A perfect girlfriend theory

That theory is so simplistic. It is based on a very selfish and static vision of a relationship : "the other must think like me", "people never change". Arguing, debating, ... with people about your respective points of view do not prevent you to like/love them. If you always hang out with the same boring people who always are on your side, how will you learn new interesting things outside of your usual points of interest ?

".. while this approach [randomness] has actually been proven to be a disappointment .. "

I did not see any reference linking randomness and divorce rates, even as being merely correlated. Where is the "proof" ?

I would not rely on that theory in practice, because it abstracts too much of the existing complexity between people, and do not solve the real problems in relationships.

As a filtering algorithm for dating sites, it may give many false positives (you do not like that person, who still shares many of your interests), and may prevent you to meet a "perfect" girlfriend, only because she is/seems/looks radically different than you.

Rather than "interests", you might be able to mine common fan pages via FB...