pso.velocity {gena}

Velocity

Description

Calculates (updates) velocities of the particles.

Usage

pso.velocity(
  population,
  method = "hypersphere",
  par = list(w = 1/(2 * log(2)), c1 = 0.5 + log(2), c2 = 0.5 + log(2)),
  velocity,
  best.pn,
  best.nh,
  best.pn.fitness,
  best.nh.fitness,
  iter = 1
)

Arguments

population

numeric matrix which rows are particles i.e. vectors of parameters values.

method

string representing method to be used for velocities calculation. See 'Details' for additional information.

par

additional parameters to be passed depending on the method.

velocity

matrix which i-th row is a velocity of the i-th particle.

best.pn

numeric matrix which i-th row is a best personal position known by the i-th particle.

best.nh

numeric matrix which i-th row is a best personal position in a neighbourhood of the i-th particle.

best.pn.fitness

numeric vector which i-th row is the value of a fitness function at point best.pn[i, ].

best.nh.fitness

numeric vector which i-th row is the value of a fitness function at point best.nh[i, ].

iter

iteration number of the genetic algorithm.

Details

If method = "classic" then classical velocity formula is used:

v_{i,j,(t+1)}=w\times v_{i,j,t} + c_{1}\times u_{1,i,j} \times b^{pn}_{i,j,t} + c_{2}\times u_{2,i,j} \times b^{nh}_{i,j,t}

where v_{i, j, t} is a velocity of the i-th particle respect to the j-th component at time t. Random variables u_{1,i,j} and u_{2,i,j} are i.i.d. respect to all indexes and follow standard uniform distribution U(0, 1). Variable b^{pn}_{i,j,t} is j-th component of the best known particle's (personal) position up to time period t. Similarly b^{nh}_{i,j,t} is j-th component of the best of best known particle's position in a neighbourhood of the i-th particle. Hyperparameters w, c_{1} and c_{2} may be provided via par argument as a list with elements par$w, par$c1 and par$c2 correspondingly.

If method = "hypersphere" then rotation invariant formula from sections 3.4.2 and 3.4.3 of M. Clerc (2012) is used with arguments identical to the classical method. To simulate a random variate from the hypersphere function rhypersphere is used setting type = "non-uniform".

In accordance with M. Clerc (2012) default values are par$w = 1/(2 * log(2)), par$c1 = 0.5 + log(2) and par$c2 = 0.5 + log(2).

Value

This function returns a matrix which i-th row represents updated velocity of the i-th particle.

References

Maurice Clerc (2012). Standard Particle Swarm Optimisation. HAL archieve.