Can I use Keras to give fitness scores to a genetic algorithm? I know that I can use Keras to solve classification problems but is it possible to get it to output a float between 0 and 1000 for instance? I want train my network to approximate the simulation that gives my GA a fitness score because the simulation takes a long time to run.
Yes, you can get a neural network to predict real numbers instead of for classification. This type of problem is called regression.
You can find dozens of tutorials for doing regression with Keras. The official one is here.