![](https://csdnimg.cn/release/download_crawler_static/15755318/bg3.jpg)
selectively removing low-quality components and replac-
ing them with randomly selected components. Meanwhile,
this appro ach requires a suitable representation which
permits individual solution components to be assigned a
quality measure. However, it is not easy to design a suit-
able local fitness function for each component in many
practical applications, which is a defect of the canonical
EO algo rithm.
In addition, it should be stressed that an emergent effect
of the negative-component-selection principle is funda-
mental to the algorithm. Here, a detailed examination
reveals some interesting principles of EO. Consider a
solution containing 60 components and each component is
distributed between 0 and 1 randomly. For the sake of
simplicity, the local fitness of each component is the pre-
sent random value and the fitness of the solution is the
minimal unchanged value of all the components values. At
each time step, the system is updated by locating the site
with the lowest fitness, mutating it by assigning a new
random value and changing the landscapes of the two
neighbors to the right and left by assigning new random
numbers. Figure 1 illustrates the optimizati on dynamics of
EO algo rithm.
As shown in Fig. 1a, we can see that all the com ponents
in the solution are initialized with random values. The
components are improved by updating the worst compo-
nent and its two nearest neighbors after 2000 generations,
as shown in Fig. 1b. If the number of iterations is large
enough, the solution will evolve into a self-organized
critical state and all the components will locate above the
critical value 0.667. Punctuated equilibrium with genera-
tions is shown in Fig. 1c and the fitness value of the
solution changes over generations as shown in Fig. 1d.
In addition, a modified EO selects the component to
update on the basis of the probability distributions over the
rank k . In other words, if the component h
i
is ranked as k in
all the components according to its local fitness, then it has
the change probability with pðh
i
Þ/k
s
where s is a pos-
itive constant, called critical exponent of power-laws.
2.2 Hybrid Gaussian-Cauchy mutation
It is generally known that mutation operator has a great
impact on optimization performance of EO. We introduce
two typical mutation strategies in Sects. 2.2 and 2.3.
Hybrid Gaussian-Cauchy mutation combines fine-grained
1 10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
Components
Local Fitness
1 10 20 30 40 50 60
0
0.2
0.4
0.6
0.667
0.8
1
Components
Local Fitness
(b)(a)
0 500 1000 1500 2000
0
500
1000
1500
2000
Generation
Punctuated equilibria
0 500 1000 1500 2000
0
0.2
0.4
0.6
0.8
1
Generation
Global Fitness
(c) (d)
Fig. 1 The optimization dynamics of EO algorithm. a Initial components distribution. b Final components distribution. c Punctuated equilibrium
with generations. d Variation of fitness with generations
An improved extremal optimization based on the distribution... 137
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