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In particle swarm optimization algorithm, what is the dimension exactly mean. Is it the number of particles (population size) in the search space? or it is the coordinates of each particle?

shdotcom
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2 Answers2

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It is the dimension of your search space. To better understand this check code line:

Update the particle's velocity: vi,d ← ω vi,d + φp rp (pi,d-xi,d) + φg rg (gd-xi,d)

So, velocity of each particle has d components.

EDIT: Look at this excerpt from the article:

It solves a problem by having a population of candidate solutions, here dubbed particles, and moving these particles around in the search-space according to simple mathematical formulae over the particle's position and velocity.

So, dimension of the search-space is the number of components in a particle.

Yola
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  • In this case the dimension of search space depends on the number of coordinates in each particles. for example if each particle is a vector of size 1×M then the dimension of search space will be: d=M. Is that correct or not? – shdotcom Jun 03 '17 at 08:58
  • so, the curs of dimensionality problem can be solved by decreasing **d** value, right? – shdotcom Jun 03 '17 at 12:02
  • @shdotcom yes, you can throw away less important features – Yola Jun 03 '17 at 14:08
  • thank you for your help, I have another question related to PSO and features extraction, but I can not ask here. Would it be possible to give me your email, so I can send the question with details. Thank you – shdotcom Jun 03 '17 at 14:41
  • @shdotcom sorry, but no, you can post another question on this site. If for some reason you don't want to disclosure the nature of your work, you can disguise it somehow. – Yola Jun 03 '17 at 14:51
  • one more question please, in my work I want a particle to be a matrix of size MxM not a vector 1xM, in this case the dimension of search space will be D = MxM, is that correct? – shdotcom Jun 15 '17 at 07:06
  • @shdotcom, right, you can always see MxM matrix as 1x(M^2) vector – Yola Jun 15 '17 at 12:09
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By xij, it is meant that i th particle is taken from j dimensional search space. If number of particles is limited by n, number of dimensions of the search space is restricted by m, then i is less than equal to n, j is less than equal to m. So dimension means the coordinates of the position of the particle. Number of velocity components will be the same as the number of coordinates of the particle. In mathematical problems like
Minimize x2 – 5x + 20, always j = 1

DILIP BHATTACHARYA
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