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How to find the optimal layout and be sure about it?

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KnowArt:
I can do some simple math and a tiny bit of coding, but for the life of me I can't figure out how I would find an optimal keyboard layout when there are 403291461126605635584000000 possibilities. Can't brute force that! How in the world would I be sure that my layout is the best for the parameters set?

To give a bit of context. I'm building a 32-key board with just 26 keys for characters. Exactly the alphabet. 3 keys for pinky, ring and middle finger and 4 keys for index. (modifiers and (back)space for thumbs)

Goals are as follows ranked by importance:
1. Low repeated finger use (even better if same finger is only used after two others)
2. High home row usage
3. Hand alteration and even hand usage
4. High usage of index, mid and ring. medium usage of pinkies.

I think it makes sense to first create groups of letters that have a optimal alternation rate for my languages. These groups can then be assigned to fingers to create alternation between hands and right amount of usage to pinkies. Then the keys can be put in a specific order within the groups to ensure high home row usage.

But... I have no idea if this is a way to come to an optimal solution. Even worse, I don't even know how to make these groups and allocate them to fingers.

I'll be working in Python probably, but as it's just math I think that doesn't matter a whole lot.

Looking forward to your input

nevin:
there are tons of alternate layouts that people have already spent a great deal of time compiling. search around and see if any of them have most of the same goals you have. check some of the links i posted in the previous thread on layouts.

here's some more reading on the subject: http://mkweb.bcgsc.ca/carpalx/?popular_alternatives

most of the goals look good. pretty common for alternate layouts. #1 might be tricky though, too many different words to make this a reality.

also look into stenographer layouts for extreme minimal layouts.(there's been a couple projects on the subject already)
- these are usually chording keys (holding more than one key at a time)

i thought the one with mods on the home row was very interesting. besides blabbering here... i do more shortcuts than actual typing in my job.

KnowArt:
Thanks for the recommendation. Interesting site! I'll have a look if his program is of any use for me :)

One of the problems recurring in most different layouts is that they almost always use a regular keyboard design. Horizontally staggered and 6 keys per index finger, while leaving all the real estate that's occupied with ,.;'/[ alone. Especially the 6 key index finger problem is a tough one... everyone seems to be doing it and for the keyboard design I have in mind it's not applicable. But maybe his program is customizable. I'll have a look

nevin:
here's a link to the Open Steno Project & Plover
http://www.openstenoproject.org/

another way to think of tiny layouts.....

_rubik:
I initially wrote a response discussing "how to (potentially) optimize for multi-variable layout problems", but then I realized one of the steps was "find the optimal layout for single variable"

Optimizing for single variables (I feel) is a sufficiently complex problem in its own right. So... are you trying to optimize a layout as a multi-variable function? Have you tried picking your single most important layout consideration and optimizing for that?

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