Optimizing a four-year-old MySQL database
I want to optimize the database as I think in these years many records
  have been deleted and many added.


You have some other reason for wanting to fiddle with a database that is "running well"?

Good reasons might include:


The backups are getting unmanageably large
The customer has mentioned a specific area of performance they want improved


If you don't have a good reason, then my advice would be to do nothing