1. MODIFICATIONS OF PARTICLE SWARM OPTIMIZATION
PARAMETER AND PERFORMANCES
JITENDRA SINGH BHADORIYA1 ,School of Instrumentation DAVV, Indore
AASHISH KUMAR BOHRE2,Maulana Azad National Institute of Technology, Bhopal
Dr. GANGA AGNIHOTRI3, Maulana Azad National Institute of Technology, Bhopal
Dr. MANISHA DUBEY4, , Maulana Azad National Institute of Technology, Bhopal
ABSTRACT- modifications have been made to
specific problem.
The importance of soft computing
techniques is increasing day by day. In
this paper we have focused on the I. INTRODUCTION-
particle swarm optimization that is Rapid developments in computing-related
landmark for engineering optimization disciplines and technologies have enabled
problems. The changes in pso are taking the collection of unprecedented amounts of
place and today we have large number data at unprecedented rates from systems
of modified PSO method. In this paper as diverse as the World Wide Web, the
we are dealing with the modified PSO to human body, the human genome, planetary
overcome of the disadvantage of environments (the Earth as well as other
standard PSO. Study is carried out to planets), as well as many industrial
the modification of standard PSO for systems such as financial markets, aircraft
eliminating certain disadvantages. Some engines, and power plants. Soft computing
new ideas are also given for refers to algorithms that are able to cope
modification in pso keeping mind with uncertainty and incomplete
several parameter of this technique. information and that are still capable of
PSO always converges very quickly discovering approximate, good solutions to
towards the optimal positions but may complex computational problems, and
slow its convergence speed when it is doing so faster from a computational
near a minimum. We empirically study standpoint. These algorithms include
the performance of the particle swarm neural nets, fuzzy logic, rough set,
optimizer (PSO). Four different Bayesian algorithms, evolutionary
computing (genetic algorithms and particle

2. swarm optimization). PSO is getting when compared with mathematical
popularity due to its good convergence algorithm and other heuristic optimization
rate, however for some specific problems Techniques.
modification in original PSO have been
done. We have presented some modified
PSO algorithm to overcome the III. PSO ALGORITHM-
disadvantage of standard PSO The PSO algorithm is initialized with a
population of random candidate solutions,
conceptualized as particles. Each particle
II. PARTICLE SWARM is assigned a randomized velocity and is
OPTIMIZATION- iteratively moved through the problem
space. It is attracted towards the location
Particle swarm optimization (PSO) is one of the best fitness Achieved so far by the
of the modern heuristic algorithms, which particle itself and by the location of the
can be used to solve nonlinear and non- best fitness achieved so far across the
continuous optimization problems [1]. It is whole population (global version of the
a population-based search algorithm and algorithm). The Particle Swarm
searches in parallel using a group of Optimization (PSO) belongs to the
particles similar to other AI-based category of Swarm Intelligence methods.
heuristic optimization techniques. The PSO, which was first proposed by
original PSO suggested by Kennedy and Kennedy and Eberhart in 1995, is a
Eberhart is based on the analogy of swarm famous population-based search algorithm
of bird and school of fish [2]. Each particle In PSO, each individual (particle) flies
in PSO makes its decision using its own through the problem space with a velocity.
experience and its neighbor’s experiences The speed and direction of the velocity are
for evolution. That is, particles approach to adjusted based on the particle’s previous
the optimum through its present velocity, best experience (self-cognitive) and the
previous experience, and the best historical best experience in its
experience of its neighbors [3]. The main neighborhood (social-influence). In this
advantages of the PSO algorithm are way the particle has a tendency to fly
summarized as: simple concept, easy towards a promising area in the search
implementation, robustness to control space. In PSO, each individual flies in the
parameters, and computational efficiency search space with a velocity which is

