Quantum-behaved Particle Multi-Swarm Optimization
Introducing Multi-Swarms to QPSO
The basic idea of the Multi-Swarm extension is to have the search area explored by a number ($ns$) of smaller swarms instead of one large swarm.
The movement of the $i$-th particles within the $s$-th swarm are basically “swarm-centered”, i.e. they are primarily oriented to the best particle of the swarm or the mean best position of the swarm - just like in QPSO:
\[\boldsymbol{x}^{t+1}_{i,s} = \boldsymbol{\Omega}^{t}_{i,s} \pm \dfrac{\boldsymbol{L}^t_{i,s}}{2} \ln\left(\dfrac{1}{\boldsymbol{u}^{t+1}_{i,s}}\right)\]Note that in above equation, the stochastic attractor is replaced by a new attractor $\boldsymbol{\Omega}_{i,s}^{t}$. The definition of $\boldsymbol{\Omega}^{t} _{i,s}$ and the characteristic length $\boldsymbol{L}^t _{i,s}$ depends on the particle type. We propose four basic (but different) types of particles, namely Type-1, Type-2, Type-3 and Type-4 particles. Their behaviour is described in the following sections: