Try to change the compatibility level, worked for me.
Verify what level it is
USE VJ_DATABASE;
GO
SELECT compatibility_level
FROM sys.databases WHERE name = 'VJ_DATABASE';
GO
Then make it compatible with the older version
ALTER DATABASE VJ_DATABASE
SET COMPATIBILITY_LEVEL = 110;
GO
100 = Sql Server 2008
110 = Sql Server 2012
120 = Sql Server 2014
By default, Sql Server 2014 will change the db versions compatibility to only 2014, using the @@ version you should be able to tell, which version Sql Server is.
Then run the command above to change it the version you have.
Additional step: Ensure you look at the accessibility of the DB is not reset, do this by right clicking on properties of the folder and the database. (make sure you have rights so you don't get an access denied)
For me using solution provided by codedom did not worked. Here we can only changed compatibility version of exiting database.
But actual problem lies that, internal database version which do not matches due to changes in there storage format.
Check out more details about SQL Server version and their internal db version & Db compatibility level here
So it would be good if you create your database using SQL Server 2012 Express version or below.
Or start using Visual Studio 2015 Preview.
Another solution is to migrate the database to e.g 2012 when you "export" the DB from e.g. Sql Server manager 2014. This is done in menu Tasks-> generate scripts when right-click on DB. Just follow this instruction:
It generates an scripts with everything and then in your SQL server manager e.g. 2012 run the script as specified in the instruction. I have performed the test with success.
I use VS 2017. By default SQL Server Instance name is (LocalDB)\MSSQLLocalDB.
However, downgrading the compatibility level of the database to 110 as in @user3390927's answer, I could attach the database file in VS, choosing Server Name as "localhost\SQLExpress".