[R] Problem with minimization that I failed to understand

Daniel Lobo d@n|e|obo9976 @end|ng |rom gm@||@com
Fri Mar 28 22:41:37 CET 2025 

Hi Rui,

I was not aware of this function, however it looks like it should work for
me. Many thanks for this intuition.

However, in my optimization there are 3 constraints as below,

1) sum of all parameters should be 1
2) all parameters should be positive
3) last parameter should be greater than 2.05/100

I can see that the constraint #2 is implemented in the function argument
lower = rep(0.01, 21),

How can I impose other 2 constraints?

Many thanks,

On Sat, 29 Mar 2025 at 01:49, Rui Barradas <ruipbarradas using sapo.pt> wrote:

> Às 13:59 de 28/03/2025, Daniel Lobo escreveu:
> > Hi Duncan,
> >
> > Thanks for your comment, I agree with that.
> >
> > But, how it can be justified that an Optimizer gives a result which is
> > inferior to the starting value? At most, resulting value can remain at
> the
> > same level, isnt it?
> >
> > On Fri, 28 Mar 2025 at 14:34, Duncan Murdoch <murdoch.duncan using gmail.com>
> > wrote:
> >
> >> I haven't run your code, but since Kendall correlation is based on
> >> ranks, your Fn is probably locally constant with jumps when the ranks
> >> change.  That's a really hard kind of function to maximize, and the
> >> algorithm used by fmincon is not appropriate to do it.
> >>
> >> Sorry, but I don't know if there is an R function that can do
> >> constrained discrete maximization.
> >>
> >> Duncan Murdoch
> >>
> >> On 2025-03-27 2:35 p.m., Daniel Lobo wrote:
> >>> Hi,
> >>>
> >>> I have below minimization problem
> >>>
> >>>
> >>> MyDat = structure(list(c(50L, 0L, 0L, 50L, 75L, 100L, 50L, 0L, 50L, 0L,
> >>> 25L, 50L, 50L, 75L, 75L, 75L, 0L, 75L, 75L, 75L, 0L, 25L, 75L,
> >>> 75L, 0L, 75L, 100L, 0L, 25L, 100L), c(75L, 0L, 0L, 50L, 100L,
> >>> 50L, 75L, 75L, 100L, 25L, 0L, 25L, 100L, 0L, 50L, 0L, 25L, 25L,
> >>> 100L, 75L, 0L, 0L, 0L, 50L, 0L, 75L, 75L, 0L, 50L, 25L), c(50L,
> >>> 0L, 0L, 0L, 100L, 25L, 0L, 0L, 25L, 50L, 0L, 25L, 75L, 50L, 100L,
> >>> 50L, 0L, 75L, 25L, 50L, 0L, 0L, 25L, 0L, 50L, 100L, 100L, 0L,
> >>> 75L, 50L), c(25L, 0L, 0L, 75L, 75L, 25L, 50L, 50L, 100L, 25L,
> >>> 0L, 100L, 50L, 25L, 100L, 25L, 25L, 100L, 50L, 100L, 0L, 0L,
> >>> 100L, 50L, 0L, 50L, 75L, 0L, 50L, 25L), c(50L, 0L, 0L, 75L, 75L,
> >>> 75L, 25L, 25L, 0L, 100L, 0L, 25L, 25L, 75L, 100L, 0L, 25L, 0L,
> >>> 75L, 25L, 25L, 25L, 75L, 25L, 0L, 75L, 100L, 0L, 100L, 100L),
> >>>       c(50L, 0L, 0L, 50L, 100L, 25L, 25L, 25L, 50L, 50L, 0L, 50L,
> >>>       75L, 0L, 100L, 50L, 25L, 100L, 50L, 75L, 0L, 0L, 50L, 25L,
> >>>       0L, 100L, 100L, 0L, 75L, 50L), c(50L, 0L, 0L, 50L, 75L, 25L,
> >>>       75L, 50L, 100L, 25L, 0L, 75L, 25L, 0L, 50L, 0L, 50L, 75L,
> >>>       100L, 75L, 0L, 0L, 100L, 0L, 0L, 50L, 75L, 0L, 100L, 100L
> >>>       ), c(25L, 75L, 50L, 25L, 75L, 50L, 100L, 75L, 100L, 25L,
> >>>       0L, 75L, 25L, 50L, 25L, 25L, 75L, 75L, 100L, 75L, 75L, 100L,
> >>>       75L, 25L, 0L, 75L, 75L, 0L, 75L, 100L), c(55L, 30L, 20L,
> >>>       30L, 45L, 30L, 30L, 30L, 70L, 30L, 10L, 45L, 45L, 45L, 45L,
> >>>       30L, 30L, 55L, 45L, 45L, 30L, 30L, 30L, NA, 30L, 55L, 45L,
