather than global minima.

Try different methods  (SANN, CG, BFGS) and see if you get the result  
you need. As with all numerical optimsation, I would check the  
sensitivity of the results to starting values.


Nikhil Kaza
Asst. Professor,
City and Regional Planning
University of North Carolina

nikhil.list at gmail.com

On Jun 26, 2010, at 4:27 PM, Derek Ogle wrote:

> I am trying to use optim() to minimize a sum-of-squared deviations  
> function based upon four parameters.  The basic function is defined  
> as ...
>
> SPsse <- function(par,B,CPE,SSE.only=TRUE)  {
>  n <- length(B)                             # get number of years of  
> data
>  B0 <- par["B0"]                            # isolate B0 parameter
>  K <- par["K"]                              # isolate K parameter
>  q <- par["q"]                              # isolate q parameter
>  r <- par["r"]                              # isolate r parameter
>  predB <- numeric(n)
>  predB[1] <- B0
>  for (i in 2:n) predB[i] <- predB[i-1]+r*predB[i-1]*(1-predB[i-1]/K)- 
> B[i-1]
>  predCPE <- q*predB
>  sse <- sum((CPE-predCPE)^2)
>  if (SSE.only) sse
>    else list(sse=sse,predB=predB,predCPE=predCPE)
> }
>
> My call to optim() looks like this
>
> # the data
> d <- data.frame(catch=  
> c 
> (90000,113300,155860,181128,198584,198395,139040,109969,71896,59314,62300,65343,76990,88606,118016,108250,108674 
> ),  
> cpe 
> = 
> c 
> (109.1,112.4,110.5,99.1,84.5,95.7,74.1,70.2,63.1,66.4,60.5,89.9,117.0,93.0,116.6,90.0,105.1 
> ))
>
> pars <- c(800000,1000000,0.0001,0.17)                   # put all  
> parameters into one vector
> names(pars) <- c("B0","K","q","r")                      # name the  
> parameters
> ( SPoptim <- optim(pars,SPsse,B=d$catch,CPE=d$cpe) )    # run optim()
>
>
> This produces parameter estimates, however, that are not at the  
> minimum value of the SPsse function.  For example, these parameter  
> estimates produce a smaller SPsse,
>
> parsbox <- c(732506,1160771,0.0001484,0.4049)
> names(parsbox) <- c("B0","K","q","r")
> ( res2 <- SPsse(parsbox,d$catch,d$cpe,SSE.only=FALSE) )
>
> Setting the starting values near the parameters shown in parsbox  
> even resulted in a movement away from (to a larger SSE) those  
> parameter values.
>
> ( SPoptim2 <- optim(parsbox,SPsse,B=d$catch,CPE=d$cpe) )    # run  
> optim()
>
>
> This "issue" most likely has to do with my lack of understanding of  
> optimization routines but I'm thinking that it may have to do with  
> the optimization method used, tolerance levels in the optim  
> algorithm, or the shape of the surface being minimized.
>
> Ultimately I was hoping to provide an alternative method to  
> fisheries biologists who use Excel's solver routine.
>
> If anyone can offer any help or insight into my problem here I would  
> be greatly appreciative.  Thank you in advance.
>
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