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I remember reading about a study that attempted something similar, they found that dietary guidelines were in fact impossible to meet using a "natural diet" without supplements (scare quotes because I don't remember the exact dietary constraints). I think the constraints also included lower bounds for things like sodium and potassium (this model only has upper bounds for them).
No, this model has lower bounds on all nutrients humans need and upper bounds on some based on their toxicity.
Yeah I misinterpreted the constraints. Still, this model has no lower bound on sodium and no upper bound on potassium; ideally both would be bounded on both sides.
That was hilarious. Figuring out sensible constraints seems to be a long iterative process.

One diet suggested drinking 32l (~8.5 gallons) of water.

This one was the computed "maximize protein" diet:

  status = solve(m) = :Optimal
     10 grams 	Folic acid
      1 grams 	Vitamin C
    667 grams 	Flour, soya
  24034 grams 	Lard
    800 grams 	Suet
    845 grams 	Amino acid or creatine powder
  42752 grams 	Intense sweetener, containing aspartame, 
  powdered formulation
Almost 43 kg (~94 pounds) of intense sweetener? Sounds healthy!
I wonder if you could get actionable results if recipes were the level of granularity you ran the analysis on.
The idea is interesting, though the results have indeed zero applicability unless a few additional rules are added to the system - like proportion of macro-nutrients (fats/proteins/carbohydrates) and some sensible variability to the meal plans (ie, no point in suggesting "1 gram" of some food source, either you suggest a "portion" or nothing).

Personally, I think it would be easier to start with one's own dietary approach and try to put that into rules, then optimize it using additional guidelines (or removing some rules) instead of starting with something too loosely defined and letting the program choose different sources randomly.

Yes, portions need to be defined per thing though. 1 gram of a vitamin supplement is fine. 1 gram of eggs, not so much.