Should I use a permanent magnet inside a solenoid for an electromagnet shuttle?
I was unsatisfied with my solenoid actuator that consist of double solenoid that pulls core in both directions and after replacing original soft iron plunger with the neodymium magnet plunger I got solid improvement in the force.

I do not know the theory behind the magnetic saturation and I don't know which is more efficient in particular cases, but maybe you could give it a try.

There is even an article on using permanent magnets for this application: http://www.mdpi.com/2076-3417/5/3/595/htm

EDIT: After additional research I want to add the following:

Using soft iron or permanent magnet works on different principles:


Soft iron is always attracted to the solenoid.  Therefore, you need to have either two solenoids, one pulling up and other pulling down, or you need one solenoid to pull and one spring to push.  In the latter case when solenoid is on magnetic force prevails and pulls core into the solenoid and when solenoid is off spring force pushes away.
Permanent magnet will try to go either way depending on the direction of the current within the solenoid.  If current goes one way it will push core in one direction, if current goes the other way it will push core in the other direction.  You don't need the spring or double solenoid, however you must be able to change the direction of the current.


A more detailed description can be found here: Automatic switcher operation and improvement

Now it depends on you what you really want.