Hardware Reference
In-Depth Information
is different with respect to [
2
] because the latter uses a linear combination of cost
functions
. Linear combination can be heavily biased on highly valued
cost-functions disregarding low-valued ones.
Dealing with the discrete design space.
The essential nature of the solution
space of the problems faced with the MULTICUBE project is discrete, while the
PSO approaches presented so far deal with a continuous search space. Several pro-
posals have been made so far in the literature to extend classical PSO to the discrete
domain. One method for addressing the discrete design space exploration problem is
applying particle swarm optimization to binary-valued solution elements [
8
]. In this
case, while the velocity term is still real-valued, the position term is actually chosen
between 0 and 1 by means of a sigmoidal function. Another method leverages the
construction of a probability distribution for each value of the position vector [
12
].
The probability distribution is derived from the current value of the position vector
which, in turn, depends on the velocity vector. The probability distribution is then
transformed into a single integer number during fitness evaluation of each particle.
Enhanced-MOPSO is based on the concepts of
random walk
theory. A random
walk is a path with the following properties:
{
f
1
...f
m
}
It has a starting point.
The distance from one point to the next is constant
The direction from one point to the next is picked up at random.
The position of the particle is still updated with the traditional rule:
x
i
(
t
)
=
x
i
(
t
−
1)
+
δ
i
(
t
)
(3.4)
while each component
k
of the direction vector is updated with the following rule:
sign(
x
gbest
,
k
−
x
i
,
k
(
t
−
1))
if(rand()
<p
)
δ
i
,
k
(
t
)
=
(3.5)
randint(
−
1, 1)
otherwise
where
p
[0, 1] is a parameter of the algorithm.
As can be noted, the direction of the particle is updated following two rules: rule 1
attracts the particle versus the leader of the swarm (
gbest
), rule 2 forces the particle
to follow a random walk. This ensures us to jump out from local minima in the
objective function shown in Eq.
3.3
.
∈
3.3.3
New Algorithms
The algorithms listed below can be considered as completely new proposal in the
scientific literature [
17
].
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