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Math Help - Genetic Algorithm

  1. #1
    Senior Member Sampras's Avatar
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    Genetic Algorithm

    Find the value of  x that maximizes  \sin^{4}(x) ,  0 \leq x \leq \pi to an accuracy of at least one part in a million. Use a population size of fifty and a mutation rate of  1/(\text{twice the length of string}) .

    So randomly select a population of 50 binary string of length 8. Decode them into base 10. Look at their fitness levels (e.g.  \sin^{4}(x) ). Now exclude  25 of the strings with the lowest fitness levels. Use crossover between random pairs of strings to get 25 "child strings." Now use a mutation rate of  1/16 on this new population of strings? Because you dont want a population of strings with end digit 0. This will cause domination.

    Is this generally correct? How would you decide the length of the strings?
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  2. #2
    Senior Member Sampras's Avatar
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    The maximum value of  \sin x is  1 . So the maximum value of  \sin^{4} x is  1 . So maybe use a string length of  3 ? Because  111 = 7 in base 10.
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