> >>>       20L, 45L, 70L), c(85L, 40L, 40L, 40L, 55L, 40L, 20L, 30L,
> >>>       30L, 30L, 20L, 30L, 70L, 40L, 85L, 55L, 30L, 40L, 30L, 55L,
> >>>       20L, 30L, 55L, 0L, 40L, 55L, 70L, 40L, 85L, 70L), c(45L,
> >>>       45L, 0L, 45L, 45L, 45L, 0L, 0L, 100L, 45L, 0L, 100L, 45L,
> >>>       45L, 100L, 45L, 45L, 100L, 45L, 45L, 45L, 45L, 25L, 45L,
> >>>       0L, 100L, 45L, 0L, 45L, 45L), c(55L, 45L, 45L, 45L, 55L,
> >>>       45L, 45L, 45L, 45L, 45L, 45L, 45L, 45L, 45L, 55L, 55L, 45L,
> >>>       55L, 45L, 45L, 45L, 45L, 45L, 45L, 45L, 55L, 45L, 45L, 45L,
> >>>       45L), c(100L, 100L, 50L, 100L, 100L, 100L, 100L, 100L, 100L,
> >>>       100L, 50L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L,
> >>>       100L, 100L, 100L, 100L, 50L, 100L, 100L, 100L, 100L, 100L,
> >>>       100L), c(100L, 25L, 25L, 0L, 100L, 60L, 0L, 0L, 25L, 60L,
> >>>       0L, 60L, 100L, 60L, 100L, 100L, 25L, 100L, 60L, 100L, 100L,
> >>>       60L, 100L, 60L, 100L, 100L, 100L, 100L, 60L, 60L), c(0L,
> >>>       0L, 50L, 50L, 100L, 100L, 0L, 0L, 100L, 100L, 0L, 100L, 100L,
> >>>       0L, 100L, 100L, 0L, 100L, 100L, 100L, 100L, 100L, 100L, 0L,
> >>>       100L, 100L, 100L, 100L, 100L, 100L), c(40L, 100L, 40L, 100L,
> >>>       100L, 40L, 100L, 100L, 100L, 40L, 100L, 100L, 100L, 100L,
> >>>       100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L,
> >>>       100L, 100L, 100L, 0L, 100L, 100L), c(100L, 100L, 100L, 100L,
> >>>       100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L,
> >>>       100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, -10L,
> >>>       100L, 100L, 100L, -10L, 100L, 100L), c(70L, 0L, 25L, 0L,
> >>>       100L, 25L, 0L, 0L, 0L, 45L, 0L, 25L, 100L, 100L, 100L, 100L,
> >>>       0L, 70L, 0L, 100L, 45L, 45L, 0L, 0L, 100L, 100L, 100L, 0L,
> >>>       100L, 100L), c(55L, 55L, 55L, 55L, 55L, 55L, 55L, 55L, 55L,
> >>>       55L, 55L, 55L, 55L, 55L, 55L, 55L, 20L, 55L, 20L, 55L, 20L,
> >>>       20L, 100L, 55L, 55L, 55L, 55L, 0L, 55L, 55L), c(65L, 65L,
> >>>       100L, 65L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L,
> >>>       100L, 100L, 100L, 100L, 65L, 100L, 100L, 100L, 65L, 100L,
> >>>       0L, 65L, 100L, 100L, 100L, 100L, 100L, 100L), c(85L, 85L,
> >>>       85L, 85L, 85L, 85L, 85L, 85L, 85L, 85L, 85L, 85L, 56L, 85L,
> >>>       100L, 85L, 85L, 85L, 0L, 85L, 85L, 85L, 85L, 85L, 85L, 85L,
> >>>       85L, 28L, 56L, 56L)), row.names = c(NA, -30L), class =
> "data.frame")
> >>>
> >>> Fn = function(Wts) return(-Kendall::Kendall(1:Nobs,
> >>> rank(-as.vector(as.matrix(MyDat) %*% matrix(Wts, nc = 1)[, 1, drop =
> >>> T])))$tau[1])
> >>> q1 = pracma::fmincon(c(0.12, 0.04, 0.07, 0.03, 0.06, 0.07, 0.07, 0.04,
> >>> 0.09, 0.08, 0.02, 0.02, 0.03, 0.06, 0.02, 0, 0.07, 0.05, 0.02, 0.02,
> >> 0.02),
> >>> fn = Fn,
> >>>             A = matrix(c(rep(0, 20), -1), nrow = 1), b = -2.05/100,
> Aeq =
> >>> matrix(c(rep(1, 20), 1), nrow = 1), beq = 1,
> >>>             lb = rep(0.01, 21),
> >>>             tol = 1e-16, maxfeval = 10000000, maxiter = 5000000)
> >>>
> >>>
> >>> However with above code, I got sub-optimal value in terms of
> minimization
> >>> of the objective function:
> >>>