3. dynamically adjusted according to its own iteration is computed by adding its
flying experience and its companions velocity vector to its current position.
flying experience. Consider that we are searching in a d-
dimensional search space. Let Xi = (Xi1 Xi2
... Xid) and Vi = (Vi1 Vi2...Vid). Be i-th
particle's position vector and velocity
vector respectively. Velocity of each
particle is adjusted according to eq. (1) [].
v(i+1) = w*v(i) + c1*r1* (pbest-
currentposition) + c2*r2* (gbest-
currentposition)……………………… (1)
x(i+1)=x(i) + v(i+1)………………… (2)
Where, d is the dimension, the superscript
i indicates the iteration number, w is the
inertia weight, r1 and r2 are two random
Figure – 1: Flow chart for Particle Swarm vectors with values in the range [0, 1], C1
Optimization (PSO) algorithm and C2 are the cognitive and social scaling
parameters which are positive constants .
PSO stores a population of potential
solutions to solve problems, like IV. ADVANTAGES AND
DISADVANTAGES OF PSO
evolutionary algorithms. The populations
initialized by random particles in each
A PSO is considered as one of the most
iteration of the algorithm, particles update
powerful methods for resolving the non-
their position according to their personal
smooth global optimization problems-and
experiences and their neighbor's best has many key advantages as follows:
position. The velocity vector of each PSO is a derivative-free technique
particle is responsible to update the just like as other heuristic
particle position which is given in eq. (2). optimization techniques.
The position of each particle in the next

4. PSO is easy in its concept and theories. Also, it can have some limitations
coding implementation compared for real-time applications such as 5-
to other heuristic optimization minute dispatch considering network
techniques. constraints since the PSO is also a variant
PSO is less sensitivity to the nature of stochastic optimization techniques
of the objective function compared requiring relatively a longer computation
to the conventional mathematical time than mathematical approaches.
approaches and other heuristic However, it is believed that the PSO-based
methods. approach can be applied in the off-line
PSO has limited number of real-world ED problems such as day-ahead
parameters including only inertia electricity markets. Also, the PSO-based
weight factor and two acceleration approach is believed that it has less
coefficients in comparison with negative impact on the solutions than other
other competing heuristic heuristic-based approaches. However, it
optimization methods. Also, the still has the problems of dependency on
impact of parameters to the initial point and parameters, difficulty in
solutions is considered to be less finding their optimal design parameters,
sensitive compared to other and the stochastic characteristic of the
heuristic algorithms [4]. final outputs. PSO may lack global search
PSO seems to be somewhat less ability at the end of a run due to the
dependent of a set of initial points utilization of a
compared to other evolutionary linearly decreasing inertia weigh. The PSO
methods, implying that may fail to find the required optima in
convergence algorithm is robust. cases when the problem to be solved is too
PSO techniques can generate high- complicated and complex[12].
quality solutions with in shorter
calculation time and stable V.MODIFIED
convergence characteristics than METHODOLOGY
other stochastic methods [5].
OF PSO-
The major drawback of PSO, like in other
PSO have been modified to overcome the
heuristic optimization techniques, is that it
disadvantage of conventional pso for
lacks somewhat a solid mathematical
increase the reliability , convergence ,
foundation for analysis to be overcome in
divergence . the changes have been done
the future development of relevant

5. in factors or co-efficient related to PSO a. MPSO Algorithm
equation like weighting factor , Begin
acceleration and so on. There is while NFC < MAXNFC
description of some of the modified do
version of PSO . for i=1 to ps
In MPSO , author propose a do
modified PSO algorithm to Update velocity of the ith
enhance the performance of particle according to (1);
PSO[6]. The proposed approach, Update position of the ith
namely MPSO, employs a novel particle according to (2);
local search technique, which helps Calculate the fitness value of
to concentrate the particles in the ith particle;
current search space around the NFC++;
global best particle In MPSO, end for
author propose a new local search Update the pbest and gbest, if
technique to create trail particles, needed;
in order to replace the worst Calculate the boundaries of
particle in the population. This current search space;
technique helps to concentrate the Create a random particle Y
particles in current search space according to (3);
around the global best particle. In Create a trail particle X*
every generation, we create a trail according to (5);
particle X*, and compete it with the Calculate the fitness value of
worst particle is current population. X*;
The trail particle can be regarded NFC++;
as a neighbor around the global If X* is better than Xw
best particle. This will be then
beneficial to generate high quality Replace Xw with X*;
candidate solutions and accelerate end if
the convergence speed. The main Update the pbest and gbest, if
steps of the proposed approach are needed.
described as follows. end while
End.

