Hi ! If your only need is to get the numerical part, I propose this solution :

 #!/usr/bin/perl
use strict;

my $komp_dir ='/Users/mydirectory/Desktop/BioinfDev/SequenceAssemblyPr
+oject/KOMP/';
my @komp_dir_content = glob("$komp_dir/*");
my $k_dir;

foreach $k_dir(@komp_dir_content) {
    if (-d $k_dir){
        $k_dir =~ s(.*/)();
        next if ( $k_dir !~ /^\d+_/); 
        $k_dir =~ s(_.*)();
        print "$k_dir\n";
        next;
    }
}
[download]

I hope it helps ! The problem came from the "use strict" and the loop variable being not declared at main level :

either don't use "use strict" or declare the loop variable (became $k_dir here)

I changed a little variable-names because I think reusing the same name for different usages is an unuseful risk for programs maintenance.

But, of course, you're quite free ...