PSO

$\displaystyle v_{ij}(t + 1)$	$\displaystyle =$	$\displaystyle \chi (v_{ij}(t) + R_1 \varphi_1 (P_{ij} - x_{ij}(t)) + R_2 \varphi_2 (P_b - x_{ij}(t)))$
$\displaystyle \chi$	$\displaystyle =$	$\displaystyle \dfrac{2k}{\vert 2 - \varphi - \sqrt{\varphi^2 - 4\varphi}\vert}$
$\displaystyle \varphi$	$\displaystyle =$	$\displaystyle \varphi_1 + \varphi_2 > 4$

It performs particularly well on real-valued problems with single single objectives. Table 3.4 lists the settings available for this optimization algorithm.

Table 3.4: PSO Settings
Name Description

max-velocity The maximum particle velocity as a fraction of the parameter space

cognitive-factor The PSO cognitive factor as described in the literature ( $\varphi_1$ )

social-factor The PSO social factor as described in the literature ( $\varphi_2$ )

constriction The velocity update constriction as described in the literature ( $\chi$ ).

boundary-condition The action to take when particles reach the parameter boundaries (None, Stick or Bounce). The default is Bounce.

boundary-damping A velocity damping factor when the boundary condition is Bounce.

Name	Description
max-velocity	The maximum particle velocity as a fraction of the parameter space
cognitive-factor	The PSO cognitive factor as described in the literature ( $\varphi_1$ )
social-factor	The PSO social factor as described in the literature ( $\varphi_2$ )
constriction	The velocity update constriction as described in the literature ( $\chi$ ).
boundary-condition	The action to take when particles reach the parameter boundaries (`None`, `Stick` or `Bounce`). The default is `Bounce`.
boundary-damping	A velocity damping factor when the boundary condition is `Bounce`.