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Corresponding Author: Soodabeh Darzi is currently Master in Electrical Engineering, Universiti Tenaga Nasional. E-mail: sdtutn@yahoo.com

490

Overview of Particle Swarm Optimization (PSO) on its Applications and Methods

1

Soodabeh Darzi,

2

Tiong Sieh Kiong,

3

Balasem Salem

1

Faculty of Electrical Engineering, Universiti Tenaga Nasional

2,3

Center of System and Machine Intelligence, Universiti Tenaga Nasional

Abstract: Particle Swarm Optimization (PSO) that is famous as a heuristic robust stochastic optimization technique works in field of Artificial Intelligence (AI). This technique of optimization is inspired by certain behaviors of animals such as bird flocking. The base of PSO method is on swarm intelligence that has a huge effect on solving problem in social communication. Hence, the PSO is a useful and valuable technique with goal of maximizing or minimizing of certain value that has been used in wide area and different fields such as large field of engineering, physics, mathematics, chemistry and etc. in this paper, following a brief introduction to the PSO algorithm, the method of that is presented and it’s important factors and parameters are summarized. The main aim of this paper is to overview, discuss of the available literature of the PSO algorithm yearly.

Key words: Heuristic Optimization, Particles Swarm Optimization (PSO), Applications.

INTRODUCTION

Nowadays, optimization plays a significant key role in a mathematical discipline that concerns the finding of minima and maxima of functions or process. Maximization of a function f is equivalent to minimization of opposite of this function, −f (Frans, 2002). Optimization consists of different techniques that improves the throughput of system and is used in different fields such as computer knowledge and AI and also has a great effect on industrial and business.

According to (Mukherjee and Ray, 2006), there are two types of optimization techniques including of conventional techniques that is optimal solution and non conventional techniques that is near optimal solution. In the non conventional techniques there are various Meta heuristic techniques that a large number of these inspired by animal behaviors and their environment. For example, Genetic Algorithms (GA), Artificial Bee Colony (ABC), PSO, Ant Colony Optimization (ACO), and Simulated Annealing (SA). As said by (Vob, 2001), the Meta heuristic technique is an advanced process that solves the problem by high quality solution. The Meta heuristic search has a large family of different methods that cannot be limited to ant system variable neighborhood search, neural network evolutionary methods and their hybrids.

One of the best optimization techniques based on population search is PSO and GA as search of (Ganesan et al., 2011). Furthermore, for enhancing the performance of controller can use the various methods of AI and random search such as Fuzzy System (FS), GA and Neural Network (NN) while, there are some shortage for them. The GA has complex calculation and FS for optimizing uses many parameters and also NN has not common standard for organization and composition. But PSO is a biologically-inspired technique that can solve and optimize the nonlinear problems in complex search region (Kennedy and Eberhart, 1995, Van and Engelbrecht, 2001).

The earliest PSO technique opened by (Kennedy and Eberhart, 1995) based on two ideas. The first one is depending on behavior of animals and based on swarm intelligence. But the second one is separated idea from the first one and based on evolutionary calculation. The certain kind of animals which have significant effect on generating of PSO are members of bird flocking and fish schools that can take the synchronize movement by any collide that various researcher studied about that (Heppener and Grenander, 1990, Reynolds, 1987). PSO is the stochastic technique that has related to GA and Evolutionary Strategies (ES), and also from time to time with the Evolutionary Computation (EC) techniques (Kennedy et al., 2001).

Description of PSO:

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Nowadays, PSO works with particle as bird that randomly generates them and moves in limited search space. Each particle has position and velocity separated from other one (Figure1). There is fitness function in PSO technique in order to take the best answer during optimization that can to calculate for each particle. Among the search space, each particle generates the new position and velocity and updates the previous one to facilitate for earn the better fitness value. This updating is cause of the moving the group of particles towards the desired region that is the section with the highest fitness value. Finally, all of particles gather in wanted spot with the best fitness value that is the best objective value known as global best fitness with best position and velocity (Karl, 2005, Shi and Eberhart, 1998).

Fig. 1: Produce Randomly Population and Velocity.

