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Table 2.1.
Comparison of typical EA and PSOA concepts
concept
EA
PSOA
candidate solution
individual
particle
set of solutions
population
swarm
variation (exploration) mutation
randomized factors
φ
1
,φ
2
variation (exploitation) crossover
equation parts (
pb
−
x
), (
b
−
x
)
direction of search
parent & survivor selection best individuals
pb
,
b
Both work with a set of candidate solutions. In terms of EAs they are called
population of individuals, in terms of PSOAs they are denoted as a swarm of
particles. This similarity is not restricted to the algorithmic scheme, but fur-
thermore holds for the used
operators
. The three genetic operators mutation,
crossover and selection can be identified within the PSOA equations. We com-
pare them to the equations of the (1+
λ
)
ES. In a (1+
λ
)-ES the best individual
b
is chosen as the only parent for creating
λ
offspring solutions. The equation
of a (1 +
λ
)-ES looks as follows
−
x
=
b
+
φ
(2.9)
with mutation
φ
. It is structurally very similar to the PSOA equation 2.10.
Assuming that
pb
and
b
are almost identical, the PSOA equation can be written
as
x
=(
φ
1
+
φ
2
)
b
+(1
−
φ
1
−
φ
2
)
x
+
v
.
(2.10)
Hence, the new solution is built by combining the old solution with the best one -
or at least one of the best solutions - weighting the ratios with randomized
parameters.
Mutation.
Mutation, i.e. exploration of the search space, is achieved by mul-
tiplication with the random numbers
φ
1
and
φ
2
.InESmutationofobjective
variables is usually achieved by adding a random value based on Gaussian mu-
tation. But multiplicative mutation is also known for strategy parameters, e.g.
for correlated mutation [18] or biased mutation, see section 4.2.
Crossover.
Crossover or recombination can be found in equation 2.10 as the new
solution is the weighted sum of the best particle (or the best particle and the
best position of one particle's history) and its last position
x
=
α
1
b
+
α
2
x
+
v
(2.11)
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