Genetic Algorithm, large population vs small one

Question

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

I'm also wondering if the following is correct:

Larger Population Size.

Pros: Larger diversity so more likely to pick up on traits that return 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 to compensate for the 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 to 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 a lot 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

Researchers usually argue that a “small” population size could guide the algorithm to poor solutions and that a “large” population size could make the algorithm expend more computation time in finding a solution. Due to the significant influence of population size on the solution quality and search time more thorough research should be done for this GA parameter. The main goal of this research is to carry out an investigation of the influence of one of the key GA parameters – population size (number of chromosomes) – on the algorithm performance for identification of a cultivation process model. 

The use of smaller populations results in lower accuracy of the solution, obtained for a smaller computational time. The

further increase in the population size increases the accuracy of the solution. This effect is observed to a population size of

100 chromosomes. The use of larger populations does not improve the solution accuracy and only increase the needed

computational resources.

For more information regarding the same, refer to the following link:

https://annals-csis.org/Volume_1/pliks/167.pdf

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