A Review on Gravitational Search Algorithm and its Applications to Data Clustering & Classification

Автор: Yugal kumar, G. Sahoo

Журнал: International Journal of Intelligent Systems and Applications(IJISA) @ijisa

Статья в выпуске: 6 vol.6, 2014 года.

Бесплатный доступ

Natural phenomenon’s and swarms behavior are the warm area of research among the researchers. A large number of algorithms have been developed on the account of natural phenomenon’s and swarms behavior. These algorithms have been implemented on the various computational problems for the sake of solutions and provided significant results than conventional methods but there is no such algorithm which can be applied for all of the computational problems. In 2009, a new algorithm was developed on the behalf of theory of gravity and was named gravitational search algorithm (GSA) for continuous optimization problems. In short span of time, GSA algorithm gain popularity among researchers and has been applied to large number of problems such as clustering, classification, parameter identification etc. This paper presents the compendious survey on the GSA algorithm and its applications as well as enlightens the applicability of GSA in data clustering & classification.

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Classification, Clustering, Gravitational Search Algorithm, Optimization, Nature Inspired Algorithm

Короткий адрес: https://sciup.org/15010573

IDR: 15010573

Текст научной статьи A Review on Gravitational Search Algorithm and its Applications to Data Clustering & Classification

Published Online May 2014 in MECS

in 2006 proposed a new algorithm Big Bang Big Crunch (BB-BC) based on the big bang theory (Theory of Evolution of Universe) for optimization problems. BB-BC algorithm is used to solve large numbers of optimization problems such as multi modal optimization problem [35], multi-objective optimization problem [36], clustering [37] etc. A brief description about the nature inspired algorithms has been given above that are used to solve the optimization problems but till date there does not exists any algorithm that can solve the entire optimization problems exactly.

The rest of paper is organized as follows. Section II gives the detail about GSA. Section III describes variants and modifications in GSA. The hybridization of GSA with other techniques is discussed in section IV. Section V and VI focus the application of GSA algorithm in clustering and classification. These sections are followed by conclusion of paper.

II. Gravitational Search Algorithm

• Identification of search space.
• Generate Initial population.
• Evaluate fitness function for each particle in population.
• Update the gravitational constant value.

G (t) = G (G₀, t), Best (t) = min i ∈ {1,…, } Fit i ( t )

Worst (t) = max Fit( t ) i ∈ 1 …․

• Calculate the total force in different direction (M) and Acceleration (a) by following equations:

_ ^mi( t ) Fit; ( t ) -Worst ( t )

M i ( t )= "FT¹ ^{( )} Where m i ( t )= () ( )

∑ () () ( )

Acceleration at ( t )= ^ ₍ - ⁾ , where Ff ( t )= ( t )

∑ j=i , j^randjFfj ⁽ t )

• Update the particle velocity and position. Velocity and position of particle is calculated by following equations:

Velocity ^V ( t +1)= randt ^× dy ( t )× ^d_ta ( t )

Position Xf ( t +1)= Xf ( t )+ VA ( t +1)

• Stopping criteria (repeat until stopping criteria met).

18%

55%

26%

GSA

GSA Variants

Hybrid GSA problems till date as well as to improve the statistics of original GSA.

Fig. 1. Applicability of Gravitational Search Algorithm in different domains

Fig. 2. Statistics of Gravitational Search Algorithm

III. GSA Variants, Comparisons and

Modifications

IV. GSA Hybridization and Applications

Discussion: Lot of algorithms have been developed by the researcher based on the gravitational search algorithm to improve the capabilities of GSA, increases the coverage area of GSA, overcome the limitations of some existed algorithms etc. and compared the performance of GSA to others techniques such as PSO, GA, DE, BBO, ABC etc. in which GSA provided better performance than others. The Table 1 provide the year wise development in the field of gravitational search algorithm as well as the problems addressed by the GSA & GSA based algorithms with performance matrices.

