The combination Genetic Algorithm and Neural Network, is called Neuroevolution, the benefits of this Technic depend on the problem, it is generally useful when applied to artificial life, computer games, and evolutionary robotics.
unlike other machine learning algorithm the main benefit of neuroevolution is that it do not necessarily require a syllabus of correct input-output pairs, it only requires a measure of a network's performance at a task.
you will find more explanation on the links.
personally for neural network creation in java, i use weka which is really easy to integrate, you will find a tutorial in the links.
https://en.wikipedia.org/wiki/Neuroevolution
Research Using WEKA in your java code (Clustering)