  The range of applications of traditional optimization methods are limited by
the features of the object variables, and of both the objective and the
constraint functions. In contrast, population-based algorithms whose
optimization capabilities are emergent properties, such as evolutionary
algorithms and particle swarm optimization, present almost no restriction on
those features and can handle different optimization problems with few or no
adaptations. Their main drawbacks consist of their comparatively higher
computational cost and difficulty in handling equality constraints. The
particle swarm optimization method is sometimes viewed as an evolutionary
algorithm because of their many similarities, despite not being inspired by the
same metaphor: they evolve a population of individuals taking into account
previous experiences and using stochastic operators to introduce new responses.
The advantages of evolutionary algorithms with respect to traditional methods
have been greatly discussed in the literature for decades. While the particle
swarm optimizers share such advantages, their main desirable features when
compared to evolutionary algorithms are their lower computational cost and
easier implementation, involving no operator design and few parameters to be
tuned. However, even slight modifications of these parameters greatly influence
the dynamics of the swarm. This paper deals with the effect of the settings of
the parameters of the particles' velocity update equation on the behaviour of
the system.
