Genetic algorithm: Rule of thumb for choosing parameters to solve large solution space

Question

Simply put: no, there is no simple way to choose these numbers. Everything depends on your domain and required outcome.

Population size can be determined with an experiment relatively quickly: try 100, 1000, 10K, 100K and a million. Which one gives you a better result - go with that.

Number of generations is the hardest one to determine. Usually improvement of a best result sky-rockets in the start of the processing, then slows down almost to a halt. Usually that is a time to either stop and take the best result or change some parameters, like mutation rate. So it is up to you to decide when the result is good enough: usually the balance between time spent and rate of improvement.

During my experiments and confirmed by a scientific literature, in the start of the processing, it is recommended to have mutation rate to be a minimum (like 0.01%). And once your rate of improvement slows down, introduce more mutation to explore wider range of solutions. At one point, I increased the mutation rate to something ridiculous, like 50%. This helped to disturb the stable state of the system, but the system returned back to the stable state pretty fast and the final result was not much better than the one I had before "nuclear bomb". I came to conclusion that highest mutation (in my domain) should be no more than 5% and only when the rate of improvement is almost zero.

Hopefully this can help you a bit, but what you ask is not trivial and people write dissertations on each of the topics separately. I also recommend to read through couple articles on the topics - this will help you significantly.