$ls *.xml
123_20070303_REFNUM.xml
123_20071225_REFNUM.xml
123_20080101_REFNUM.xml
923_20070227_REFNUM.xml

##</code><code>##

#!/usr/bin/perl 
use strict;
use warnings;
use Date::Simple (':all');
use Data::Dumper;

my $dir = q{/home/LarryTheLobster/};

opendir(DIR, $dir) or die $!; 

my @xml_files =
sort { d8( (split /_/, $a)[1] ) cmp  d8( (split /_/, $b)[1] ) } 
grep { -f and /[.]xml\z/ } readdir DIR;

closedir DIR;

print Dumper \@xml_files;

##</code><code>##

Output:
$VAR1 = [
          '923_20070227_REFNUM.xml',
          '123_20070303_REFNUM.xml',
          '123_20071225_REFNUM.xml',
          '123_20080101_REFNUM.xml'
        ];