This game was originally designed as a substrate for experimenting with procedural puzzle generation (for generating interesting puzzles given a rules set, not for generating new rules sets). I thought I'd post it here, since it ended up being kind of fun to play in it's own right, not just an algorithmic experiment.
I was wondering as I played it if you had come up with some 'evil' to create the levels, as each one has an element of 'gotcha' to them. Any info on how you did this? Novice programmer here, and probably not capable of understanding anything too complex, but I'd be interested if there's anything you could point me at to try to understand how you do this sort of thing.
Stage one is just to generate a level by randomly placing numbers on the grid.
Stage two is to run a special solver for the puzzle, which tries to solve the puzzle the way a human would (applying different kinds of local deduction rules, e.g. "only this number can reach that dot, so that's how the line has to be drawn" or "there's not enough space to draw this line vertically, so it has to be horizontal", and then a handful more of increasing complexity). If the solver gets stuck, it adds more dots to the board, with the locations of the dots being such that they're going to provide as little information as possible at the start of the game.
That gives a seed puzzle to work with, which is solvable but usually not very interesting.
Stage three is optimizing the puzzle. That's done with what's basically a hill-climbing algorithm. So take a puzzle (either the original, or a better puzzle that's been found during the optimization) and change it a bit by moving or changing the numbers. Then run the solver again on the modified board, but with all the dots removed. If the new puzzle is solvable, it's scored on a bunch of metrics, and if it's good enough it goes into the pool of improved puzzles for the next iteration to work on.
Obviously for this to produce the feeling of gotchas, the metrics have to be chosen to match human intuition on easy vs. hard moves. That's the tricky part.
That's the gist of it. I'm planning on writing a blog post on it later with more details.