Thank you, Brian and Ross.

That was very helpful.

DEoptim and random solvers gave good results. I tested the same using
GenSA, which performed worse than pso.

Thank you again! :)

On Tue, Sep 20, 2016 at 8:53 PM, Brian G. Peterson <br...@braverock.com>
wrote:

> The attached .R file should demonstrate what Ross was talking about.
>
> The cardinality constraint is directly supported by the stochastic
> global solvers 'DEoptim' and 'random', as described in the
> documentation.
>
> It can also be formulated as a mixed integer linear problem for certain
> objective functions, but because you're looknig for the Markowitz
> mean/variance portfolio, you have a quadratic problem, and can't
> formulate it using an MILP.
>
> The attached file fixes the minimum position box constraint to 0, which
> aalows all solvers to converge.
>
> pso still doesn't get a good solution, but this solution may be improved
> by increasing the maximum number of iterations via the parameter
> 'maxit'. After increasing maxit, it gets closer to the solutions
> returned by 'random' and 'DEoptim'.
>
> Both 'random' and 'DEoptim' produce similar solutions which meet the
> constraints and objectives, but they are not identical, and change over
> multiple runs.  (This is stochastic optimization, after all, so the only
> way to get the same answer would be to artificially, and incorrectly,
> set the random seed.).
>
> This suggests two things:
>
> 1> that there are not enough random portfolios (for 'random') or that
> the population size and number of generations are insufficient to find
> the global solution (for DEoptim).
>
> 2> that the problem may still be somewhat over constrained, most likely
> by the max weight box constraint.  You might want to use random
> portfolios and portfolio sets to compare and plot the difference between
> the unconstrained search space and the constrained search space to sort
> out whether this is really what you want to do.
>
> Regards,
>
> Brian
>
> --
> Brian G. Peterson
> http://braverock.com/brian/
> Ph: 773-459-4973
> IM: bgpbraverock
>
>
> On Tue, 2016-09-20 at 07:18 -0500, Ross Bennett wrote:
> > Hi Abhay,
> >
> > The cardinality constraint is not directly support by the pso solver so
> we
> > have to implement that constraint as a penalized objective. Also note
> that
> > your box constraint is greater than 0, so the box constraint and position
> > limit constraint are fighting each other (i.e your problem is
> > overconstrained).
> >
> > I recommend using DEoptim or random portfolios as a solver when dealing
> > with position limit constraints. Position limit constraints are supported
> > directly by the algorithm in the random portfolios 'sample' method. We
> use
> > the mapping function supported by DEoptim to handle more complex
> > constraints such as position limit when using DEoptim as the solver.
> >
> > Hope that helps.
> >
> > Ross
> >
> >
> > On Mon, Sep 19, 2016 at 10:25 AM, Abhay Bhadani <abhad...@gmail.com>
> wrote:
> >
> > > Thanks, Brian!
> > >
> > > I implemented the following:
> > > ------------------------------------------------------------
> > > ----------------------------------
> > > data("edhec")
> > > returns <- edhec[,1:12]
> > > colnames(returns) <-
> > > c("CA","CTAG","DS","EM","EN","ED","FIA","GMLS","MA","RV","SS","FF")
> > > print(head(returns,5))
> > > fund.names <- colnames(returns)
> > >
> > >
> > > #Giving Portfolio Specifications
> > > pspec <- portfolio.spec(assets=fund.names)
> > > print.default(pspec)
> > >
> > > #Adding Constraints
> > > #Full investment constraint: sum of all x_i is 1
> > > pspec <- add.constraint(portfolio= pspec, type =
> > > "weight_sum",min=0.99,max=1.01)
> > >
> > > #Box constraint: value of x_i varies between 0.2 to 0.8
> > > pspec <- add.constraint(portfolio= pspec, type="box", min = 0.01, max =
> > > 0.25)
> > >
> > > #Cardinality constraint
> > > pspec <- add.constraint(portfolio= pspec,
> type="position_limit",max_pos =
> > > 6,enabled=TRUE)
> > >
> > > #Adding Objective
> > > pspec <- add.objective(portfolio=pspec, type="risk", name="var")
> > > pspec <- add.objective(portfolio=pspec, type="return", name="mean")
> > >
> > > opt_meanvar <- optimize.portfolio(R=returns,portfolio = pspec,
> > >                                   optimize_method="pso", trace=TRUE)
> > >
> > > ------------------------------------------------------------
> > > ------------------------------
> > >
> > > Results:
> > >
> > > Optimal Weights:
> > >     CA   CTAG     DS     EM     EN     ED    FIA   GMLS     MA     RV
> > > SS     FF
> > > 0.1319 0.0551 0.0312 0.1312 0.1127 0.1467 0.0641 0.0218 0.0805 0.1101
> > > 0.0296 0.0952
> > >
> > > _____________________________________________________
> > >
> > > I obtained weights for all 12 assets. That's why I was not sure whether
> > > position_limit constraint is same as cardinality constraint.
> > >
> > >
> > > On Mon, Sep 19, 2016 at 8:32 PM, Brian G. Peterson <
> br...@braverock.com>
> > > wrote:
> > >
> > > > On Mon, 2016-09-19 at 20:22 +0530, Abhay Bhadani wrote:
> > > > > I just started exploring PortfolioAnalytics package.
> > > > >
> > > > > Similar to setting up custom objective functions, is there a way
> to set
> > > > up
> > > > > custom constraints too?
> > > > >
> > > > > I would like to know how to set up cardinality constraint (i.e.,
> > > limiting
> > > > > number of assets in a portfolio).
> > > >
> > > > cardinality constraints are already supported via the
> 'position_limit'
> > > > constraint which is an integer constraint limiting the maximum
> number of
> > > > non-zero weight positions in the portfolio.  It may be added like
> this:
> > > >
> > > >
> > > > pspec <- add.constraint(portfolio=pspec,
> > > >                         type="position_limit",
> > > >                         max_pos=3,
> > > >                         enabled=TRUE)
> > > >
> > > > assuming that your portfolio specification object is 'pspec'.
> > > >
> > > > As with other constraint types, this may not be efficiently
> supported by
> > > > all optimization engines. (This is a limitation of the underlying
> > > > optimizers/solvers, not of PortfolioAnalytics).
> > > >
> > > > On a more general note, any constraint may be expressed as an
> objective
> > > > by creating a penalty for violating the constraint.  As noted above,
> > > > this may lead to very inefficient or non-converging optimization.
> > > >
> > > > Regards,
> > > >
> > > > Brian
> > > >
> > > > --
> > > > Brian G. Peterson
> > > > http://braverock.com/brian/
> > > > Ph: 773-459-4973
> > > > IM: bgpbraverock
> > > >
> > > >
> > > >
> > > >
> > > >
> > >
> > >         [[alternative HTML version deleted]]
> > >
> > > _______________________________________________
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> > > -- Also note that this is not the r-help list where general R questions
> > > should go.
> > >
> >
> >       [[alternative HTML version deleted]]
> >
> > _______________________________________________
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>

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