Personally, I like DateTime (usually together with DateTime::Format::Strptime for parsing).

use warnings;
use strict;
use DateTime;
use DateTime::Format::Strptime;

my @time_strs = qw/
    2018-09-14T14:35:56Z  2018-09-13T09:32:12Z  2018-09-12T20:12:16Z
    2018-08-07T07:12:45Z  2018-08-01T23:55:59Z  2018-07-24T15:39:01Z
    2018-01-04T18:19:20Z  2017-11-03T10:26:49Z  2017-07-17T17:22:04Z/;

my @target_strs = qw/
    2018-09-13T23:55:00Z  2018-09-14T00:55:00Z
    2018-04-14T09:33:12Z  2018-04-15T09:33:12Z/;

for my $target_str (@target_strs) {
    
    my $strp = DateTime::Format::Strptime->new( on_error=>'croak',
        pattern => '%Y-%m-%dT%H:%M:%SZ', time_zone=>'UTC' );
    
    my $target_dt = $strp->parse_datetime($target_str);
    
    my @dts;
    for my $t (@time_strs) {
        my $dt = $strp->parse_datetime($t);
        my $diff_s = $dt->subtract_datetime_absolute($target_dt)
            ->in_units('seconds');
        push @dts, { dt=>$dt,
            diff_s=>$diff_s, absdiff_s=>abs($diff_s) };
    }
    @dts = sort { $a->{absdiff_s} <=> $b->{absdiff_s} } @dts;
    
    my $closest = $dts[0];
    print "Closest is ",
        $closest->{dt}->strftime('%Y-%m-%dT%H:%M:%S %Z'),
        ", which is ", $closest->{diff_s}>0 ? 'after  ' : 'before ',
        $target_dt->strftime('%Y-%m-%dT%H:%M:%S %Z'), "\n";
}

__END__

Closest is 2018-09-13T09:32:12 UTC, which is before 2018-09-13T23:55:0
+0 UTC
Closest is 2018-09-14T14:35:56 UTC, which is after  2018-09-14T00:55:0
+0 UTC
Closest is 2018-01-04T18:19:20 UTC, which is before 2018-04-14T09:33:1
+2 UTC
Closest is 2018-07-24T15:39:01 UTC, which is after  2018-04-15T09:33:1
+2 UTC
[download]