Update the velocity and population are as below:

(1) V: Velocity

Weight

Cognitive coefficient Random cognitive coefficient

Individual best solution Social coefficient

Random social coefficient : Global best solution

The parameters W, C1, and C2 are user-supplied coefficients. The weight can change from 0 to 1.2 and C1 and C2 value change from 0 to 2. The value of R1 and R2 that change from 0 to 1 are random standards that regenerated for each updating velocity. In the updating velocity each gathering plays the considerable task in the PSO technique.

The first one include: that plays the duty of inertia part. The task of this part is caring of particles movement that means keeping travel of particles in same direction. The weight W also has great effect on accelerate of particles in its original path. The majority of time the researchers chose value for W from 0.4 to 1.2 while in this case is choosing the two value for W. In this research for increasing the speed of convergence the weight W at beginning of optimization is 0.9 because of upper value push the particle to seek out in every part of search space and the end reach to 0.4 for the reason that the poorer value amplifies the rate of meeting the particles to optimization.

The second gathering is including: which the name of that is

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The last gathering takes account of: which the given name of

that is the social element. The task of this part plays the ending task and completed the task of interest group because in this step all particles that gathered in defined place with high individual fitness value now shift to the next and finest place mean the place with peak fitness value. That’s why all of particles get-together in preferred place. C2 in this part is the social coefficient and the value of that is 2 or close to that (same C1) because this value has great effect on period of this step that particles shift toward the best global fitness function gbest. Other one of the social coefficient in this part is R2 that also same to the R1 in second gathering is random coefficient. The random value as coefficient for this part is important decides on the movement of particles toward the desired place (place with best global fitness function) is the semi-random.

In this study uses Equations and assumes for update velocity as below:

(2)

Where:

(3)

Ws: Start weight=0.9 We: End weight=0.4

Wst: Weight step it: iteration

Max it: Maximum iteration

Later on updating the velocity for each solution be able to calculation the new population for everyone one. In support of updated population need call the previous population with new velocity according to Equation (4):

(4) Where the V is updated velocity (Zŭperl et al., 2007) have suggested seven different steps for solving the problem by using the PSO as below:

a. Generation of 50 particles with random velocities and positions with two dimensions in velocity vectors. b. Evaluation of fitness functions for each one.

c. For each new position calculated the objective value if achieved to better position, the p best is replaced by current value.

d. Determination if the particles achieve to maximum one in population. Compare the g best value with previous one and replace and store that if the new one is better.

e. Update the particles velocities f. Update particles position

g. Repeated steps c, d, e and f until the iteration number be the maximum one.

While other researcher suggested repeat just three steps for PSO algorithm until stopping iteration (Kennedy and Eberhart, 1995).

1. Calculate the fitness function for each population 2. Update local and global best position

3. Update population and velocity for each particle

Figure 2 illustrates standard flowchart of PSO by (Zŭperl et al., 2007) as below:

Figure 3 shows the operation of PSO briefly. At second picture there is produce randomly velocity and population while pictures 4, 5, and 6 illustrate particles are trying to gather in local and global best position. According to picture 9, at final all of the particles gather in global best position.

Review on Major PSO Based Algorithms Yearly:

In this part the previous researches in various years have been done by PSO technique is described and discussed. (Kennedy and Eberhart, 1997) has been generated a new type of PSO that probability of region of search is zero or one, known as Binary PSO (BPSO). After four years Shi and Eberhart in 2001 have been generated other types of PSO that used fuzzy method and PSO together in order to optimization by Fuzzy PSO (FPSO) technique. In this technique the operators are various for example reproduction and mutation (Shi and Eberhart, 2001).

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grouping of PSO and evolutionary programming, and SEPSO (Krink et al., 2002) used for enhanced convergence in some group consist of set of related particle in sub swarm.

Fig. 2: Proposed Algorithm for PSO.

Fig. 3: Operation of PSO.

In 2003 Peram et al, Secrest and Lamont discovered new kinds of PSO algorithms with the names of Fitness to Distance Ratio PSO (FDRPSO) and Gaussian PSO (GPSO). FDRPSO operates based on maximum fitness value. The particle has higher fitness value is placed in best position and the change of other particle position is depend on ratio of relative of that and distance of other one (Peram et al., 2003). One of the variant kinds of PSO is GPSO that shows the random nature of PSO in order to consider of tuning for represent the weak point in algorithm and optimize that. In this technique, the Gaussian distance between global and individual best and moving swarm is requirement (Secrest and Lamont, 2003).

