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While working on a genetic algorithm, I needed to devise a fitness function for each chromosome. Each chromosome has 2 attributes: maximum accuracy and minimum accuracy.

The fitness should increase with both maximizing the maximum accuracy and the minimum accuracy

So I thought of one of these 2 fitness functions:

max*min/(max+min) vs max*min/(max-min)

what is the difference between both?

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  • $\begingroup$ The question is too vague to answer. There are many functions of two variables that have the required properties. Go back to first principles and figure out what would make one fitness function a better description of nature than another one, and look for the best possible one. You are missing a key piece of science, which mathematicians can't help you find. $\endgroup$
    – Ben McKay
    Mar 30, 2013 at 10:18
  • $\begingroup$ In addition, the second function is not increasing in the maximum. $\endgroup$
    – Douglas Zare
    Mar 30, 2013 at 10:22
  • $\begingroup$ Needs to increase with both? What’s wrong with Max+Min? If you can give a clear answer to “What’s wrong”, you’ll be well on the way to knowing what you want. Alternatively, for some value of Max and Min, rank these into order of desirability: • Max, Min; • 2×Max, ½×Min; • Max + ½×Min, ½×Min. That choice (and I have no idea which you might or should prefer), and the motivation behind that choice, will help. $\endgroup$
    – jdaw1
    Mar 30, 2013 at 15:47

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