How to divorce a spouse that you can't find?

You can serve by publication - but some law firms (like ours) have resources to help find people.  You should try that first.  You have a complicatd situation, and should seek legal help. 

Clint

If you fulfill the residency requirements for the state of Washington and are able to file Divorce papers there then that is how you would start getting divorced. 

If you do not know her whereabouts specifically then most jurisdictions allow you to bring a motion to serve her by publication. That means you would take out an ad usually in the county in which the motion in pending that advises her that she needs to appear and answer the complaint.  However, there is usually what is known as a "due diligence" requirement for finding her.  And because you know that she lives elsewhere - just not exactly where - the court could have you publish there as well.  The fees may be high but you may be able to make an application to have them waived. 

The fact that there are no children of the marriage is good.  Are there assets to distribute?  You really should seek legal help with all this.  It can get complicated.  Good luck.