I have a 4-dimensional function $F(a,b,c,d)$ which I need to optimize (find the minimum) Each of the 4 parameters of my function $(a,b,c,d)$ are made to vary in steps over a range, so each one can take only a certain finite number of values:

$a:\{a_1,a_2, ...a_A\}\,;\, b:\{b_1,b_2, ...b_B\}\,;\, c:\{c_1,c_2, ...c_C\}\,;\, d:\{d_1,d_2, ...d_D\}$

The total number of possibles solutions is then the combination of all the values each parameter can take: $N=A*B*C*D$, and I need to find the optimal one among those $N$ solutions.

Given $N$, is there a rule of thumb for the population size one should feed a genetic algorithm to ensure optimal coverage of the parameter space? Or is this decision too complicated for a simple rule of thumb to apply?

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    $\begingroup$ See cstheory.stackexchange.com/a/20759/1654 if you have no crossover you are missing the power of a genetic algorithm. In your description you have no crossover (though maybe you just abstracted it away for simplicity). $\endgroup$ – kasterma Jan 28 '14 at 15:42
  • $\begingroup$ @kasterma indeed I did not mention it for simplicity but I apply both a crossover and a mutation operation on my population for each run of the GA. $\endgroup$ – Gabriel Jan 28 '14 at 16:00

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