Sorry if the title is confusing. Essentially, supposed I have two variables; height and weight. My goal is to find the individual who is equally very tall and very skinny (low weight). The idea here is that I, as the researcher, and specifying that I want the weight to be as low as possible while also seeking to find higher height. Is there an algorithm like this or does anyone have an idea of where to look? I've never studied something like this.
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You're contradicting yourself here a bit. First you say you want to find someone who is "equally" tall and skinny, and then you say "weight to be as low as possible", and you want "higher height".
The latter description suggests that for individuals $x$ and $y$, you've defined the ordering $x < y \iff \text{weight}_x > \text{weight}_y$ or $\text{weight}_x = \text{weight}_y\,\wedge \text{height}_x < \text{height}_y$. You can use the standard algorithm which takes the maximum element in a set.
The former description isn't well defined. You can't maximize or minimize two different quantities at the same time. At best, you can find a pareto optimal set of individuals such that for any single individual, no one else weighs less while being taller. You can find the pareto optimal frontier by sorting individuals using the lexicographic order described in the last paragraph and taking the tallest person for every distinct value of weight.
shimao
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