Refer the link may helpful for you.

http://medal-lab.org/files/99014.pdf

That depends on what are you using GA for ?!

Basically, you have two variables: the size of the population N and the length of the genotypes L.

Like Bashar said, the answer to your question mainly depends on the fitness function you try to optimize. If it's a simple function like Rastrigin, you get O(NL) to evaluate the whole population. Otherwise, the complexity can be of any kind and is problem dependent.

The rest depends on the genetic operators you want to use.

For example, a stochastic selection will require you to sort the population so you end up with O(N log N). Tournament selection will be O(N).

Transforming the population with crossover and mutation operator will usually take O(NL).

To sum up, the anwser to your question will usually depend on (in order of significance):

1. The fitness function

2. The selection operator

3. The variation operators

Time Complexity  of the objective function is the prime factor, multiplied by the generation number and population size. 

Space complexity is twice the population storage (old and new)

Finer details may be incorporated as per requirements.

if you are using GA for sentiment analysis

i find time/space complexity: O(NP * NC)

here:

NP= number/size of population

NC=number/size of chromosome (size of keywords)

it will be employ when you omit the constant. Dilip Kumar

the following paper would be useful

The following paper would be useful

"Time Complexity Analysis of the Genetic Algorithm Clustering Method" by NOPIAH et al.