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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008
vidual will be eliminated as soon as possible, we will get a
more effective algorithm.
2.6 Mutation Operator
Although the probability is very small, it plays an important
role in preventing premature convergence and enhancing the
algorithm’s global search capability.
optimality.
The aim of using partial perturbation tracking is to find a high
convergence rate searching route. That is to say to increase or
reduce some times of the step such as X t ±k*(X i -X'), so we
can obtain some new candidates. The most sufficient one will
be chosen as the final result.
2.6.1 Adaptive Mutation Probability: In our algorithm the
population’s mutation probability is determined by two
variations: the difference of population genes and the
individual’s mutation. It can be defined as follows:
fo.01x£ m x(l-^)x( 7 ^) X -l^ x Mut n
Mut„
Mut =
Mut„
if £> Mut ■
J min
others
(12)
Let’s put t as a temporal variable, dif as the population differ
ence, ft(x) as the individual’s fitness, fit_ave as the average
fitness, a, k m ( k m >0,a>0 )are adjustable parameters,, a con
trol the degree of individual fitness which effects mutation
probability. Usually it is 1, 0.5 or 2. Mut max is maximum mu
tation probability, Mut mm is minimum mutation probability, t
represents the current generation number, T is the maximum
generation number.
2.6.2 Custom Mutation Approach: As for the mutation
operator, the step is very difficult to determine: small step is
helpful in getting the global optimal solution, yet increases
computing time; the big one consumes shorter time but is un
able to guarantee the global optimal solution. This paper adds a
partial perturbation tracking operation to the Multi-variable in
homogeneous mutation operator for real-coding method which
presented by Michalewicz, this method could determine the
most appropriate mutation direction and enhance the search ef
ficiency at the same time guarantee the result’s accuracy. Muta
tion formula is as follows:
X,+P ( , ) *(b-X l ) ifi=M< 0.5
•X-P^to+X,) ifi=M< 0.5 P^rSd-t/Dt
X i others
(13)
In the formula, a j , h t stands for the parameter boundary, r x ,r 2 as
the random variable in (0,1), j means an random number, t is
the current algebra, / represents current generation number, T
is the maximum generation number, b is the attribute variation
step of the curve shape factor which drops along with the gen
eration. The step in this method has the features as follows: the
bigger step in the initial evolution period is greatly advanta
geous as enhancing the search efficiency, while the shorter one
in the later evolution period when the population tends to stably
and searches nearby the optimum value, can guarantee solution
2.7 Selection Strategy
In this paper, we use the synchronous selection strategy on
multi-subpopulations. First, the original population is divided
into two classes: “stable subpopulation” and “exploring sub
population”. Different class has different evolution strategy and
operators. Concretely, in the former we set a bigger probability
of crossover and mutation, make full use of its exploring ability;
In stable subpopulation avoiding excellent gene to be destroyed
is our main purpose. In order to guarantee the population’s di
versity, excellent individuals in the two subpopulations should
be exchanged in every generation so they could share the ad
vantages of each other. Individuals in Middle generation comes
from the above two subpopulations, the most outstanding indi
vidual in each population will be selected as candidate directly,
the remains will be chosen by competitive selection method.
For the sake of fusing the genetic characteristic of the two sub
populations, middle population is endowed with small probabil
ity of crossover and mutation. So that the best gene will be
merged adequately and it is more likely to find new potential
excellent genes.
The synchronous selection strategy on multi-subpopulation is a
eclectic method between avoiding premature and destroying
excellent individuals. Simultaneously the optimal gene reserved
strategy and the optimal individual reserved strategy are
merged properly.
2.8 Evolution Control Parameters:
Population Size: Usually it is a constant and even number.
Crossover Probability: reference to section 2.5, usually it is not
more than 0.75;
Mutation Probability: reference to section 2.6, usually it does
not exceed 0.05;
Generation Number: In view of the population evolution and
the algorithm’s efficiency, generally set it around 100 genera
tions
Termination Criteria: if any of the following conditions are met,
terminating the algorithm.
1) The population difference is smaller than thresh
old.
2) The best individual is sufficient to meet the fitness
requirements.
3) Achieved maximum evolution algebra.
3. MORPHOLOGY FILTER
There are two important aspects in image processing using
morphology: Morphological operation and Structural element
chosen. Morphological open operation is good at removing
bright details which is smaller than structure element and main-