# Finding optimal recipe proportions

Is there a mathematical optimisation technique or algorithm that could, at least in principle, be applied to find optimal ingredient proportions for a given recipe using a minimal number of experiments.

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Optimal in what sense? –  Qiaochu Yuan Mar 17 '13 at 18:53
I feel like optimal ingredient proportions would be subject to individual taste and preference, so no. –  Jeremy Mar 17 '13 at 18:53
@Jeremy It would be individual taste and preference. For simplicities sake I would assume this is unchanging, at least for the individual in question, and it is possible to say from one experiment to the next that one is better or worse than the other. –  Chris Steinbach Mar 17 '13 at 18:59
@QiaochuYuan Optimal pretty much in the sense that Jeremy inferred. I'm afraid I'm not mathematically savvy enough to see whether that disqualifies my question from being answered here, or in that case, whether there are assumptions that could be made to salvage the question. –  Chris Steinbach Mar 17 '13 at 19:10
@ChrisSteinbach You would have to define a utility function for yourself based on the ingredients in your dish. If you really like salt, then weight that one more and so on. I suppose you could then set up a program for yourself and let $X_1,\ldots,X_k$ be the amounts of ingredients 1 though $k$ you're putting into your dish and then $\operatorname{max} U(X_1,\ldots, X_k)$ (your utility function) s.t. $\sum{X_i}$ still makes the dish you have in mind. The constraints are pretty arbitrary though and what qualifies as "same dish" I really don't know. –  Jeremy Mar 17 '13 at 19:27

(This is an extended comment, not an answer)

One problem is that you need to make some assumptions about how the quality of the result can depend on the ration of ingredients. For example, suppose we're dealing with a dish with only two ingredients, a priori the response function could be something like:

where there's a sweet spot that makes it taste heavenly, but the proportions have to be just right, otherwise it's so-so. If the peak is narrow, it's unlikely that any systematic-but-mindless search will be able to find the optimum.

For a completely unknown utility function, the best you can hope to find with finitely many tests is a local sort-of-perhaps maximum. And if the only experiment you can do is to compare two recipes at a time to find out which is best, but you have no quantitative notion of how much better (which would probably be too much to ask for), then exploring a high-dimensional parameter space algorithmically is not going to be easy.

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