You have some problems with your code.    For example, you have created 55 variables, some of them duplicates, while I was able to write the same code with only 21 variables.    You use a hash to collect the file list and then copy its keys to an array when you only need the array.    You use lists of scalars when you could just use a single array.    You use three separate hashes when you could use a hash of arrays.

Here is my version of your code:

#!/usr/bin/perl
use warnings;
use strict;

for my $files ( 1 .. 50 ) {
    $files *= 200;

    my @file_list;    # list of files
    my %file_gene;
    for my $i ( 1 .. $files ) {
        open my $INF, '<', "$i.txt" or die "Cannot open '$i.txt' becau
+se: $!";
        chomp( my @g = <$INF> );
        @{ $file_gene{ $i } }{ @g } = ();
        push @file_list, $i;
        }

    # overlapping percentage of file pairs
    # percentage of common items in file1
    # percentage of common items in file2
    my %file_pairs;
    my $time = time;

    my $pairs = 0;
    for my $i ( 0 .. $#file_list ) {
        my $m1 = $file_list[ $i ];
        my ( @values, $pair ) = ( 0, 0, 0 );
        for my $m2 ( @file_list[ $i + 1 .. $#file_list ] ) {
            ++$pairs;
            my @Nvalues = find_common_items( @file_gene{ $m1, $m2 }, 0
+.1 );
            if ( $Nvalues[ 0 ] > $values[ 0 ] ) {
                $pair = $m1 . '_' . $m2;    # file pair name
                @values = @Nvalues;
                }
            }
        if ( $pair ) {
            $file_pairs{ $pair } = \@values;
            }
        }

    $time = time - $time;

    print "$files files\t$pairs pairs\t$time sec\n";
    }

sub find_common_items {
    my ( $m1, $m2, $cutoff ) = @_;

    # find number of intersection items
    my $isn = grep exists $m2->{ $_ }, keys %$m1;

    # number of union items
    my $un = keys %{ { %$m1, %$m2 } };

    # only store qualified file pairs
    my @values = ( 0, 0, 0 );

    if ( $isn / $un > $cutoff ) {
        # For file pair m1_m2, overlapping percentage of file pairs = 
+intersection/union
        # For file pair m1_m2, percentage of common genes in file m1 =
+ intersection/size of file m1
        # For file pair m1_m2, percentage of common genes in file m2 =
+ intersection/size of file m2
        @values = ( $isn / $un, $isn / keys %$m1, $isn / keys %$m2 )
        }

    return @values;
    }
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