Databases Reference
In-Depth Information
where
w
is the inertia weight,
r
1
,r
2
are the random numbers (mutually
independent) in the range [0, 1],
c
1
,
c
2
are the positive constants,
PB
i
is the best position of the
i
th particle achieved so far, and
P
g
is the
best position of any particle achieved so far. The particles new velocity
is based on its previous velocity and the distances of its current position
from its best position and the groups best position. After updating velocity
the particle flies toward a new position (defined by the above equation).
Parameter
w
that represents particles inertia was proposed by Shi and
Eberhart.
29
Parameters
c
1
and
c
2
represent the particles confidence in its
own experience, as well as the experience of other particles. Venter and
Sobieszczanski-Sobieski
30
used the following formulae to calculate particles
velocity:
P
k
−
PB
i
X
k
X
k
∆
t
−
V
k
+1
V
k
+
c
1
·
=
w
·
r
1
·
+
c
2
·
r
2
·
,
(1.3)
∆
t
In other words, when calculating the particles velocity, Venter and
Sobieszczanski-Sobieski
30
replaced the best position of any particle achieved
so far
P
g
, by the best position of any particle achieved in the
k
th iteration
P
k
.
The PSO represents search process that contains stochastic components
(random numbers
r
1
and
r
2
). Small number of parameters that should be
initialized also characterizes the PSO. In this way, it is relatively easy to
perform a big number of numerical experiments. The number of particles is
usually between 20 and 40. The parameters
c
1
and
c
2
were most frequently
equal to 2. When performing the PSO, the analyst arbitrarily determines
the number of iterations.
1.3.2.2.
Ant Colony Optimization
(
ACO
)
We have already mentioned that the ants successful at finding food leave
behind them a pheromone trail that other ants follow in order to reach
the food. In this way ants communicate among themselves, and they are
capable to solve complex problems. It has been shown by the experiments
that ants are capable to discover the shortest path between two points
in the space. Ants that randomly chose the shorter path are the first
who come to the food source. They are also the first who move back to
the nest. Higher frequency of crossing the shorter path causes a higher
pheromone on the shorter path. In other words, the shorter path receives
the pheromone quicker. In this way, the probability of choosing the shorter
