Great questions—let’s break these down clearly:

1. Can GA fitness functions use "minimum value as optimal"? #

Absolutely! There’s no universal rule that fitness functions have to be maximization-focused. Genetic algorithms are flexible tools, and minimization-oriented fitness functions are totally valid for problems where lower values mean better performance (like reducing costs, minimizing error, or your case of shrinking variation).

The only thing you need to adjust is your selection logic to match. For example:

• In tournament selection, instead of picking the individual with the highest fitness score, you’d choose the one with the lowest.
• If you prefer sticking to maximization-style selection methods, you can easily convert the minimization problem by using a transformation like 1/(1 + fitness_value) (to avoid division by zero) or subtracting the value from a fixed upper bound.

2. Is a COV-based fitness function (where closer to 0 is better) valid? #

Yes, 100%—this is a perfectly valid fitness function. The core job of a fitness function is to measure how well a solution meets your problem’s objectives, and your COV-based function does exactly that: it assigns a score that directly reflects performance (lower COV = more consistent, better solution).

If you’re worried about the "usually maximization" convention, you have two simple paths:

• Stick with minimization: Tweak your selection step to prioritize individuals with the smallest COV values. This is straightforward and avoids unnecessary transformations.
• Convert to maximization: Adjust the COV value to turn it into a higher-is-better score. For example:
  • Use 1/(1 + COV) (add 1 to prevent division by zero when COV is 0)
  • Or define fitness = max_possible_COV - COV (if you know the upper limit of COV in your dataset)

Either way, as long as your GA’s selection, crossover, and mutation steps are aligned to favor solutions that move toward your goal (COV approaching 0), your fitness function is doing exactly what it’s supposed to.

内容的提问来源于stack exchange，提问作者Brijgopal Bharadwaj