[Solved]: How to optimize a function by maximizing 1 variable and minimizing another?

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Problem Detail: Problem I want to implement an optimization algorithm for my file transfer program. The program buffers data in a local file before uploading to central server periodically and it compresses the files before transferring. I would want the program to intelligently predict the time and size thresholds before transferring. The objective function could be defined as following f(u) = theta1*u + (theta2*u)/b + theta3 where

  • u is the size of data
  • b is the network bandwidth (bps)
  • f(u) is the time taken to transfer u bytes of data.
  • theta1*u refers to amount of time taken to compress u bytes of data
  • theta2*u*b refers to time taken to transfer compressed data.
  • theta3 is constant protocol overhead

I want to be able to optimize the transfer by minimizing time and maximizing uncompressed size. If I were to simply minimize f(u) that would have been easy but then in this particular case , I would also want to maximize amount of data to be transferred. The idea is to be able to come up with a machine learning algorithm which can change as per different network scenarios and fluctuating bandwidth , rather than user providing it at start of program. Of course, I would implement it with some sane seed values and keep them within sane boundaries. Solution space Given the nature of this problem , which class of algorithms should I be looking into? Would gradient descent be the right way to approach this? is it possible to apply maximize and minimization on same function of 2 different variables? Am I over-thinking this ?

Asked By : rajeshnair

Answered By : Jonathan Silva

You would have to look at multiobjective optimisation, with these methods you can optimise two functions at the same time. Just be aware that, depending on the method that you end up using, you might have in the end a number of solutions equally good (trade offs) which you would have to choose from.
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