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In 2005 the researchers paid more attention to PSO and generated the more kind of PSO such as Angle Modulated PSO (AMPSO), Parallel PSO (PPSO) and Niching PSO (NPSO). According to (Pampara et al., 2005), AMPSO similar to Binary PSO (BPSO) used the bit string but in operation is different. Because this technique attempts to simplicity the problem and generation of lower dimensional binary vector in order to decrease the complexity. In this time a parallel calculation is used in PPSO in order to decrease the period of time of optimization. This technique saves the time when large level of problem is solving (Chang et al, 2005). According to Brits in order to solve the multiple problems can use the NPSO technique. In this technique particles moves with the goal of multiple optimization. In NPSO method, particles with small amount of vary fitness value separated in each iteration and kept in sub swarm in order to help to find the global and local best (Brits et al, 2005).

In 2006 there is an increasing various types of PSO in compare to previous years. Sedlaczek and Eberhard proposed the new kind of PSO in order to optimize and reach to best value with equivalent and different boundary for limitations (Sedlaczek and Eberhard, 2006) because the defined boundary in PSO has a significant effect on throughput of the system. While according to (Zeng et al., 2006), acceleration information has a huge effect on adaptive PSO and attempts to enhance efficiency of system for find best value as soon as possible. In PSO technique the optimization of free parameter needs to various swarms consideration inside the main one. As said by (Meissner et al., 2006), mentioned method result has better performance in compare to other ones. In the combined technique with PSO method the stability among the extract and finding is essential point. (Ozcan and Yilmaz, 2006) presented the Craziness PSO (CPSO) in order to make this balance. In this study the researchers used craziness and hill climbing algorithm to facilitate growing discovery and removal respectively. Self-Organization PSO (SOPSO) is another technique of PSO that used the enhancing extract and discovered of PSO in order to increase the performance of particle in each iteration (Jie et al., 2006). In keeping with Li, there is another attractive type of PSO technique that uses two swarms for optimization. These two swarms searching in defined space with moving particles in various direction in order to increase the chance of finding global best, and also other swarm simultaneously attempts to increase local discovery base on selected method (Li.T et al., 2006, Li.W et al., 2006)

In 2007 a large number of researchers studied on PSO and tried to construct new method for improving the performance of systems. (Huang et al., 2007), proposed a new technique based on combination of Neural Network (NN) and PSO technique for solving the problems. The results of this optimization in compared with NN presented more accurate estimation and faster convergence. (Jaafreh and Jumaily, 2007) used two different intelligence techniques known as PSO and Type-2 Fuzzy System (T2FS) and also tried to improve the system by new suggested technique that improves and adds accuracy to the T2FS by PSO and finally took the better answer and rate. (Alviar et al., 2007) used Best Rotation PSO (BRPSO) in order to optimize of multi-model functions via sub swarm extracted from particular swarm. Combinatorial PSO (CPSO) presented by (Jarbouia et al., 2007) with the goal of solving hybrid problems with integer variables. Optimization of single objective problem which consists of external file for save information of particle is done by using Constrained Optimization by PSO (COPSO) (Aguirre et al, 2007). According to (Felix et al., 2007) for solving multidimensional or large problems, Cooperative Multiple PSO (CMPSO) algorithm is used. To facilitate to design NN contain on combined weights, (Subrananyam et al., 2007) proposed Dual Layered PSO (DLPSO) technique that experienced by improving power transformer. Heuristic PSO (HPSO) is used to improve the convergence speed. In this algorithm, the best particle selecting for updating the previous position and velocity, has some differences from original PSO technique (Lam et al., 2007). To improve the efficiency of PSO, Predator Prey PSO (PPPSO) technique was proposed by (Jang et al., 2007) for solving prey and predator problem. The main objective of this technique is gathering particle in global best and avoids moving them toward local optima.

