Revision 5488327 of "RPSO" on enwiki

== RPSO ==


RPSO stands for '''R'''epulsive '''P'''article '''S'''warm '''O'''ptimization.
This is an Algorithm for [[Wikipedia:Global Optimization|Global Optimization]] (GO) of objective functions. Belonging to the class of [[Wikipedia:stochastic|stochastic]] [[Wikipedia:evolutionary algorithm|evolutionary]] global optimizers, it is a variant of [[Wikipedia:Particle Swam Optimization|Particle Swam Optimization]] (PSO). 

There are several different realizations of RPSO. Common to all realizations is the repulsion between particles. This can prevent the [[Wikipedia:swarm intelligence|swarm]] beeing trapped in [[Wikipedia:local minimum|local minima]], which would cause a premature [[Wikipedia:convergence|convergence]] and would lead the optimization algorithm to fail to find the global optimum. 

In RPSO1 the future velocity <math>\mathbf{v}_{\mathrm{next}}</math> of a particle at position <math>\mathbf{x}</math> with a recent velocity <math>\mathbf{v}</math> is calculated by

:<math>\mathbf{v}_{\mathrm{next}} = \omega \mathbf{v} + a \ \chi_1 \ (-\mathbf{x}+\hat{\mathbf{x}})
                     + b \ \chi_2 \ \omega (-\mathbf{x}+\hat{\mathbf{y}})
                     + c \ \chi_3 \ \omega \ \mathbf{z}</math>

where 
*<math>\chi_1,\ \chi_2,\ \chi_3</math> : random numbers <math>\in [0,\ 1]</math>
*<math>\omega</math> : inertia weight <math>\in [0.01,\ 0.7]</math>
*<math>\hat{\mathbf{x}}</math> : best position of a particle
*<math>\hat{\mathbf{y}}</math> : best position of a randomly chosen other particle from within the swarm
*<math>\mathbf{z}</math> : a random velocity vector
*<math>a,b,c</math> : constants


The main difference between PSO and RPSO is the propagation mechanism to determine new positions for a particle in the search space. 
RPSO is capable to find [[Wikipedia:global optimum|global optima]] in more complex [[Wikipedia:search space|search spaces]]. On the other hand, compared to PSO it may be slower on certain types of optimization problems.