Does local optimization in a genetic algorithm decrease diversity?
Adding on Raphael's answer:


in a hybrid genetic algorithm (HGA), mutation plays a different  role than it does in a "pure" GA.

The local refinement requirement of the mutation operator is unnecessary in the existence of an explicit local operator allowing the mutation operator to take a more exploratory role (see Evolutionary algorithms with local search for combinatorial optimization by Mark Land).

Using larger mutations, at least large enough to move from one basin to another, is a good idea.
you can introduce parameters to control the frequency / duration / probability of local search so reaching a balance between GA and hill climbing.

Hybrid Genetic Algorithms: A Review by Tarek El-Mihoub, Adrian Hopgood, Lars Nolle and Alan Battersby contains further details.
a nice approach you can try is to perform a local search only when the best offspring (solution) in the offspring population is also the best in the current parent population (aka BOHGA:  Best Only Hybrid Genetic Algorithm).

This allows GA to explore a wide search space.