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If I wanted to maximize two variables can I just rank the two variables from the sample as a point system and then sum the points? I know this probably isn't the most mathematically correct way. For example, if I have an average and a variance for 150 different samples from one population and I rank each average and variance and then add the points from both rankings could I maximize the sum?

Austin Johnson
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  • What does maximising variables mean? – copper.hat Jun 06 '19 at 17:52
  • @copper.hat I want to maximize average and variance – Austin Johnson Jun 06 '19 at 18:32
  • @copper.hat and instead of trying to write a multivariate optimization program I was wondering if you could just rank each variable using a point system and then just sum the points and maximize – Austin Johnson Jun 06 '19 at 18:33
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    Can you write an expression for what your ranking and point system would be? Also can you clarify - do you have 1 average across 150 samples or are you saying you have 150 averages? – E. Tucker Jun 06 '19 at 21:50
  • Also, I agree with copper.hat. I'm not sure what your variables are. – E. Tucker Jun 06 '19 at 22:08
  • @E.Tucker 150 averages and 150 variances – Austin Johnson Jun 07 '19 at 16:29
  • Aha. So it sounds like the fact that they're averages and variances doesn't really matter to the optimization (because you're not considering the original populations?). Would it be correct to say that (i) you have 150 data points each with 2 components, and (ii) you're trying to find which data point has the highest combination of the 2 components? – E. Tucker Jun 07 '19 at 16:35
  • @E.Tucker yes that is correct – Austin Johnson Jun 07 '19 at 19:10

1 Answers1

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Based on our conversation in the comments of your post (=trying to find the data point with the highest combo of 2 components), yes, it would be correct to calculate the combination for each data point, order these, and select the highest value.

For example, if $\alpha \in [0,1]$ were the weight of the $x$ components, you could

  • Calculate the score for each data point as $z_i, \forall i\in 1..150$:

$\alpha*x_1+(1-\alpha)*y_1 = z_1$

$\alpha*x_2+(1-\alpha)*y_2 = z_2$

and so on until $z_{150}$

  • Order all the values of $z_i$ from highest to lowest.
  • Select the highest value of $z_i$ and find the associated $x_i$ and $y_i$
E. Tucker
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