International Journal of Intelligence Science, 2011, 1, 1-7
doi:10.4236/ijis.2011.11001 Published Online July 2011 (http://www.SciRP.org/journal/ijis)
1
Using Intelligent Computational Methods for
Optimizing Niching Method
Mohsen Jahanshahi
Computer Engineering Department, Central Tehr an Bra nch , Islamic Azad University, Tehran, Iran
Received June 22, 20 1 1; revised July 18, 2011; acc epted July 25, 2011
Abstract
Optimization implies the minimization or maximization of an objective function. Some problems have sev-
eral optimum points which all, should be computed. Niching method is presented to do so. However, its effi-
ciency can be improved via combining it with Memetic algorithm. Therefore, in this paper, Memetic method
is used to improve this method in terms of convergence rate and diversity. In the proposed methods, genetic
algorithm, PSO, and learning automata are used as a local search algorithm of Memetic method. The result
of simulations demonstrates that proposed methods are more effective compared with Niching in terms of
convergence and diversity.
Keywords: PSO, Niching, Genetic Algorithm, Learning Automata
1. Introduction
Optimization is the minimization or maximization of an
objective function that normally is done with considera-
tion of limitation s identifying condition s of a problem. In
other words, it means the finding of the best solution for
a given problem. Some problems have several local op-
timums which may be computed using Niching method
[1]. In this paper, memetic meth od is used for increase of
convergence speed and also the increasing rate of parti-
cles’ diversity in Niching method, as two assessment
factors of search methods. In this research, genetic algo-
rithms (GA) [2], particle swarm optimization (PSO) [3],
and learning automata (LA) [4] are used as three local
search algorithms in memetic method.
The rest of the paper is organized as follows. In sec-
tion 2, PSO method is briefly introduced. In section 3,
NichePSO is discussed in summary. Section 4 explains
used local search methods and then proposed methods
are discussed in section 5. The results of simulations are
included in section 6. Section 7 concludes the manu-
script.
2. Particle Swarm Optimization
Particle swarm optimization (PSO) was discussed in [3]
and then has been improved for many years. It is com-
bined by GA in [5] and modified in [6-8] work on dis-
crete PSO as a new direction. PSO has been successfully
utilized for aircraft transportation [9] and optimal path
discovery in automated drilling operations [10], to name
a few. There are also some other works which concen-
trated on its functionality which are not in the scope of
this manuscript [11,12].
The main idea of PSO had been taken from Birds or
fishes swarm behavior which are searching for meal.
Some birds are searching for meal randomly. Only a
piece of meal may be found in the mentioned space.
None of them knows about the real place of the meal.
One of the best strategies is to follow a bird that is placed
in minimum distance to a meal. In fact, this strategy is
basis of PSO algorithm.
This method is an effective technique for solution of
optimization problems based on a swarm behavior. In
this method, each member of a swarm is called a particle
who attempts to achieve a final solution with adjustment
of its route and movement to the best personal and
swarm experiences. In PSO algorithm, a solution is
called a particle the same as a bird in swarm scheme.
Each particle is described using a quality factor is given
by a fitness function. The more nearness to the goal, the
more qualification is obtained. Each particle also moves
with a specified speed which conducts its movement.
Each particle that follows the optimum particles in cur-

M. JAHANSHAHI
2
rent position will continue its movement in the space of
problem.
PSO starts in this way that a swarm of particles (solu-
tions) are generated randomly and are updated during the
generations and attempt to find an optimum solution. In
each step, every particle is updated using two best values.
First, is the best situation that a particle has ever been
reached. It is known and kept by personal best (pbest).
Another best value is used by the algorithm is the best
position that has ever been obtained by a swarm of parti-
cles. It is known by global best (gbest). In some PSO
editions, a particle chooses parts of populations that are
its topological neighbors and only involves those in its
behavior. In this case, the best local solution is shown by
lbest (local best) and is used instead of gbest. After find-
ing the best values, the velocity and position of particles
are updated by formula (1) and (2) given below:










   
1* *-
2**-
vvc randpbestposition
c randgbestposition

 (1)






positionposition V (2)
In (1) and (2) equations,


V is the particle velocity
and


position is current position of a particle. Both
are arrays as long as th e number of prob lem dimension s.

