Most likely, there is no precise and universal answer.  Minimal population size may be found for classical Genetic Algorithms (see my paper "Biology, Physics, ...), but PSO is different - there are no generations here, just calculation's steps.  Also the danger of the so called premature convergence seems less important in PSO than in GA. Therefore the optimal population would be such that the number of steps multiplied by population size squared is minimal.  Why squared?  That's because you need to compute N(N-1)/2 ~ O(N2) (for N > 1, of course) interactions between agents to complete each step.  This suggests to keep the population as small as possible.  So, the question is rather how small can be the population to be still called swarm.  I think that  n < N < 2n, where n is the search space dimension, is the safe choice.  For n < 10 I would fix N at some value, say a dozen or more. However, I cannot offer any better foundation for this rather obvious hint.

We've found that PSO performs quite well with constant population size as a function of problem dimension.  Also, due to the growth in convergence times, it becomes computationally prohibitive to use a population size larger than the problem dimension for n > 50.

full paper:

http://link.springer.com/article/10.1007/s10489-014-0613-2

short paper:

Conference Paper Some Measurements on the Effects of the Curse of Dimensionality

Unfortunately, there are no universal rules to setting the size, and only experimental results give an idea of the behavior of the algorithms since it is problem dependent;I would recommend you to begin with a small number of particles and then simply just increase the size and analyse the results.

I reffers you also to this paper:

Investigating Smart Sampling as a population initialization method for Differential Evolution in continuous problems

de Melo, Vinícius Veloso; Botazzo Delbem, Alexandre Cláudio (2012)

Information Sciences vol. 193 p. 36-53

The question is really whether your problem has computationally expensive function evaluations or not. If so, try any of the parameter settings found to be effective for similar problems / setups. If not, use offline parameter tuning, and you'll probably see a significant performance improvement.

It is a rule of thumb with heuristic optimization algorithms to start with 10 times the number of search variables in case of small problem dimensions (I would say n < 10). However, it is a design problem which depends on the nature, nonlinearity, and complexity of your objective function and search space. it also depends on the inherent feature of the very PSO algorithm you use. In short, nothing but trial and error starting by a swarm size of 10*n.

Good luck,

Mohamed

Marek Wojciech Gutowski- Sir, thanks for the inputs

Stephen Chen- But there are scenarios you might have to take more than that, lets say if we use PSO as a part of a Big data analytics

naziha- Mam thanks for the inputs

Leonardo-Sir thanks for the input

Awadallah sir- Lets us say the aim is to obtain both accuracy and optimal computational complexity what should be swarm size

https://www.researchgate.net/publication/297245624_Particle_Swarm_Optimization_Algorithm_and_its_Codes_in_MATLAB

Research Particle Swarm Optimization: Algorithm and its Codes in MATLAB

https://www.researchgate.net/publication/296636431_Codes_in_MATLAB_for_Particle_Swarm_Optimization

Code Codes in MATLAB for Particle Swarm Optimization

https://www.researchgate.net/publication/280244004_A_comparative_study_of_metaheuristic_optimization_approaches_for_directional_overcurrent_relays_coordination

Article A comparative study of metaheuristic optimization approaches...

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