Difference between revisions 5489003 and 5565312 on enwiki

'''RPSO''' stands for '''R'''epulsive '''P'''article '''S'''warm '''O'''ptimization.
This is an Algorithm for [[Global_O 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 Sswarm Ooptimization|Particle Swarm 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|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]]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.
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See Also:

*[[Wikipedia:Genetic Algorithms|Genetic Algorithm]]
*[[Wikipedia:Swarm Intelligence|Swarm Intelligence]]
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--[[User:80.134.50.95|80.134.50.95onay urfalioglu]] 22:36, 27 Aug 2004 (UTC)