use Math::Complex;
[download]

It doesn't look like this module is used anywhere.    Is it actually needed?

use Win32;
...
        "generation $generation_counter time: " . Win32::GetTickCount 
+. " \n" );
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Perhaps you could use Time::HiRes and make your code more portable.

    my $gene_length         = gene_length();
...
            if ( defined( $genome{$gene} ) ) {
                push( @phenotype, $genome{$gene} );
...
sub gene_length {
    my @gls = ();
    foreach my $key ( keys(%genome) ) {
        push( @gls, length($key) );
    }
    @gls = sort(@gls);
    if ( $gls[0] != $gls[$#gls] ) {
        die("Invalid genotype");
    }
    return ( $gls[0] );
}
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You never modify the %genome hash and the keys are always the same size so you don't really need the gene_length subroutine.

If you wanted to you could just do:

    my $gene_length         = length +( keys %genome )[ 0 ];
[download]

Some of the places where you use arrays could be made more efficient by using strings instead.