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(Xi and Liao, 2009) employed the PSO technique for optimizing the problem with three objective values. From the experimental results, they found the value that is much better than manual value. In addition, the experimental value is more reference value for others. Besides, (Kim et al., 2009) used the PSO in design of Type -2 Fuzzy Neural Networks (T2FNNs) and compared the result with conventional neural network and finally, obtained better performance. To enhance the performance of system, (Ho et al, 2009) presented the result of multiple assessment criteria and parallel test sheets and compare them with GA. In order to comparison, they used the published search in previous year (Ivan and Ciurea, 2008). (Sedighizadeh and Masehian, 2009) classified the PSO algorithm based on activity, divisibility, accordance, fuzziness, attraction, mobility, interaction, topology, continuity, cooperation, restriction, hierarchy, objective, grouping, recursively, and etc. They presented 41 various applications with PSO technique. These applications operate in extensive area and support large number fields such as chemical, mathematics, electrical and civil engineering. But these two researchers did not present application of PSO in field of e-education. (Dheeban et al., 2010) completed the Sedighizadeh and Masehian research by present the PSO with inertia-coefficient in order to improve e-learning courses composition. They also arranged the variant of PSO with experimental results better than Basic particle swarm optimization (BPSO) algorithm. (Bharathi and Baskar, 2010) optimized the matching process parameter for single and multi pass turning operation and surfaced one by using three different method of optimization including PSO and GA and SA. In this study they found that, the result of PSO is much better than other both. The result in single pass for PSO is 4.7% while this show 1% more than other one, and also in multi pass the result of PSO is 19.8% better than SA and GA equal to 12.5%. In the surface operation the amount of more percentage of result in compare to before one is equal to result of single one. It means 1% better than GA and SA while is 6.2%. In addition to, (Martinez et al, 2010 a, b) presented the PSO technique for solving the problem of control and taking the certain parameter. (Yang et al., 2011a) recommended the Fuzzy PSO (FPSO) technique based on fuzzy velocity updating for optimizing the parameters of problem. It shows the FPSO algorithm is the effective one and does not have any problem in converging toward optimize the objective. And also mentioned researchers (Yang et al., 2011b) proposed Fuzzy based Multi Objective PSO (F-MOPSO) as an optimization technique. This technique used for optimizing the multi objective problem and does not have any problem for various objective optimization. (Mohankumar et al., 2011) used the PSO and GA technique for solving the problem by minimization of time. The achieved result presented the t=3.131min in GA technique and t=0.000180min in PSO method. It is clear that PSO result is better than GA result. In addition, (Bingual and Karahan, 2011) and (Oh et al., 2011) presented PSO technique in their research and developed their work. The summary of the history of PSO research is illustrated in Table 1 as a below.

Table 1: Simplified History of PSO Research.

Year Authors Method Result

1995 Kennedy , Eberhart Particle swarm optimization(PSO)

1997 Kennedy, Eberhart Binary PSO (BPSO) increase the performance

2001 Shi , Eberhart Fuzzy adaptive PSO (FAPSO) increase the performance

2002 -Xie, Zhang,Yang

-Wei, He, Zhang, Pei

-Krink, Vesterstrom, Riget

-Adaptive PSO (APSO) -Evolutionary Programming and

PSO(EPPSO) -PSO with spatial particle extension

(SEPSO)

-solve the problem of inactive particles -set of scales between different search

-enhance convergence

2003 - Peram, Veeramachaneni, Mohan -Secrest, Lamont

-Fitness to Distance ratio PSO (FDRPSO) -Gaussian PSO (GPSO)

-higher fitness value -tuning for represent the weak point

2004 -Janson, Middendorf

-Wang, Li

-Hierarchical PSO (HPSO) -Hybrid PSO with simulate

annealing

-particles move in dynamic hierarchy -higher quality

2005 -Pampara, Franken, Engelbrecht

-Chang, Chu, Roddick, Pan

-Brits, Engelbrecht, Van den Bergh

-Angle Modulated PSO (AMPSO)

-Parallel PSO(PPSO)

-Niching PSO(NPSO)

-generation of lower dimensional binary vector to decrease the

complexity -decrease the period of time of

optimization -solving the multiple problems

2006 -Sedlaczek , Eberhard

-Zeng, Hu, Jie -Meissner, Schmuker, Schneider

-Ozcan ,Yilmaz -Jie, Zeng, Han -Li, Lai, Wu -Li, Yushu, Xinxin, Yuanqing

-augmented lagrangian PSO -Adaptive PSO guided by acceleration

information -Optimized PSO (OPSO)

