The OP want the solenoid to move the armature, hold the armature and then release the armature all in 50 ms. Therefore the resistance must be quite low so the magnetic field can accelerate the armature and move it to it's seat and release it to return to the initial location all in 50ms. The coil must be low resistance to allow this to happen and this would cause an initial high current, a reduced current as the armature moves and produces back EMF, and finally high current when the armature is seated.
There is no requirement for repetition, as I read the spec, so heating is not a problem. If there is a rep rate, then the solenoid has to be designed to handle the heating.
My thoughts on the problem.