Anyway, it turned out to be a matter of using ST

I don't think you need a Schwartzian Transform here.  An ST makes sense if the individual comparison operation is computationally expensive. This is not the case with interpreting a string as a number, in particular as the conversion is done only once for each string and then "cached" in the NV/IV fields of the scalar variable^(*).  In other words, the simple approach (not using ST) is even faster in this case:

#!/usr/bin/perl

use strict;
use warnings;
no warnings 'numeric';
use Benchmark 'cmpthese';

for my $e (2..5) {
    my $n = 10**$e;
    print "\nNumber of file names: $n\n";
    
    my @data;
    push @data, join(".", int(rand($n)), int(rand($n)), 'force.0.5.1LG
+Y.pdb') for 1..$n;
    
    cmpthese( 10**(6-$e),
        {
            'simple' => sub {
                my @unsorted = @data;
                my @sorted = sort { $a <=> $b } @unsorted;
            },
            'ST'     => sub {
                my @unsorted = @data;
                my @sorted = map $_->[0],
                               sort { $a->[1] <=> $b->[1] }
                                 map { [ $_, int $_ ] } @unsorted;
            },
        }
    );
}

__END__

Number of file names: 100
          Rate     ST simple
ST      3247/s     --   -75%
simple 12987/s   300%     --

Number of file names: 1000
         Rate     ST simple
ST      248/s     --   -79%
simple 1176/s   375%     --

Number of file names: 10000
         Rate     ST simple
ST     10.3/s     --   -74%
simple 39.2/s   280%     --

Number of file names: 100000
       s/iter     ST simple
ST       1.87     --   -50%
simple  0.943    99%     --
[download]

Another beneficial side effect of the simple approach is that if you happen to have two names like this

    30.31.force.0.5.1LGY.pdb
    30.32.force.0.5.1LGY.pdb
[download]

they would be ordered in some useful way, because the fractional part of the number is automatically taken into consideration when just treating the name as a number.

---

(*)

use Devel::Peek;

my $s = "30.31.force.0.5.1LGY.pdb";
Dump $s;
print 0+$s, "\n";  # treat as number
Dump $s;

__END__
SV = PV(0x605150) at 0x604fa0
  REFCNT = 1
  FLAGS = (PADBUSY,PADMY,POK,pPOK)
  PV = 0x6370d0 "30.31.force.0.5.1LGY.pdb"\0
  CUR = 24
  LEN = 32
30.31
SV = PVNV(0x607880) at 0x604fa0
  REFCNT = 1
  FLAGS = (PADBUSY,PADMY,NOK,POK,pIOK,pNOK,pPOK)
  IV = 30       <---
  NV = 30.31    <---
  PV = 0x6370d0 "30.31.force.0.5.1LGY.pdb"\0
  CUR = 24
  LEN = 32
[download]

---

---

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