Rand is a random variable in the random domain. (0,
1) c1 and c2 are learning parameters, normally both are
the same values as c1= c2 = c. In each dimension, veloc-
ity of particles is limited to a Vmax. In case, the sum of
accelerations cause that the velocity in one dimension
exceeds the maximum value, it is considered as Vmax.
The right hand side of Equation (1) is composed of three
components, the first part, is the current velocity of a
particle, the second and third parts take responsibility for
variation of the velocity and its rotation towards the best
personal and swarm experiences. Combining these two
factors in Equation (1) helps create a balance between
local and global searches. Let us we don’t consider the
first part of the equation then the particles velocity is
determined only with consideration of current position
and the best single and swarm experiences of particles.
Therefore, the best particle is fixed in its positio n and the
rest of the particles move towards it. In fact, if we ignore
the first part of Equation (1), PSO will be a process in
which, search space gradually becomes smaller and local
search is performed around the best particle. In contrast,
if we consider only first part of the Equation (1), then the
particles will continue their normal route up to border
and it is said those are doing global search. Pseudo code
of PSO algorithm is shown in Figure 1.
Since in this algorithm, particles gradually tend to
current optimum solution so if this is a local optimum
solution then whole particles move towards it conse-
Figure 1. Pseudo code of PSO algorithm.
quently PSO is not a practical way to leave this local
optimization. Meanwhile, some problems have more
than one general optimum solution that all have to be
computed. These are the greatest problems of PSO algo-
rithm that make it unable to solve multi peak problems
particularly with a large state space.
3. Niche PSO
Niche PSO is presented to find all the solutions of prob-
lems with more than one general optimum solution [1].
In this algorithm, niches are parts of the environment and
main operation of each niche is to self-organize the par-
ticles to independent sub-swarm. Each sub-swarm de-
termines the positio n of one niche and keeps it. The task
of each sub-swarm is to find one of the optimum solu-
tions. No information is exchanged amongst sub-swarms.
This independency lets sub-swarms to keep niches. In
summary, it can be said that performance of sub-swarms
is stable and independent of the other swarms.
Niche PSO begins its operation with one swarm that is
called main swarm that includes whole particles. As soon
as, a particle gets close to an optimum solution, one
swarm will be formed with classification of particles.
Then these particles are put out of the main swarm and
continue the operations for finding the solution in their
own sub swarms. In fact the main swarm is broken into
some sub-swarms. Niche PSO is convergent when
smaller sub-swarms improve their presented solutions,
and then in continue, the best global position for each
sub-swarms is accepted as a solution. Pseudo code for
Niche PSO is shown in Figure 2. Different steps of this
algorithm are explained in details in section below.
3.1. Training Main Swarm
Here, congnition-model (PSO) is used to update velocity

M. JAHANSHAHI
3
Create and initialize a
x
n demensioal main swa r m, S;
R
epeat
Train the main swarm, S, for one iteration using the
cognition-only model;
Update the fitness of each mai n swarm particle,
i
Sx
;
for each sub-swarm
k
S
do
Train sub-swarm particle,
ki
Sx , using a full model PSO;
Update each particle’s fitness;
Update the swarm radius
k
SR
;
End for
I
f possible, merge sub-swarms;
A
llow sub- swarm s to absorb any particle from t he m ai n swarm th at
moved in t o the s u b- s w arm ;
I
f possible, create new sub-swarm;
Until sto pping condition is true;
R
eturn
ˆ
k
Sy for each sub-swarm
k
S as a solution;
Figure 2. Niche PSO algorithm.
and position of the particles.
3.2. Training Sub-Swarms
Sub-swarms are independent swarms. In this paper, for
training those, local search methods are used such as
genetic algorithms, memetic and PSO. Use of methods
above for training sub-swarms improves this method.
3.3. Identification of Niches
When a particle is getting close to a local optimum, a
swarm is formed. If the acceptability rate of a particle
indicates tiny variation of some repetitions, then the
swarm will be formed by this particle and its nearest
neighbors. In simpler word, standard deviation (i

