This was really cool! I realize there are many DoF in this so pure optimization likely wouldn't solve it, but I'd like to see an optimization on the form of the keyboard itself in addition to just the ordering of the keys (like minuum?)
Technically it could be done and the framework we wrote allows you to create keyboards of any geometry but, as you already pointed out, the number of possible keyboards blows up with every extra parameter you add. Plus this would be even worse for geometric parameters that have a continuous spectrum of possible values. Given our modest computational resources we had to limit our search. It already took about ten days to run the final optimizations on a cluster with 256 cores.