Table1. List of proposed algorithm using GSA and its variants

Year	Author	Algorithm	Problem	Performance Metrics
2009	Rashedi et al (2009)	GSA	Optimization problems in continuous space	23 Non linear benchmark functions i.e. unimodal, multi model
2010	Rashedi et al (2010)	BGSA	Binary optimization Problems	23 Minimization and 2 maximization benchmark functions
2010	Hamid Reza Hassanzadeh et al (2010)	MOGSA	Multi Objective optimization problems	Spacing & gravitational distance criteria
2010	Xiangtao Li et al (2010)	SIGSA	Permutation flow shop scheduling problem	29 Problems of two classes of PFSSP such as car1, car2 to car8 etc.
2010	A. Chatterjeeet al (2010)	GSA	To improve Side lobe in concentric ring arrays(Antenna)	Fitness Value & Computational Time
2010	Seyedali Mirjalili et al (2010)	PSOGSA	To avoid slow convergence due to memory less feature of GSA	23 Non linear benchmark functions i.e. unimodal, multi model
2011	Jianhua Xiao and Zhen Cheng (2011)	GSA	DNA sequences optimization problem	Continuity, H- measure and Similarity
2011	S. Sarafrazi et al (2011)	Improved GSA	To increases the exploration and exploitation ability	23 Non linear benchmark functions
2011	M. Soleimanpour-moghadam et al (2011)	QGSA	Position and Velocity of an object in GSA	Unimodal & multimodal
2011	Saeid Saryazdi (2011)	GSA worked as heuristic search	Parameter estimation problem of IIR and Nonlinear rational filters	Unimodal function, multimodal function & complexity of problem
2011	Jianhua Xiao et al (2011)	GCSA	Partner selection problem with due date constraint	Cost criteria & convergence rate
2011	Radu-Emil Precup et al (2011)	GSA with modified deprecation equation	Tuning the fuzzy control systems	Performance indices
2011	Radu-Emil Precup et al (2011)	GSA with three modifications	To improve parametric sensitivity	Performance indices

2011	Serhat Duman et al (2011)	GSA	Economic Dispatch problem	Three test system
2011	J. P. Papa et al (2011)	OPF-GSA	Feature selection Task	Number of features selected
2011	M. Ghalambaz et al (2011)	HNNGSA	To solve wessinger’s equation	………………………………..
2011	Chaoshun Li et al (2011)	IGSA	To identify the parameter for hydraulic turbine governing system	Frequency
2011	Abdolreza Hatamlou et al (2011)	GSA	Data clustering	Sum of intra cluster distance and Standard deviation
2011	Minghao Yin et al (2011)	IGSAKHM	Slow convergence problem of GSA in clustering	F- measure, run time, mean and standard deviation
2011	Abdolreza Hatamlou et al (2011)	GSA-HS	Clustering	Sum of intra cluster distance and center of corresponding cluster
2011	Soroor Sarafrazi et al (2011)	GSA-SVM	To increases classification accuracy in Binary Problems	Std. Dev., Mean, Max. & Min.
2012	Nihan Kazak et al (2012)	Modified GSA (MGSA).	To increases searching and convergence rate	3 Benchmark functions Such as unimodal, multimodal
2012	Mohadeseh Soleimanpour et al (2012)	Improved QGSA	Diversity loss problems	Unimodal & multimodal
2012	Lucian-Ovidiu Fedorovici et al (2012)	GSA with BP	OCR applications	Convergence and recognitions rates
2012	Nanji H. R et al (2012)	multi agent based GSA	Computational cost of original GSA	Six bench mark functions such as unimodal, multimodal
2012	Radu-Emil Precup et al (2012)	Adaptive GSA	To minimize the objective function	Sensitivity
2012	S. Duman et al (2012)	GSA	Reactive power dispatch problem	Minimization of system real power, improvement voltage profile & enhancement of voltage
2012	Serhat Duman et al (2012)	GSA	Optimal Power Flow problem	IEEE 30 Bus power system including six different cases
2012	Chaoshun Li et al ( 2012)	CGSA	Parameter identification problem of chaotic system
2012	Abdolreza Hatamlou et al (2012)	GSA-KM	Clustering problem(For improve searching capabilities of GSA)	Number of steps and cost
2012	Chaoshun Li et al (2012)	GSAHCA	Identification of T-S fuzzy model	Model accuracy
2012	Hossein Askari et al (2012)	Intelligent GSA	Classification of data	Accuracy, minimum, maximum and average score of recognition
2012	Ahmad Asurl Ibrahim et al (2012)	QBGSA	Power quality monitor placement (PQMP) problem	Radial 69 bus distributed system and IEEE 118 bus system with Bolted three phase, Double line to ground and Single phase to ground
2012	Hamed Sadeghiet et al (2012)	GSA with sparse optimization	Identification of switch linear system and Parameter estimation	Statistical Robustness under excitation, noise and switching sequence
2012	Mohammad Khajehzadeh et al (2012)	MGSA	Slope Stability Analysis	Minimum factor of safety and reliability index
2012	Abbas Bahrololoum et al (2012)	prototype classifier based on GSA	Data classification	Average misclassification percentage error
2012	Li Pei et al (2012)	GSA with PSO & DE(IGSA)	Routing (Path planning for UAE)	Cost of threats & Evolution Curve
2013	Soroor Sarafrazi et al (2013)	GSA-SVM	Parameter Setting of SVM & Increased accuracy(Classification)	Accuracy (Mean & Standard Deviation)

