Re: [R] Problem with minimization that I failed to understand

Rui Barradas Fri, 28 Mar 2025 13:19:18 -0700

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.dun...@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?

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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@solution)
#> [1] 21 21
apply(g1@solution, 1L, Fn)

#> [1] 0.2735632 0.2735632 0.2735632 0.2735632 0.2735632 0.27356320.2735632#> [8] 0.2735632 0.2735632 0.2735632 0.2735632 0.2735632 0.27356320.2735632#> [15] 0.2735632 0.2735632 0.2735632 0.2735632 0.2735632 0.27356320.2735632

Fn(StartingValue)
#> [1] 0.1586207

suggestions <- g1@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@solution)
#> [1] 41 21
apply(g2@solution, 1L, Fn)

#> [1] 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 0.28735630.2873563#> [8] 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 0.28735630.2873563#> [15] 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 0.28735630.2873563#> [22] 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 0.28735630.2873563#> [29] 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 0.28735630.2873563

#> [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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R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
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Re: [R] Problem with minimization that I failed to understand

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