) oc-
curs in some repetition in objectiv e function (


i
f
x) for
each particle. If (i

 ), the swarm is formed. To pre-
vent the dependency problem, (i

) is normalized based
on domain. The nearest neighbor of for position of (i
x
)
of particle i, is given by Euclidean distance as follow:

argmin ia
a
lxx (3)
The process of swarm generation or niche identifica-
tion is summarized in Figure 3. In this algorithm, the
symbol Q indicates set of sub-swarms (

1,,
K
QS S)
where, (QK). Each sub-swarm has the number of
(ks
Sn) particles. At the time of Niche PSO generation,
the value of K is zero and Q is an empty set.
3.4. Absorbing Particles in Sub-Swarms
Particles of main swarm move towards an area that is
covered by the sub-swarms (k
S). These particles com-
bine with su b -swarm for reasons below:

if then
1
create su b-swarm ,;
Let ;
Let ;
i
kil
k
k
kk
Sxx
QQS
SSS
 




Figure 3. Generation algorithm of sub-swarms in Niche PSO.
 The particles move in search area for creation of a
sub-swarm may improve the diversity of sub-swarms.
 These particles in a sub-swarm increase the dispersion
of those to an optimum space via increase of general
information.
If for pa rt i cl e i we have:
ˆ
ik k
x
Sy SR

 (4)
Then the particle i is absorbed to sub-swarm (k S) in
such a way


kki
i
SSx
SSx

 (5)
In equation above, (k
SR) points to radius of
sub-swarm (k
S) and is defined as follow:


ˆ max..1, ,
kkkiiks
SR SySxSn

 (6)
Here, (ˆ
k
Sy

) is the best general position of
sub-swarm (k
S).
3.5. Merging of Sub-Swarms
Perhaps, more than one sub-swarms points to an opti-
mum point. Here, it is possible that a particle moves to a
solution is not absorbed to a sub-swarms. As a result, a
new sub-swarm will be generated and it leads to a prob-
lem that a solution is followed by several sub-swarms in
form of redundancy. For solving this problem, similar
sub-swarms must merge together. The sub-swarms are
the same if their space is considered in such a way that
radiuses of particles converge in sub-swarms. The new
merged sub-swarm has more general information and
uses experiences of both old sub-swarms. The results of
new sub-swarm are normally more accurate than the
smaller old sub-swarm. In simpler word, two sub-swarms
(k
S) and (1k S

) merge together if:

121 2
ˆˆ
kkk k
SySy SRSR

  (7)
If (12 0
kk
SRSR

) the following formula will be
replaced with equation 8.
12
ˆˆ
kk
SySy


 (8)
where µ is a tiny value tends to zero (e.g. 3
10 

). If µ
is a very large value, perhaps unsuitable sub-swarms
merge together and lead to failure of finding some solu-

M. JAHANSHAHI
4
tions. In order to keep µ in the domain, (12
ˆˆ
kk
SySy )
is normalized in (0, 1).
3.6. Stop Conditions
Several stop conditions may be used to finish the search
of solutions. Note that each sub-swarm has founded a
unique solution.
4. Used Local Search Method
We applied the PSO algorithm as a local search method
in Memetic which was introduced in section 2. We have
also utilized genetic algorithm and learning automata
which are briefly introduced in the next sub-section.
4.1. Genetic Search Algorithm
Genetic algorithm was introduced by John Haland for the
first time in 1975 and since then has been used for solv-
ing optimization problems [2]. Genetic algorithms have
great applications in random searches and optimization
techniques. Today's those are known more as type of
evolutional calculations. This algorithm is similar to
natural evolution process and unlike the other methods,
uses a population for search in solution space and always
applies the principle “survival based on eligibility” to
population. Based on this principle, after creation of
every generation, unqualified chromosomes will be
killed and eliminated from populations, only suitable
chromosomes will be remained and create next genera-
tion and make suitable solutions from those.
If genetic algorithm is designed well, all the popula-
tion will converge to a unique global optimum solution.
Genetic algorithms are so powerful and effective and
practical for problems with no systematic solutions.
4.2. Theory of Learning Automata
In this section the Learning Automata for the proposed
framework will be briefly reviewed;
Learning automata (LA) is an abstract model that
chooses an action from a finite set of its actions ran-
domly and takes it [4,13]. In this case, environment
evaluates this taken action and responses by a reinforce-
ment signal. Then, learning automata updates its internal
information regarding both the taken action and received
reinforcement signal. After that, learning automata
chooses another action again. Figure 4 depicts the rela-
tionship between learning automata and environment.
Every environment is represented by {, ,}Ec