V. GSA in Clustering

Table 2. Comparisons of GSA and its variants to other techniques

Method	Iris		Wine		Glass		CMC		Cancer
Method	Avg.	Std.	Avg.	Std.	Avg.	Std.	Avg.	Std.	Avg.	Std.
KM	106.05	14.63	18061.00	793.21	235.50	12.47	5893.60	47.16	3251.21	251.14
KMH	113.41	0.09	18386.00	0.00	257.18	0.00	5852.96	25.00	3234.40	0.00
GA	125.19	14.56	16530.53	0.00	282.32	4.14	5756.59	50.37	3249.46	229.73
SA	99.95	2.02	17521.09	753.08	282.19	4.24	5893.48	50.87	3239.17	230.19
ACO	97.17	0.37	16530.53	0.00	273.46	3.58	5819.13	45.63	3046.06	90.50
HBMO	96.95	0.53	16357.28	0.00	247.71	2.44	5713.98	12.69	3112.42	103.47
PSO	97.23	0.35	16417.47	85.49	275.71	4.55	5820.96	46.95	3050.04	110.80
GSA	96.72	0.01	16376.61	31.34	225.70	3.40	5699.84	1.72	2973.58	8.17
GSA-KM	96.69	0.01	16294.31	0.04	214.22	1.14	5697.36	0.27	2965.21	0.07
GSA-KMH	96.58	0.002	16234.560	0	185.710	0.035	5685.350	0.310	2954.250	0.056
GSA-HS	96.65	0.0	16292	0.0	----	----	5693.7	0.0	2964.4	0.0
PSOGSA	97.23	0.060	16331.260	0.450	205.710	2.090	5699.100	0.540	2969.410	0.063

Discussion : The study of the literature of GSA in clustering, it has been observed that five GSA based algorithms have been proposed to solve the clustering problems. These algorithms are GSA, GSA-KM, GSA-KMH, GSA-HS and PSOGSA. To evaluate the relatively performance of GSA and its variant to others techniques, a table is constructed using common datasets & parameters with help of literature [37,78, 79, 80] and compares the GSA & its variants to other clustering techniques. The table 2 provides the comparisons between the GSA & its variants to other well known techniques that are used to solve the clustering problems. The performance of these techniques evaluate with five different dataset using sum of intra cluster distance & standard deviation parameters. These parameters deduce the efficiency of techniques in data clustering. Minimum value of parameters means better the efficiency of the technique. The GSA provides minimum sum of intra cluster distance with all five datasets as compares to KM, KMH, GA, SA, ACO, HBMO and PSO. To analyze standard deviation parameter, GSA has minimum value for Iris and CMC datasets while second minimum value for all other datasets. So, Table 2 states that GSA provides more accurate and significant result than other techniques except GSA variants. Table 2 also provides the comparisons of different GSA variants i.e. GSA, GSA-KM, GSA-KMH, GSA- HS and PSOGSA. From the table 2, it is conclude that GSA-KMH provides the minimum sum of intra clusters distance and GSA-HS provides almost zero value of standard deviation parameter. The quality of cluster depends on the minimum value of objects from its cluster centroid. So, minimum sum of intra cluster distance mean objects are tightly bound with cluster. From the Table 2, it is observe that GSA-KMH is the best technique among all GSA variants and other nature inspired techniques for clustering problem.

VI. GSA in Classification

Discussion: To the depth study of GSA in classification problem, it has been observed that there exist some common data sets on which GSA & its variants compare with other classification methods using some parameters and GSA & its variants provides better performance than others. Such datasets are Iris, wine, glass & cancer and performance of classification methods evaluate with misclassified instance, accuracy, rank parameters etc. Table 3 [66,85, 86, 87] provides the comparisons of GSA & its variants (that are proposed for classification problems) with other techniques using above discussed common datasets with two parameters: accuracy & rank as well as some other methods also include such as ID3, J48, SVM, IBK etc.

ABC (88.92, 5) algorithm get fifth position while multi boost (68.21, 20) provides worst results.

