[R] DEoptim example illustrating use of fnMap parameter for enforcement of cardinality constraints

[Joshua Ulrich]

David,

On Sat, Jun 16, 2012 at 2:41 PM, David-Michael Lincke
<dlincke at lincke.com> wrote:
> Hi Joshua,
>
> Thank you very much for the comprehensive response.
>
> In the meantime, I had taken a look at the source code of function
> DEoptim() and your example below confirms the conclusions that I have
> arrived at from that review as to the expected nature of the function passed
> as fnMap. What I continue to find confusing and a bit disconcerting,
> however, is that DEoptim() actively tries to avoid duplicates in the
> parameter vector which of course is the intended result when enforcing a
> cardinality constraint on a vector of allocation weights by forcing some of
> them to 0. As DEoptim() will make five attempts at randomly perturbing the
> parameter vector and resubmitting it to the mapping function before giving
> up I am concerned that this may at least slow down if not potentially even
> derail or otherwise interfere with convergence. I have yet to run a
> practical test but I wonder whether there is a deeper reason for this or if
> this can be safely ignored.
>
I'm not sure I understand your concern.  The example before the
"trivial full-investment function" example in slimLargeN_map.R creates
a mapping function that always produces the same result, which means
the search space is never explored.  That is the extreme case of why
duplicates are not desirable.

Removing duplicates does slow the algorithm, but a slower algorithm
was more desirable to one that less effectively explores the search
space.

*Any* mapping function has the potential to derail or otherwise
interfere with convergence, so the user must be very careful when
using this functionality.  I will make sure to clearly state this in
the documentation and possibly include a handful of mapping function
examples (suggestions welcome).

> Btw, I have checked out the SVN repository and had a quick look at the
> example in slimLargeN_map.R, but I do not see the fnMap functionality being
> used in the large-scale optimization vignette. The vignette performs
> rescaling of the allocation weights vector to meet the budget constraint
> inside the objective function but does not seem to enforce any cardinality
> constraints.
>
I didn't mean that the mapping functionality is used in the portfolio
optimization vignette.  I meant that the mapping example near the end
of slimLargeN_map.R uses the objective function in the vignette.

> Best regards,
> David
>

Best,
--
Joshua Ulrich  |  FOSS Trading: www.fosstrading.com



> -----Original Message-----
> From: Joshua Ulrich [mailto:josh.m.ulrich at gmail.com]
> Sent: Saturday, June 16, 2012 3:29 AM
> To: David-Michael Lincke
> Cc: r-help at r-project.org
> Subject: Re: [R] DEoptim example illustrating use of fnMap parameter for
> enforcement of cardinality constraints
>
> Hi David,
>
> I apologize for the lack of documentation.  I added it quickly and didn't
> have adequate time to document it.
>
> The function below works with the objective function in the "Large-scale
> portfolio optimization with DEoptim" vignette.
> Also, I just committed the full example
> (pkg/DEoptim/sandbox/slimLargeN_map.R) to the DEoptim repository on
> R-forge: https://r-forge.r-project.org/projects/deoptim/
>
> mappingFun <- function(x) {
>  x[which(order(x) < 6)] <- 0
>  x <- round(x,2) # produce some dups
>  x/sum(x)
> }
> set.seed(1234)
> out <- DEoptim(fn=obj, lower=lower,
>  upper=upper, control=controlDE, fnMap=mappingFun)
>
> Best,
> --
> Joshua Ulrich  |  FOSS Trading: www.fosstrading.com
>
>
> On Fri, Jun 15, 2012 at 3:24 AM, David-Michael Lincke <dlincke at lincke.com>
> wrote:
>> Function DEoptim in package DEoptim for differential evolution defines an
>> optional parameter fnMap:
>>
>> fnMap
>>
>> "an optional function that will be run after each population is created,
>> but before the population is passed to the objective function. This allows
>> the user to impose integer/cardinality constriants."
>>
>> Unfortunately, there is no further documentation decribing the kind of
>> parameters being passed to this function on invocation or the structure of
>> the return value expected. I would very much appreciate it if somebody
>> familiar with this package could provide an example illustrating how this
>> interface is meant to be used to enforce cardinality constraints.
>>
>> Thanks,
>> David
>>
>>
>>        [[alternative HTML version deleted]]
>>
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