How to cite a method that has a huge history of contributors?

To cite a body of work large enough to have generated textbooks or comprehensive review papers, you should cite a good recent textbook or comprehensive review paper. You may not need to, however, depending on why and how you are using the algorithm. The key is to provide the reader with everything they need to know about why you chose that algorithm and the significance of the choice.

In this case, if your work is focused on genetic algorithms and/or their applications, then you should position it within the comprehensive space of genetic algorithms work. You would then cite both the textbook/review sources and the more specific "nearby" pieces to compare it to.

In the other hand, if your work is focused on an application, it's its more just about needing some tool and you happened to find genetic algorithms promising, then you don't need the comprehensive references because that's not the point. Instead, if you chose Algorithm X for particular reasons, then you should explain why you didn't pick competitor Algorithms Y, Z, and W (citing each). If you just chose Algorithm X because you thought that probably any algorithm would likely do, then be clear about that fact and don't worry about positioning it within a larger field, because honestly you haven't.

Assuming you are writing an article for an audience that knows what a genetic algorithm is (at least, anyone in CS and related fields), it is not so important to explain what it is, as much as the implementation details. In your shoes, I would cite the paper of the implementation.

If there is a risk of readers not knowing what a genetic algorithm is, or you are using advanced details that are not common knowledge, I think it is best to add a modern textbook, or whichever explanation you think is clearest.

For a general reference I usually cite two papers: original/influential and a review paper.

In the case where the idea is relatively well-known and there is no single original paper, a review paper or textbook should suffice.

Unless you talk specifically about history of a discovery, or trying to put things in a historical context, there is no need for historical reviews.

In the case of doubt think about the reader. (Or imagine that you are a reader, new to this topic.)