The population size is a parameter of evolutionary algorithms. It depends of the problem. Some authors calibrate this parameter according to the problem and instance. What is the problem that are you aiming to solve?

This paper presents an approach for optimize GA's parameters:

http://www.sciencedirect.com/science/article/pii/S0305048305000174

I'm not thinking about any specific problem. I use to calibrate the population size as well, but since there are many adaptative parameters...

Goldberg, Deb, et al. did some early and excellent work on sizing populations for GAs:

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.6625

If you want to use parallel GAs, Cantu-Paz's work with Goldberg is a great place to start:

http://link.springer.com/book/10.1007/978-1-4615-4369-5

You are right, it has long been known that the size of the population is an important control parameter in the performance of population-based metaheuristics. Almost all research involving population-based metaheuristics involves tuning of the population size, and a large amount of research has been dedicated solely to the optimization of this parameter. The population size may influence the convergence rate, exploration and diversification of the heuristic. As state by Bruno, the optimal size depends on the problem at hand. Dimensionality, multi-modality, ill-conditioning, depending on this (and other) characteristics the optimal size may strongly vary even for different instance of a same problem.

Currently some research has been developed on micro-algorithms (which use a very small population and specific operators to maintain diversity) and variable population sizes.

Although it is not directly related with genetics algorithms and harmony search you may find the following work interesting, since it directly adresses the issue of population size on population-based heuristics. You may also find some useful references there.

https://www.researchgate.net/publication/236952683_Minimum_Population_Search__Lessons_from_building_a_heuristic_technique_with_two_population_members?ev=srch_pub

Conference Paper Minimum Population Search – Lessons from building a heuristi...

When your chromosomes contain Nb bits each, then the minimal population size Ni

should satisfy Ni^2 > 2 Nb. This is a necessary, but not sufficient condition. Anyway, in practice it may suffice if mutations are not to rare.

Where from all this? See my paper at RG:

https://www.researchgate.net/publication/216486175_Biology_Physics_Small_Worlds_and_Genetic_Algorithms?ev=prf_pub

Here you will also find the lowest recommended mutation rate. All this - problem independent (continuous and discrete problems are fine).

Chapter Biology, Physics, Small Worlds and Genetic Algorithms

I would like to recommend you the following article: I may be helpful to you..

Mahamad Nabab Alam, Biswarup Das, Vinay Pant, A comparative study of metaheuristic optimization approaches for directional overcurrent relays coordination, Electric Power Systems Research, Volume 128, November 2015, Pages 39-52, ISSN 0378-7796, http://dx.doi.org/10.1016/j.epsr.2015.06.018.

(http://www.sciencedirect.com/science/article/pii/S0378779615001947)

Thank you for your useful comments. I will read the papers carefully.