Is it possible to separately evolve a part of the population? In a classic example of a genetic algorithm, you would have a population and a certain amount of simulation time to evaluate it and breeding. Then proceed to the next generation.

Is it possible, during the simulation process, to have an isolated and small part of the population and keep it evolving in their own little island for some time while the rest of the population continues to evolve normally? 
After that, they could be reunited with the rest of the population and the end of the simulation would go through. After that, breed the population and continue. 

This is a super important part of natural evolution and probably some know if it actually works with genetic programming?
There have been extensive studies within evolutionary computation in the area of island models and niching for doing exactly this.
The advantages of this approach include greater population diversity (which is particularly useful when the problem is multiobjective) and the potential for concurrent execution of each separate population.
See also the answers to the question What is the niching scheme?.
With specific reference to genetic programming, here is a recent paper that uses a parallel island model.