# Genetic Algorithm Minimum Population Size

Is there a minimum limit to a pool (population) size when using the genetic algorithm to solve an optimization problem? For example a population of size 2.

• In theory you could randomly create a perfect solution on the first try so 1 is enough. That however is a terrible answer. Take a look a schema thoery for bit vectors perhaps.
– Jake
Dec 8, 2014 at 17:07
• What do you mean by a minimum limit? I'm having a hard time understanding what you are asking. What precisely are you asking? Why do you think there is a minimum limit to pool size? What do you mean by minimum limit? What have you tried? Where did you go wrong? What research and self-study have you done? We expect you to do a significant amount of research before asking, to show us what you've tried, and to flesh out the question a bit more -- generally, a one- or two-sentence question is usually not enough.
– D.W.
Dec 22, 2014 at 2:59

I had a similar question and emailed Inman Harvey from the University of Sussex (author of Artificial Evolution: A Continuing SAGA and The Microbial Genetic Algorithm). Here is his answer (emphasis mine):

What is an optimum population size? Why?

If, like the natural world, a trillion microbes can evolve in the sea in parallel with no cost to you, then the bigger the better. In practice, on a serial machine, 10 times the pop-size costs you 10 times the time. Experience, with rather little theory, suggests that pop sizes of 30 to 100 minimum get you quite a lot of the advantages that GAs have over hill-climbing (ie pop of 2). So rule of thumb is to start here.

So basically, the bigger the population the better, but realistically you often have to make compromises to reach your goal in a reasonable amount of time. When building a genetic algorithm, you have to guess what the optimal values are for a lot of parameters. There is no good answer. Mostly there is a lot of trial and error.

There is no minimum to population size but it has a few drawbacks when it is too low.

when it is too low your genetic algorithm is almost going to be a deterministic or greedy algorithm and besides that you are going to lose the effect of weak answers. it has been proved that even the weakest answer can move the algorithm to a good answer. The nature of genetic algorithm is randomization and bias to better answers, when the population size is too low non of these are regarded.

When the population size is too low the population is going to lose the diversity so most likely your algorithm will fall in local optimums.

When the population size is too low you will face a few problems in Replacement step. because the population size is too low you will have to reject the unfeasible answers and it is a very bad idea for more illustration, look at this picture: