Capturing optional regex segment with PHP
Consider your first pattern:

~/[0-9A-Za-z_-]+_archive/[0-9]+$~


Let's break it down:


/ a literal string /
[0-9A-Za-z_-]+ one or more of 0-9, A-Z, a-z, _ or -
_archive a literal string _archive
/ literal slash again
[0-9]+ one or more digits
$ the end of the string must follow the one or more digits


So basically you want to make #4 and #5 optional.  To be more specific, you want either both 4 and 5, or neither 4 nor 5.

Consider this:

(a[b]+)?

This means that you have one a followed by one or more b, and that this grouped a/b entity is optional.

Letting a be #4 and b be digits like in #5, we're left with:

(/[0-9]+)?

Or:

~/[0-9A-Za-z_-]+_archive(/[0-9]+)?$~


This will capture the entire group though, like /5:

php -r "preg_match('~/[0-9A-Za-z_-]+_archive(/([0-9]+))?$~', '/news_archive/5', $m); var_dump($m);"
array(2) {
  [0] =&gt;
  string(15) "/news_archive/5"
  [1] =&gt;
  string(2) "/5"
}


You can just add another group to remedy that though:

~/[0-9A-Za-z_-]+_archive(/([0-9]+))?$~


Example:

php -r "preg_match('~/[0-9A-Za-z_-]+_archive(/([0-9]+))?$~', '/news_archive/44', $m); var_dump($m);"
array(3) {
  [0] =&gt;
  string(16) "/news_archive/44"
  [1] =&gt;
  string(3) "/44"
  [2] =&gt;
  string(2) "44"
}


You could technically make the outside group a non-capturing group (like (?:/([0-9]+))?), but I don't think the added complication is worth not grabbing the / part too.

(By the way, sorry if you're familiar with regex and you found this excessive.  I tend to take a very verbose approach to any regex related question :).)