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I'm applying a simple genetic algorithm to an optimization problem (I need to find a 4-parameter function's global minimum)

I start the generations run with say 100 chromosomes which I then evaluate, select, breed (crossover + mutate) and repeat for N_gen generations.

When the algorithm is done (the N_gen generations were processed) I'm left with the best fitted solution: the one which evaluates to the minimum value from the last generation's 100 chromosomes/solutions.

But this also leaves me with 99 other well fitted solutions that I have a priori no use for.

Is there a way to extract some information from these other solutions? Perhaps an uncertainty estimate for the best fitted solution?

Intuitively I'd calculate the standard deviation for the parameters values obtained from the last generation and use that as an uncertainty estimate for the best fitted solution. Kind of like using those other solutions as a bootstrap for my best solution.

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  • $\begingroup$ Could you tell us what exactly you are optimizing? $\endgroup$ – cbeleites Jan 18 '14 at 16:45
  • $\begingroup$ It's a big process but basically I'm trying to find the best model to fit with an observation, where each model is defined by 4 parameters. $\endgroup$ – Gabriel Jan 18 '14 at 17:07
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Genetic algorithms are rather aggressive optimizers (doing lots of comparisons).

  • Yes, I think it can be interesting to look at the next best models,
  • but I also think that inspecting those solutions should still be accompanied by looking at the solutions of different runs of the genetic optimizer.
  • I would hesitate to derive any concusions about uncertainty here as the next-best solutions have a higher probability to be close to the found optimum, but may (probably) leave you in the dark about other optima. It is therefore difficult to derive conclusions about the uncertainty of the final parameters from these parameter sets.

  • Last but not least, because the GAs optimize so aggressively, you usually end up with a rather large otimistically biased estimate of your target functional. Therefore, looking at the target values achieved by the next best solutions does not allow you to derive any kind of conclusion about the uncertainty of the achieved target value. This will need a proper independent validation of the final paraneter set (I assume it is a model!?).

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