-Craziness PSO (CPSO) -Self-Organization PSO (SOPSO) -An improved two-swarm based PSO

-PSO for fuzzy c-means clustering

-reach to best value with equivalent and different boundary for limitations

-enhanced efficiency of system -better performance -stability among the extract and finding, facilitate growing discovery -enhancing extract and discovery of

PSO

-increase local discovery ,increase the chance of finding global best -increase local discovery ,increase the

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2007 -Huang, Li, Lin

-Jaafreh, Jumaily - Alviar, Pena, Hincapie - Jarbouia, Cheikha, Siarryb, Rebaic

- Aguirre, Munoz Zavala, Diharce, Botello Rionda - Felix, Kumar, Mishra - Subrananyam, Srinivasan, Oniganti

- Lam, Nikolaevna, Quan - Jang, Kang, Lee, Kim, Shin

-PSO-based wavelet neural network in tool wear monitoring -Training type-2 fuzzy system by PSO

- Best Rotation PSO (BRPSO) - Combinatorial PSO (CPSO) - Constrained Optimization by PSO

(COPSO)

- Cooperative Multiple PSO (CMPSO) - Dual layered PSO (DLPSO)

- Heuristic PSO (HPSO) - Predator Prey PSO (PPPSO)

-more accurate estimation and faster convergence

-better answer and rate - optimization of multi-model functions

- solve hybrid problems with integer variables

- solve problem by external file for save information - solve multidimensional problems

- improve power transformer - improve the convergence speed - solve prey and predator problem

2008 -Li, Yao, Gao, Liu,Yuan

- Chen, Li[44] - Zhao, Gao, Zeng,Yang

- Cao, Li, Liu, Brown - Junliang, Xinping

- Yao[48] - Ho, Lin, Liauh

- Lu, Chen - Gheitanchi, FH, Stipidis

- Cutting parameters optimization by PSO

- opposition mutation PSO(OMPSO) - type-2 fuzzy logic system(T2FLS) - adaptive fuzzy logic controller(AFC)

- Multi-swarm and multi-best PSO - Cooperatively Coevolving PSO

(CCPSO) - orthogonal PSO(OPSO) - Self-Adaptive Velocity PSO

(SAVPSO) - Trained PSO (TPSO)

- faster convergence - improve the PSO - increase the performance - increase the performance

- high accuracy -solve large scale problem - solve the large size parameter

problem - improve the PSO - decrease convergence time and

complexity of completion

2009 - Kim, Ahn, Oh - PSO in design of type -2 fuzzy neural

networks (T2FNNs)

- better performance

2010 - Martinez, Rodriguez, Castillo, Aguilar

- Optimization of type-2 fuzzy logic controllers using PSO

- better performance

2011 - Yang, Guo, Liao

- Yang, Guo, Liao - Bingül, Karahan

- fuzzy PSO(FPSO) - fuzzy based multi objective PSO

(F-MOPSO)

- PSO for 2 DOF robot trajectory control

- effective result - optimize the multi objective problem

-develop system

Conclusion:

PSO technique is very simple and fast with few lines programming code and parameters that requires uncomplicated mathematical Equations. Hence, this technique is economical one based on require memory and speed. In addition, this excellent technique in compare to other techniques can solve the problem with high quality resolution in shorter period of time, operation and convergence. It is the attractive method that plays a huge significant role in part of optimization. One of the reasons for be attractive method is applied in various research field and shows the higher quality result in compare to other bio-inspired optimization methods that most of time this high performance result contained cheaper and faster parameters. Other strength of this technique is due to need of the few required parameters for reach to best solution. Besides, the third reason for attractive of that, is ability to work on wide area with multi applications as well as small area with specific application. This paper presented general view and various applications of PSO yearly for researchers and improvement of the PSO and various algorithms which derived from this. Since this method produced in 1995, the various algorithms branched from this and developed a large number of applications. Consequently this paper can be guide for researchers in order to saving the time for gathering information about PSO.

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