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Asked: 2026-05-23T18:05:42+00:00

I have a GA with a fitness function that can evaluate to negative or

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I have a GA with a fitness function that can evaluate to negative or positive values. For the sake of this question let’s assume the function

u = 5 - (x^2 + y^2)

where 

x in [-5.12 .. 5.12]
y in [-5.12 .. 5.12]

Example fitness function

Now in the selection phase of GA I am using simple roulette wheel. Since to be able to use simple roulette wheel my fitness function must be positive for concrete cases in a population, I started looking for scaling solutions. The most natural seems to be linear fitness scaling. It should be pretty straightforward, for example look at this implementation. However, I am getting negative values even after linear scaling.

For example for the above mentioned function and these fitness values:

-9.734897  -7.479017 -22.834280  -9.868979 -13.180669   4.898595

after linear scaling I am getting these values

-9.6766040 -11.1755111  -0.9727897  -9.5875139  -7.3870793 -19.3997490

Instead, I would like to scale them to positive values, so I can do roulette wheel selection in the next phase.

I must be doing something fundamentally wrong here. How should I approach this problem?

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1 Answer

  1. Editorial Team

    Your smallest possible value for u = 5 – (2*5.12^2). Why not just add this to your u?

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