# Population size for Genetic algorithm - rule of thumb

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?

• 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). – kasterma Jan 28 '14 at 15:42
• @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. – Gabriel Jan 28 '14 at 16:00