Classifiers	Iris		Cancer		Wine		Glass
Classifiers	Accuracy	Rank	Accuracy	Rank	Accuracy	Rank	Accuracy	Rank
IPS-classifier	95.3	9	95.9	9	94.9	6	70.1	6
IGA-classifier	96.7	4	97	6	96.4	4	75.2	3
DE-classifier	88.7	15	86.4	18	86.3	7	58.4	13
GSA-classifier	82.6	19	80.1	20	61.3	17	88	1
IGSA-classifier	98.1	2	96.1	8	97.6	2	79.5	2
PSO	96.14	6	95.74	10	96.22	5	60.33	9
ABC	100	1	100	1	97.19	3	58.5	12
GSA Prototype	97.54	3	99.37	3	97.64	1	67.67	7
GSA-SVM (GSA+BGSA)	-	-	99.54	2	-	-	-	-
GSA-SVM	-	-	99.37	3	-	-	-	-
Bayes Net	95.77	7	80.26	19	70.2	9	75.02	4
MLP ANN	93.96	11	97.07	5	66.12	12	64.61	8
RBF	91.66	14	79.33	21	60.55	18	55.56	14
K-Star	93.26	13	97.56	4	64.22	14	60.28	10
Bagging	96.58	5	95.53	13	63.76	16	50	16
Multi Boost	68.4	20	93.91	15	64.22	14	46.3	18
NB Tree	94.73	10	92.31	16	68.12	10	71.12	5
SMO (SVM)	88.66	16	95.7	11	66.51	11	51.4	15
IBK	85.33	18	95.56	12	65.1	13	58.87	11
Dagging	86	17	96.7	7	64.2	15	46.72	17
J48	95.33	8	94.42	14	64.2	15	37.38	19
ID3	93.55	12	92.24	17	72.34	8	36.56	20

Table 4. Average accuracy result with relative ranking of datasets

Parameter	Classifiers
Parameter	IPS	IGA	DE	GSA	IGSA	PSO	ABC	GSA Prototype
Average Accuracy	89.05	91.33	79.95	78	92.83	87.11	88.92	90.56
Rank	4	2	10	12	1	6	5	3

Table 5. Average accuracy result with relative ranking of datasets

Parameter	Classifiers
Parameter	Bayes Net	MLP ANN	RBF	K-Star	Bagging	Multi Boost
Average Accuracy	80.31	80.44	71.78	78.83	76.47	68.21
Rank	9	8	19	11	13	20

Table 6: Average accuracy result with relative ranking of datasets

Parameter	Classifiers
Parameter	NB Tree	SMO	IBK	Dagging	J48	ID3
Average Accuracy	81.57	75.57	76.22	73.41	72.83	73.67
Rank	7	15	14	17	18	16

Sum of Ranks	Classifiers
Sum of Ranks	IPS	IGA	DE	GSA	IGSA	PSO	ABC	GSA Prototype
Sum of Ranks	29 (6)	16 (3)	52 (11)	56 (14)	12 (1)	19 (5)	17 (4)	13 (2)

Sum of Ranks	Classifiers
Sum of Ranks	Bayes Net	MLP ANN	RBF	K-Star	Bagging	Multi Boost
Sum of Ranks	38(8)	35 (7)	66 (15)	40 (9)	49 (10)	66 (15)

Sum of Ranks	Classifiers
Sum of Ranks	NB Tree	SMO	IBK	Dagging	J48	ID3
Sum of Ranks	40 (9)	52 (11)	53 (12)	55 (13)	55 (13)	56 (14)

VII. Conclusion

This paper presents the review of pervious research in the field of gravitational search algorithm, its variants; hybridize GSA and its applications. Table 1 provides the complete summary of GSA literature, modification in GSA and applications of GSA. From the table 1, it conclude that GSA is four years old but this field shows tremendous growth & quite popular between researchers and large number of problems solved by GSA such as RPDP, ED, OPF and many more mentioned in table 1. The figure 1 shows the percentage of hybrid algorithms and modification in GSA has been proposed by various authors in GSA literature. The modification and hybridization of GSA with other techniques provided better results in terms of computational time, convergence etc. The figure 3 provides the year wise development in the field of gravitational algorithms and number of publications in each year published with the help of GSA. From the figure 3, it’s conclude that there is only one publication on GSA in year 2009 but in last two years large number of papers published using GSA that shows the wide popularity of GSA among researchers. The figure 4 categorizes the publications based on GSA in different domains. The figure 4 states that half of GSA publications related to computer science and computing filed that shows the GSA applicability and significance in computer science & computing field. The twenty four percent of GSA publications come from optimization & others field and very less publication from civil & mechanical field. From the figure 4, it is

Fig. 3. Year wise growth in GSA

24%

50%

21%

। । Optimization & Others

Fig. 4. Categorization of GSA publications

^e Data mining ANN i i Computing

^e Others

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