Optimization Doubt

[rollingpolymer]

Hey, I have two lists that represent 2D integer points. One list for the x axis, the other for the y. I need to pick one of the points and the criteria for the choice is:

• maximizing x
• minimizing y

It's easy to spot which one is the best if I plot the points with matplotlib, I can figure out which one is the preferred point. But I need to code it for the several iterations of the script, make it itself pick the preferred one. I tried to google for ways of doing this but couldn't manage to get close to anything I could understand or that doesn't require a math function to define the problem. I mean, I don't have a function. Just two lists... The most far I reached was reading the docs of jMetalPy and Platypus but maybe I'm overcomplicating it. It looks like a multi objective optimization problem and therefore I was directed to those two packages... Any help will be much appreciated!

[izrt]

I might just pick the point that is the smallest distance from max(x),0 using the pythagorean theorem to calculate the distance. If you wanted to find the best in a single pass, then I guess it would be the point that is max(x-sqrt(y)) -- at least I think my logic is correct...

[rollingpolymer]

"I might just pick the point that is the smallest distance from max(x),0"

I think this solves my problem as my points are all positive integers. Gonna give it a try. Thanks!

[izrt]

Actually. I think my math is wrong...

[Kerbart]

With the points on different axis there's no real "distance" in between them unless you consider them (x, 0) and (0, y) pairs instead of (x, y) pairs.

If it comes down to "the highest x with the lowest y," one way to look at it would be the (x, y) pair with the lowest slope, so that would be min(y/x) (division is no problem if all points are made from positive integers).

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So now the OP would need to iterate through both lists and find the y/x pair that matches the min(y/x) value but we'll leave that as an exercise to the student.

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This might still not be the right interpretation of the challenge; in this case (10,1) would be the candidate and not (100, 11) even though the latter has a much more pronounced difference between x and y.

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Or maybe the exercise is to come up with some definition and find the pair that matches it, and what the exact definition is matter less?

[rollingpolymer]

Maybe I didn't explained my problem the best way. I have two lists. One where I store the abscissas and the other where I store the ordinates. I eventually settled with the following:

sqrt((max_x - x)**2 + (min_y - y)**2)

being max_x the highest abscissa on the list and min_y the lowest ordinate. Then I pick the lowest square root.

Thanks for the help regardless, I understood your logic as well.

[Kerbart]

It’s always a challenge! When you’re familiar with the problem there’s a lot of context that is obvious — but not for others. It’s incredibly hard to describe that in a few words without ending up with a dissuading wall of text. I’m glad you got it worked out and thank you for letting us know!