6. In this paper, author introduce that the inertia weight is
cloud model theory to the particle nonlinearly, dynamically changed
swarm optimization algorithm to to have better dynamics of balance
improve the global search ability between global and local search
and make a faster convergence abilities during the search process.
speed of the algorithm[7]. In most In this paper, to efficiently provide
research on the PSO algorithms, a balance between global and local
population of particles is uniformly exploration abilities, we present the
generated with random positions, new method for using the normal
and then random velocities are cloud to nonlinearly, dynamically
assigned to each particle in the adjust the inertia weight through
process of initialization [13]. The the course of the run. In the mPSO
general location of potential algorithm, each particle of the
solutions in a search space may not swarm shares mutual information
be known at advance. In this paper, globally and benefits from
the cloud model is adopted to discoveries and pervious
initialize particles throughout the experiences of all other colleagues
initialization range for its position during the search process.
and velocity vectors, which can
rather reflect the flocking behavior When standard PSO optimizes
of bird or school of fish. The Complex multi-peak functions,
inertia weight is used to control the because all swarms are affected by
momentum of the particle by the historical global best position (
weighing the contribution of the gbest ) and fly to the gbest , so
previous velocity basically diversity of population reduces
controlling how much memory of quickly, whereas, the gbest may be
the previous flight direction will a local optimal solution, which
influence the new velocity and leads to all particles fast
balance the global and local search convergence in local optimum.
ability. A large inertia weight After each iteration in [14], the
facilitates global exploration, while particle of the worst fitness value
a small one tends to facilitate local of the first sub-swarm exchanges
exploration. It is crucial in finding with the particle of the best fitness
the optimum solution efficiently value of the second sub swarm. If

7. the particle of the best fitness value seeking neighborhood and diversity
of the second sub-swarm just fall of population is guaranteed.
over optimal particle’s Particle swarm optimization
neighborhood, which causes method in comparison with most of
particle to jump out the optimal optimization algorithms such as
particle’s neighborhood because of genetic algorithms is simple and
particle’s exchange. Based on fast. But the basic form of Multi-
above analysis, a modified two objective Particle Swarm
sub-swarms particle swarm Optimization may not obtain the
optimization is proposed, which best Pareto. By applying some
divides the particle swarm into two modifications to make it more
groups with the same size[8]. The efficient in finding optimal Pareto
first swarm adopts the standard front[9]. The main objective of
PSO model, the second adopts the every multi-objective optimization
Cognition Only model. In the algorithm is to find Pareto-optimal
seeking process, When the two set. These optimal set balances the
sub-swarms evolve steady states tradeoffs among the conflicting
independent(The differences of the objectives. The concept of Pareto
optimal fitness value after twice are optimality was conceptualized by
less than a predetermined the Italian economist, Vilfredo
threshold), a certain amount of Pareto, in his work, Manual of
particles of the second sub-swarm Political Economy in 1906 [15].
that are extracted randomly First step in any multi objective
exchange with the worst fitness optimization algorithm is to
value of particles of the first sub- minimize the distance between
swarm, and the steps are repeated solutions and the Pareto front. For
as above. Thus it can ensure the this objective appropriate fitness
diversity of population in the first functions must be defined.
group ,and the second groups seek Traditional type of assigning
the optimal solution in the search fitness function is aggregation–
process. When two groups based method, where the fitness
exchange, swarms recover life. function is a weighted sum of the
That is, extreme points are found in objective functions. However this
classic approach can be very

