Swarm Intelligence

Finally, when ϕ=100, the particle’s trajectory is almost entirely vi-

bratory, dominated by steps of size V

max

(see Figure 8.8). Though values

mentioned here are specific to this particular example, in general the sys-

tem behaves in this way with any V

max

value.

In sum, in the stochastic particle swarm the system parameter ϕ con-

trols the strength of the effect of (p − x) on the velocity. When ϕ is very

low, the effect is weak, and the particle’s trajectory follows a wide path,

only being drawn back toward p by the pull of (p − x) after a large num-

ber of iterations. As ϕ increases, the oscillatory wavelength shortens, but

individual steps lengthen