Genetic Algorithm, large population vs small one

Question

Im wondering if there is a general rule of thumb for population sizing. Ive read in a book that 2x the chromosome length is a good starting point. Am i correct in assuming then that if i had an equation with 5 variables, i should have a population of 10?

Im also wondering if the following is correct:

Larger Population Size.

Pros: Larger diversity so more likely to pick up on traits which return a good fitness.

Cons: Requires longer to process.

vs

Smaller Population Size.

Pros: Larger number of generations experienced per unit time.

Cons: Mutation will have to be more prominent in order to compensate for smaller population??

EDIT

A little additional info, say i have an equation which has 5 unknown parameters. For each parameter i have anywhere between 10-50 values i would like to try assign to each of these variables. So for example

variable1 = 20 different values variable2 = 15 different values ...

I thought a GA would be a decent approach to such a problem as the search space is quite large, ie worst case for the above would be 312,500,000 permutations (unless i have screwed up?) n!/(n-k)! where n = 50 and k = 1 => 50 * 50 * 50 * 50 * 50

unfortunately the number of parameters/range of values to check can vary alot so i was looking for some sort of rule of thumb as to how large i should set the population.

Thanks for ur help + if there is any more info you need/prefer to discuss in one of the chatrooms, just give me a shout.

Answer 1

I'm not sure where you read that 2x the chromosome length is a good starting point, but I'm guessing it's a book that concentrated on larger problems.

If you only have five variables, a genetic algorithm is probably not the right choice for converging upon a solution. With a chromosome length of five you're probably going to find that you very quickly reach a non-deterministic(this will change in subsequent runs) local minimum and slowly iterate around that space until you find the true local minimum.

However, if you are insistent on using a GA I would suggest abandoning that rule of thumb for this problem and really think about starting population as a measure of how far from the final solution you expect a random solution to be.

The reason that many rule of thumbs is dependent on chromosome length is because that's a decent proxy for this, if I have a hundred variables, and given randomly generating dna sequence is going to be further from ideal than if I had only one variable.

Additionally, if you're worried about computation intensity I'm going to go ahead and say that it shouldn't be an issue since you're dealing with such a small solution set. I think a better rule of thumb for smaller sets like this would be along the lines of:

(ln(chromosome_length*(solution_space/granularity)/mutation_rate))^2

Probably with a constant thrown in to scale for the particular problem.

It's definitely not a great rule of thumb (no rule is) but here's my logic for it:

• Chromosome length is just a proxy for size of solution space, so taking into account the size of the solution space will necessarily increase the accuracy of this proxy
• A smaller mutation rate necessitates a larger population size to compensate for the fact that you are more prone to get caught in local minima
• Any rule of thumb should scale logarithmically since a genetic algorithm is akin to a tree search of your solution space.
• The squared term was mostly the result of trying this out, but it looks like the logarithmic scaling was a little aggressive, though the general shape seemed right.

However I think a better choice would be to start at a reasonable number (100) and try iterating up and down until you find a population size that seems to balance accuracy with execution speed.