8. sensitive to precise aggregation of is affected by its own experience
goals and tend to be ineffective and and the experience of the best
inefficient [15]. Some newer performing member of the social
approaches for fitness assignment groups it is a member of. In the
are on the base of Pareto proposed Adaptive membership C-
dominance, where fitness is PSO (AMC-PSO), a time varying
proportional to the dominance rank default Membership is introduced.
of solutions. For better search of This modification enables the
the area and avoiding converge to particles to explore the space based
false Pareto a mutation operator is on their own experience in the first
proposed. The effect of mutation stage, and to intensify the
operator decreases with respect the connections of the social network
number of iterations. It is in later stages to avoid premature
controlled with the parameter convergence. This proposed
mutrate [16]. This algorithm dynamic neighborhood algorithm is
presents a good diversity in Pareto compared with other PSO
front. But some points in edge of algorithms having both static and
Pareto front are not found. In dynamic neighborhood topologies
practice we may be interested in on a set of classic benchmark
finding these points. For example problems. Particle swarm
in some applications, high optimizers are very sensitive to the
absorption is very important even if shape of their social network.
the thickness is high. To obtain Above modified PSO lack the
these edges in Pareto front, we ability of adapting their social
should apply a modification to this network to the landscape of the
algorithm. problem they optimize. The
This modification introduces a proposed AMC-PSO algorithm
new dynamic neighborhood overcomes this problem.
network for particle swarm This presents a modification of tlte
optimization[10]. In Club-based particle swarm optimization
Particle Swarm Optimization (C- algorithm (PSO) intended to
PSO) algorithm, each particle combat the problem of premature
initially joins a default number of convergence observed in many
social groups (clubs). Each particle applications of PSO[11]. The

9. proposed new algorithm moves all the disadvantage is not
particles towards nearby particles eliminated completely at a time.All
of higher fitness, instead of the modified PSO does not give
attracting each panicle towards good results on all of the
just the best position discovered so benchmark function ,however these
far by any particle. This is modified PSO are good for a
accomplished by using the ratio of specific application efficiently .the
the relative fitness and the distance modification in pso should be such
of other particles to determine the that it optimize the problem
direction in which each component universally not a specific problem.
of particle position needs to be The modification have been done
changed. The resulting algorithm on the basis of weight factor ,
(FDR-PSO) is shown to perform acceleration , and in PSO equation
significantly better than the , while modifying PSO a good
original PSO algorithm and some mathematical analysis should be
of its variants, on many different done before testing it on the
benchmark optimization problems. benchmark function . the
Empirical examination of the modification in PSO could be done
evolution of particles demonstrates using different particle and
that the convergence of the analyzing their social behavior ,
algorithm does not occur an early depending on the intelligence of
phase of panicle evolution, unlike particle the modification will have
PSO. Avoiding premature good results on benchmark
convergence allows FDR-PSO to function ,so it will also have good
continue search for global optima convergence rate.
in difficult multimodal
optimization problems.
REFERENCES-
VI. CONCLUSION-
[1] K. Y. Lee and M. A. El-Sharkawi
There are several modification (Editors), Modern Heuristic Optimization
have been done in Particle Swarm Techniques with Applications to Power
Optimization for enhancing the Systems, IEEE Power Engineering Society
ability of PSO. In modified method (02TP160), 2002.