> >>> q1$value
> >>> #0.1632184
> >>> Fn(c(0.12, 0.04, 0.07, 0.03, 0.06, 0.07, 0.07, 0.04, 0.09, 0.08, 0.02,
> >>> 0.02, 0.03, 0.06, 0.02, 0, 0.07, 0.05, 0.02, 0.02, 0.02))
> >>> #0.1586207
> >>>
> >>> Could you please help me to understand what went wrong with my code and
> >> how
> >>> to correct that?
> >>>
> >>>        [[alternative HTML version deleted]]
> >>>
> >>> ______________________________________________
> >>> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> >>> https://stat.ethz.ch/mailman/listinfo/r-help
> >>> PLEASE do read the posting guide
> >> https://www.R-project.org/posting-guide.html
> >>> and provide commented, minimal, self-contained, reproducible code.
> >>
> >>
> >
> >       [[alternative HTML version deleted]]
> >
> > ______________________________________________
> > R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> https://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> Hello,
>
> I don't know if this is relevant a package GA - genetic algorithms -
> gets solutions above the starting value.
>
>
>
> Fn <- function(Wts) return(
>    -Kendall::Kendall(
>      1:Nobs,
>      rank(-as.vector(as.matrix(MyDat) %*% matrix(Wts, nc = 1)[, 1, drop
> = T]))
>    )$tau[1]
> )
>
> Nobs <- nrow(MyDat)
> StartingValue <- c(0.12, 0.04, 0.07, 0.03, 0.06, 0.07, 0.07,
>                     0.04, 0.09, 0.08, 0.02, 0.02, 0.03, 0.06,
>                     0.02, 0, 0.07, 0.05, 0.02, 0.02, 0.02)
>
> library(GA)
> #> Loading required package: foreach
> #> Loading required package: iterators
> #> Package 'GA' version 3.2.4
> #> Type 'citation("GA")' for citing this R package in publications.
> #>
> #> Attaching package: 'GA'
> #> The following object is masked from 'package:utils':
> #>
> #>     de
>
> set.seed(2025)
> g1 <- ga(
>    type = "real-valued",
>    fitness = \(x) Fn(x),
>    lower = rep(0.01, 21),
>    upper = rep(1, 21L),
>    maxiter = 100L
> )
> dim(g1 using solution)
> #> [1] 21 21
> apply(g1 using solution, 1L, Fn)
> #>  [1] 0.2735632 0.2735632 0.2735632 0.2735632 0.2735632 0.2735632
> 0.2735632
> #>  [8] 0.2735632 0.2735632 0.2735632 0.2735632 0.2735632 0.2735632
> 0.2735632
> #> [15] 0.2735632 0.2735632 0.2735632 0.2735632 0.2735632 0.2735632
> 0.2735632
> Fn(StartingValue)
> #> [1] 0.1586207
>
> suggestions <- g1 using solution
> g2 <- ga(
>    type = "real-valued",
>    fitness = function(x) Fn(x),
>    lower = rep(0.01, 21),
>    upper = rep(1, 21L),
>    suggestions = suggestions,
>    maxiter = 100L
> )
>
> dim(g2 using solution)
> #> [1] 41 21
> apply(g2 using solution, 1L, Fn)
> #>  [1] 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563
> 0.2873563
> #>  [8] 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563
> 0.2873563
> #> [15] 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563
> 0.2873563
> #> [22] 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563
> 0.2873563
> #> [29] 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563
> 0.2873563
> #> [36] 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563
> Fn(StartingValue)
> #> [1] 0.1586207
>
>
> Hoep this helps,
>
> Rui Barradas
>
>
> --
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