Databases Reference
In-Depth Information
7.3.1.
Original PSO
The original PSO is a population based stochastic optimization technique
developed by Kennedy and Eberhart.
5,19
The current searching points are
modified using the following state equations:
v
k
+1
i
=
wv
i
+
c
1
r
1
(
pbest
i
−
s
i
)+
c
2
r
2
(
gbest
s
i
)
−
(7.10)
s
k
+1
i
=
s
i
+
v
k
+1
(7.11)
i
where,
v
i
: Velocity of particle
i
at iteration
k
,
w
: Weighting function,
c
i
:
Weighting coecients,
r
i
: Random number between 0 and 1,
s
i
: Current
position of particle
i
at iteration
k
,
pbest
i
: pbest of particle
i
,
gbest
:gbest
of the group.
The original PSO algorithm can be expressed as follows:
(1) State variables (searching point): State variables (states and their
velocities) can be expressed as vectors of continuous numbers. PSO
utilizes multiple searching points as agents for search procedures.
(2) Generation of initial searching points: Initial conditions of searching
points in the solution space are usually generated randomly within
their allowable ranges.
(3) Evaluation of searching points: The current searching points are
evaluated by the objective function of the target problem. Pbests (the
best evaluated value so far of each agent) and gbest (the best of pbest)
can be modified by comparing the evaluation values of the current
searching points, and current pbests and gbest.
(4) Modification of searching points: The current searching points are
modified using the state equations of PSO.
(5) Stop criterion: The search procedure can be stopped when the
current iteration number reaches the predetermined maximum iteration
number. For example, the last gbest can be output as a solution.
7.3.2.
Evolutionary PSO EPSO
The idea behind EPSO
11,12
is to grant a PSO scheme with an explicit
selection procedure and with self-adapting properties for its parameters.
At a given iteration, consider a set of solutions or alternatives that we will
keep calling particles. The general scheme of EPSO is the following:
(1) REPLICATION — each particle is replicated R times.
(2) MUTATION — each particle has its weights mutated.
