Per MSDN Docs: http://msdn.microsoft.com/en-us/library/hh510202.aspx
LocalDB supports two kinds of instances: Automatic instances and Named instances.
I had the same problem on VS2015 and SQL2016 the problem my dev station is a laptop, project explorer i think uses tcpip connection, while SQLeplorer local file or so.
It worked after i made sure that SQL used the Network card, and that it had a cable plugged in (so SQL could server the request over TCP using that IP) which it couldnt over wifi (by default?)