 , where


12
,,,
r

   is a set of inputs ,

12
,,,
r

  
is a set of outputs, and

12
,,,
r
ccc c is a set of pen-
Figure 4. Interaction between learning automata and envi-
ronment.
alty probabilities. Whenever set

has just two mem-
bers, model of environment is P-model. In this environ-
ment 11


, 20


are considered as penalty and
reward respectively. Similarly, Q-model of environment
contains a finite set of members. Also, S-model of envi-
ronment has infinite number of members. i c is the pen-
alty probability of taken action i

.
Learning automata is classified into fixed structure and
variable structure. Learning automata with variable struc-
ture is introduced as follows; Learning automata with
variable structure is represented by

,,,pT  , where


12
,,,
r

  is a set of actions,

12
,,,
r

  
is a set of inputs,


12
,,,
r
ppp p is the action
probability vector, and






1,,pnTnn pn  

is learning algorithm. Learning automata operates as
follows; learning automata chooses an action from its
probability vector randomly (i P) and takes it. Suppose
that the chosen action is i

. Learning automata after
receiving reinforcement signal from environment updates
its action probability vector according to formulas 9 and
10 in case of desirable and undesirable received signals
respectively. In formulas 9 and 10, a and b are reward
and penalty parameters respectively. If a = b then algo-
rithm is named
R
P
L

. Also, if ba then the algo-
rithm is named
R
P
L

. Similarly, if b = 0 then the algo-
rithm is called
R
I
L

.



 
 
11
1
ii i
jjj
pnpn apn
pnpn apn
jj i
 
 

(9)




 
11
11
1
ii
jj
pnb pn
b
pn bpn
r
jj i

 


(10)
5. Proposed Methods
In this paper, to make Niche PSO, more effective, me-
metic method has been used for training the particles in
each sub-swarm. This paper introduces three different
methods resulting from combination of intelligent search

M. JAHANSHAHI
5
methods by Niche PSO for improvement of this method.
In proposed methods in each sub-swarm, a set of parti-
cles is chosen and improved by one of local search
methods. Improved particles are added to set of whole
particles and from those, enough sub-swarms will be
chosen. The structure of memetic method and proposed
method are shown in order, in Figures 5 and 6.
For training the particles inside each niche, genetic
algorithm by training single particle, genetic by training
several particles and PSO have been used.
In continue, details of used algorithms are presented as
a local search in memetic method.
Figure 5. Memetic algorithm.
Initial
population
(N)
Population
after
selection
Trained
popu lation (K)
Combi ning the init ial an d
traine d po p ul at ions
(N + K)
Selection
Training
using the
proposed
methods
Figure 6. Proposed framework.
5.1. GA-Based Local Search Method
As described above, we have used GA as local search in
Memetic method. Mutation operator of GA was done as
follows. The best particle of sub-swarm is chosen and its
value is converted to a binary number. Then Mutation is
applied to it once, if the value of new particle is getting
better the old one, new particle will be replaced with the
old one. We name this method as GA1.
We also propose another GA-based method in which
the Mutation operator was accomplished as follows. In
each sub-swarm, one quarter of the particles are chosen
randomly. Then single point Mutation is applied to each
particle up to maximum three times. Each time if the
generated particle is better than the old one, it will be
replaced with the old one and next go to another particle.
We call this method as GA2
5.2. PSO-Based Local Search Method
In this method, PSO algorithm is used as local search.
This method is done in two ways: one glob al best (a ll the
swarms) and another local best (inside the sub-swarm)
that by global best method poor results are obtained.
5.3. LA (LR – P)-Based Method
This method uses learning automata to update the veloc-
ity of particles. In this method two functions are consid-
ered to update particles velocity by learning automata.
The first operation means to consider the effect of global
best of subgroup for updating a particle and the second
operation means to update velocity of the particle with-
out consideration of the global best of subgroup. After
applying these functions to whole particles of subgroup
if the total values of particles is less than the old total
value of the particles then automata is rewarded other-
wise is penalized.
5.4. LA (LR – I)-Based Method
This method is similar to method above. The only dif-
ference is that after doing Automata functions on whole
particles of subgroup, if the total values of current parti-
cles is less than the old particles then the automata is
rewarded but if the total value of particles is more than
old total values the automata is not penalized.
6. Simulation Results
In this section, the results of simulations are presented
compared with original Niche PSO method to be run in
Matlab 7.04. The aim of running all the methods in all

