Sometimes people separate from their spouse & thereafter that spouse disappears. The question becomes how to proceed with a divorce case if the spouse's whereabouts cannot be ascertained.
Try informal methods first - then a P.I.
Ultimately the spouse needs to be served with the divorce papers. Thus, one can check informal methods to locate one's spouse, such as friends, family members or associates of your spouse. One can also do informal internet searches - if one can get a good address that way, one can send a process server to that address in an attempt to serve him/her. If a good address cannot be ascertained, one will ultimately need to hire a private investigator.
P.I. first - then motion for publication notice
The P.I. must conduct a formal "diligent search" - the search does not ultimately need to actually locate the spouse, but the P.I. must document to the Court that s/he has looked for the spouse in a variety of ways, such as credit reports, public records, etc. If the spouse still cannot be located, then one will need to take the diligent search report & file a motion with the court asking for "publication notice," which basically means running a copy of the summons in a newspaper designated by the Court. If the Court approves the motion, then one may proceed to run the summons in the newspaper - same will then be considered "valid service" and one may thereafter proceed with the divorce on default.