Xapian, termed as an open source probabilistic information retrieval library, provides a full text search engine library for programmers.
It possesses a wide range of structured Boolean search operators which are allocated based on probabilistic weights. There are also Boolean filters to restrict a probabilistic search.
Xapian's search engine also has the dexterous ability to support the search's word synonyms explicitly and as an automatic form of query expansion.
Also, if you're looking for a fully packaged search engine that is derived upon Xapian, you may install Omega into your site. A great aspect about Xapian is its versatility is that allows you to extend to Omega to meet your needs as they grow.
Currently, Xapian is used as a search engine for the Library of the University of Cologne and Die Zeit (A popular German newspaper)
Programming Language: C++
License: GNU General Public License
Ranking of search results: Flexible (important words become more probable than unimportant words)
Indexing Style: Filing system
Below are couple of more open source search engines that could be of your interest.