In the Particle Swarm Optimization (PSO) algorithm, the position of each particle represented by a row vector (x).
The same with velocity, it represented by a velocity vector (v)
I have found this in the Mathworks website:
...Particle i has position x(i), which is a row vector with nvars elements.
What are the contents (elements) of posistion vector and velocity vector? Why they are not a single value?
Is it right if we say that x and v are one dimension arrays (one row and N columns)?
What are the contents(elements) of posistion vector and velocity vector?
The elements of the position are thee coordinates (see: https://en.wikipedia.org/wiki/Coordinate_system) which are used to parametrize space.
Similarly for the velocity vector you have the velocity in each of the dimensions.
So for instance if you have a 3D space, then the elements of position might be (x, y, z) and the elements of velocity could then be (vx, vy, vz)
Why it is not a single value?
In general it could be an arbitrary number of values - i.e. it could be a single value. But that would mean that your swarm lives in a 1-dimensional space and hence they could also only move back and forth along that dimension.
Is it right if we say that x and v are one dimension arrays (one row and N columns)?
In principle it is. Just make sure you don't mix implementation with the abstract algorithm. Most probably the vector is represented with an array as underlying data-structure. However, if it is one row with N columns (where N would be the dimensionality of the space where your swarm lives) or if it is N rows in a single column is a matter of how one interprets it. In Mathworks, as you quoted, it says "Particle i has position x(i), which is a row vector with nvars elements.", so I'd say for that implementation you are correct and the right interpretation is one row with nvars columns.