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The answer to this question depends on several things, the most important of which is the fitness evaluation. I'm going to ignore evaluation- you must determine this for yourself based on your application.

Some of the things the effect the time complexity are:the data structures used to represent the individuals and the population, the genetic operators used, and the implementation of the genetic operators. Roulette wheel selection, for example, can be anywhere from O(n^2) when done naively, to O(log(n)), or even O(n) using something like Vose Alias Algorithm.

The simplest case- roulette wheel selection, point mutation, and one point crossover with both individuals and populations represented by fixed length vectors- has time complexity O(gens * (mut + cross + select)) where gens is the number of generations, mut is the complexity of point mutation (n*m with n the size of the population and m the size of the individuals), cross the time complexity of crossover (n*m again), and select the time complexity of selection (n in the case of an efficiently done roulette wheel).

Therefore, the time complexity of a simple Genetic Algorithm is O(gens*n*m) as this is the dominating term.

I'm sure a much better explanation can be found in the literature.

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Q: What is time complexity of genetic algorithm?
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