In the near future, a young genius escapes a moonbase where a madman secretly enslaves scientists in his plan to wipe out life on Earth but when no one believes him, he alone must find a way to destroy the base and free the other scientists.

The obective to save the humankind is quite challenging, may be too much for a young "nerd" which has been slaved recently. To me it will be easier to connect with the character if he wants to return to save his love or his family. In the meanwhile for sure he will destroy the base and free the other scientist but for the logline it seems better to me to explain that the trigger that will push him to return is a lover or a relative.

It's a cool, dramatic premise. I don't get a feel for the character yet, though.
"Young genius" is not enough to promise an engaging character for me.
What personal challenges does the character face?

Also, the survival of mankind is only a valid stake if there is someone close to the MC that we care enough for to understand why he does it, other than out of self-preservation. This is why so many disaster movies are centred around families and/or couples.

Finally, I would prefer to see a logline following our formula, starting with 'when'.
Right now I struggle to see a clear trigger incident for the story, which means there may be a lot of exposition and backstory.