There are probably ways to communicate and train such an algorithm, but few seem to know it...I guess that is what most of these "thinking method" and middlegame strategy books try to distill.
I think with practice and trial-and-error, one learns to assess the position with an eye for what has burned them the most and what comes easier to remember for whatever reason (you like horsies so you are more keen on knight movements). I just think that you need effective practice most importantly and that principles or algorithms are an attempt by the expert to try to consciously communicate what they are mostly subconsciously evaluating. So while it does help to break things down into principles (so a process can be learned effectively in 5-6 years instead of 10-12), you need the personal experience (either drilling, playing) to create that autobiographical personal experience which burns it quicker into your long-term memory.
You may better "learn" to remember to look at your opponent's bishop on the opposite side of the board if it cost you the city championship, for instance, rather than just reading a book where the GM-author says "don't forget to look at threats, like your opponents' long-range pieces on a distant strong square, because it can cost you the game...see I told you so, you didn't listen." Rather, it is simply lack of experience in this setting than lack of "knowledge" or "principles".
If pawn structure, strategic positioning of pieces do not yield a good plan. Then all GMs rely on pure calculation to formulate their plan, because the best move is simply one that is calculated as better. I think there must be some way a GM could look into a position that is unfamiliar, never before seen, and come up with a good plan, that's not even well thought out or thought through all the way, just based on good intuition. There must also be an algorithm to generate this in your head.