10. International Conference on Advanced
[2] J. Kennedy and R. C. Eberhart, Intelligent Mechatronics July 2 - 5, 2008,
“Particle swarm optimization,” Xi'an, China.
Proceedings of IEEE International
Conference on Neural Networks [8] J. Zhao “A Modified Two Sub-swarms
(ICNN’95), Vol. IV, pp. 1942-1948, Perth, Exchange Particle Swarm Optimization “
Australia, 1995. 2010 International Conference on
Intelligent Computation Technology and
[3] J. Kennedy and R. C. Eberhart, Swarm Automation 978-0-7695-4077-1/10 $26.00
Intelligence, San Francisco, CA: Morgan © 2010 IEEE DOI
Kaufmann Publishers, 2001. 10.1109/ICICTA.2010.718 180.
[4]R. C. Eberhart and Y. Shi, “Comparison [9] S. Chamaani “Modified Multi-
between genetic algorithms and particle objective particle swarm optimization for
swarm optimization,” Proc. IEEE Int. electromagnetic absorber design” 2007
Conf. Evol. Compu., pp. 611-616, May asia –pacific conference on applied
1998. electronics proceedings dec 4-6 melaka,
Malaysia.
[5] Z. L. Gaing, “Particle swarm
optimization to solving the economic [10] Hassan M. Emara “Adaptive Clubs-
dispatch considering the generator based Particle Swarm Optimization ” 2009
constraints,” IEEE Trans. on Power American Control Conference Hyatt
Systems, Vol. 18, No. 3, pp. 1187-1195, Regency Riverfront, St. Louis, MO, USA
Aug. 2003. June 10-12, 2009.
[6] Q. Yang, G. Lili “Modifications of
Particle Swarm Optimization for Global [11] Thanmaya Peram, Kalyan
Optimization” 2010 3rd International Veeramachaneni and Chilukuri K. Mohan
Conference on Biomedical Engineering “Fitness-Distance-Ratio Based Particle
and Informatics (BMEI 2010). Swarm Optiniization” 0-7803-7914-
4/03/IEEE
[7] J. Wen “A Modified Particle Swarm
Optimizer Based on Cloud Model”
Proceedings of the 2008 IEEE/ASME

11. [12] Yuhui Shi, Russell C. Eberhart BIOGRAPHIES—
“Empirical Study of Particle Swarm
Jitendra Singh Bhadoriya,
Optimization” 01999 IEEE.
[13] R. Brits, A. P. Engelbrecht, F. van
den Bergh, “Locating multiple optima
using particle swarm optimization,”
Applied Mathematics and Computation, Jitendra Singh Bhadoriya was born in
no. 189, pp. 1859-1883, 2007. Distt. Bhopal , India, in 1989. He received
BE degree (2011) from UIT- RGPV
[14] Shen Lin-cheng , Huo Xiao-hua, Niu Bhopal in electrical engineering , and at
Yi-feng. “Survey of discrete particle the moment he is an M-Tech
swarm optimization algorithm, ”Systems (instrumentation) scholar at SCHOOL OF
Engineering and INSTRUMENTATION, Devi Ahilya
Electronics,2008,30(10):1986-1994. University (DAVV) , lndore, India. Email:
JITENDRIY@INDIA.COM
[15] A. P. Engelbrecht, fundamentals of Aashish Kumar Bohre,
computational swarm intelligence,
John Wiley & sons, 2005.
[16] C.A. Coello Coello, G. Toscano
Pulido, and M. Sazar Lechuga,
“Handling multiple objectives with
Aashish Kumar Bohre was born in Distt.
particle swarm optimization,” IEEE
Hoshangabad, India, in 1984. He received
Trans Evolutionary Computat. vol. 8,
BE degree (2009) from UIT- RGPV
pp. 256–279. 2004.
Bhopal, and M-Tech degree (Power
System) in 2011 from MANIT, Bhopal. At
the moment he is PhD. scholar at MANIT,
Bhopal, India. Email:
aashish_bohre@yahoo.co.in

12. Dr. Ganga Agnihotri, Technology, Bhopal, India. Her research
interests include power systems, Genetic
Algorithms, Fuzzy Logic systems and
application of Soft Computing Techniques in
power system dynamics and control.
Email:manishadubey6@gmail.com
Dr. Ganga Agnihotri received BE degree
in Electrical engineering from MACT,
Bhopal (1972), the ME degree (1974) and
PhD degree (1989) from University of
Roorkee, India. Since 1976 she is with
Maulana Azad College of Technology,
Bhopal in various positions. Currently she
is professor. Her research interest includes
Power System Analysis, Power System
Optimization and Distribution Operation.
Dr. Manisha Dubey
Dr. Manisha Dubey was born in Jabalpur
in India on 15th December 1968. She
received her B.E (Electrical), M.Tech.
(Power Systems) and Ph.D (Electrical
Engg.) in 1990, 1997 and 2006
respectively. She is working as Professor
at the Department of Electrical
Engineering, National Institute of