Repulsive particle swarm optimization

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In mathematics, specifically in optimization, repulsive particle swarm optimization (RPSO) is a global optimization algorithm. It belongs to the class of stochastic evolutionary global optimizers, and is a variant of particle swarm optimization (PSO).

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

In RPSO the future velocity \mathbf{v}_{\mathrm{next}} of a particle at position \mathbf{x} with a recent velocity \mathbf{v} is calculated by

\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}

where

  • \chi_1,\ \chi_2,\ \chi_3 : random numbers \in [0,\ 1]
  • ω : inertia weight \in [0.01,\ 0.7]
  • \hat{\mathbf{x}} : best position of a particle
  • \hat{\mathbf{y}} : best position of a randomly chosen other particle from within the swarm
  • \mathbf{z} : a random velocity vector
  • a,b,c : 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 of finding global optima in more complex search spaces. On the other hand, compared to PSO it may be slower on certain types of optimization problems.

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