ADPSO

Adaptive Diversity Particle Swarm Optimization is a variant of the standard PSO algorithm that introduces collision detection and particle dispersion using adaptive, per particle collision radi and adaptive collision reaction forces [Monson SeppiMonson Seppi2006]. It is a fairly elegant solution for resolving some of the deficits of the standard PSO such as premature convergence. It performs better on multi modal functions than the standard PSO.

The collision radius $c_r$ is defined by:

$$c_r = \gamma^{b_i} + \gamma^{b_j} r$$

With $\gamma$ an adaptation constant, $b_i$ and $b_j$ the respective number of times particles $i$ and $j$ have collided until now and $r$ a basic collision radius. As can easily seen, the collision radius per particle decreases the more it collides.

When two particles collide, their velocity is reflected and their new position is calculated by:

$$x'_{t + 1} = x_t - \gamma^{-b}(x_{t + 1} - x_{t})$$

Thus reflecting the current position around the old position, weighted by $\gamma^{-b}$. Thus, as the adaptive radius decreases with increased number of collisions, the bounce distance increases. This allows both good convergence and escaping of local minima.

Table 3.5 lists the settings available for this optimizer. ADPSO is an extension of the standard PSO and the PSO settings defined in table 3.4 also apply to this optimization algorithm. For more information on the available settings, see monson_ad_2006.

Table 3.5: ADPSO Settings

Name	Description
adaptation-constant	The adaptation constant ($\gamma$) with regard to the number of times a particle has collided (0 - 1)
collision-radius	The basic collision radius ($r$) as a fraction of the parameter space