M. JAHANSHAHI
6
Figure 7. Approaching the particles to the local optima.
Figure 8. Forming sub-swarms.
Figure 9. Full running of algorithm and combination of
sub-swarms and reaching all the optimum solutions.
simulations is to find optimum points of a following
standard function.


 






 
exp2log220.080.8542
sin56
yx
pi x
 
 (9)
In all simulations, PSO parameters are initially valued
as follow:
11.2c

0.01a 
1rabarand  
40pop

21.2c 1b
 2rabarand  
Also the value of inertia weight w is given by the fol-
lowing formula where, T is the maximum repetition and t
is current time of simulation.
1
0.50.3 1
t
wT


 



(10)
Figures 7 to 9 shows the result of a sample of running
algorithm and the process of reaching optimum solution
for particles during simulation.
Figure 10, depicts the diversity rate of particles during
different simulations. This results are gained from 10
times repetition of an algorithm that its accurate results is
listed in Table 1 in which the values are gained by taking
the mean of variance for whole particles during the pe-
riod of each step of simulation. As depicted in this figure,
the method LA (
R
P
L

)-based has the most diversity rate
and hence outperforms the others schemes. In this
evaluation, LA (
R
I
L

)-based method stands in the sec-
ond place. Table 2 lists the divergences behavior of the
proposed designs over the 50 runs. From the results, LA
(
R
I
L

)-based method has the least divergence rate and
hence outperforms the other methods in terms of con-
vergence rate.
7. Conclusions and Future works
In this paper, five combinational methods were presented
Figure 10. Diversity of particles in various algorithms.

M. JAHANSHAHI
7
Table 1. Diversity rate of particles in various algorithms in 10 times of simulations.
GA1 GA2 PSO-based Niche PSO
LA (
R
P
L

) LA (
R
I
L
)
0.0391 0.0309 0.0302 0.0296 0.0331 0.0331
0.0363 0.032 0.0359 0.0284 0.0315 0.0315
0.0311 0.0377 0.0319 0.0321 0.0397 0.0315
0.0299 0.0269 0.031 0.0357 0.0314 0.0314
0.0299 0.0297 0.0315 0.0265 0.0391 0.0329
0.0413 0.0316 0.0267 0.0268 0.0301 0.0301
0.0292 0.0384 0.0329 0.0256 0.0336 0.0336
0.0292 0.0327 0.0267 0.0272 0.0311 0.0397
0.0285 0.0279 0.0272 0.0292 0.0299 0.0329
0.0308 0.0283 0.0397 0.0329 0.0391 0.0317
Table 2. Divergence rate of different algorithms.
LA (
R
I
L

) LA (
R
P
L
) Niche PSO PSO-based GA2 GA1
5 11 12 15 8 12
to raise the diversity of particles and improvement of
convergence of NichePSO as two assessment factors of
search methods. From the results, LA (
R
P
L)- and LA
(
R
I
L)-based methods outperform other methods in terms
of diversity and convergence rates, respectively.
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