A Review on Gravitational Search Algorithm and its Applications to Data Clustering & Classification <s> IV. GSA HYBRIDIZATION AND APPLICATIONS <s> This paper presents an ant colony optimization methodology for optimally clustering N objects into K clusters. The algorithm employs distributed agents which mimic the way real ants find a shortest path from their nest to food source and back. This algorithm has been implemented and tested on several simulated and real datasets. The performance of this algorithm is compared with other popular stochastic/heuristic methods viz. genetic algorithm, simulated annealing and tabu search. Our computational simulations reveal very encouraging results in terms of the quality of solution found, the average number of function evaluations and the processing time required. <s> BIB001 </s> A Review on Gravitational Search Algorithm and its Applications to Data Clustering & Classification <s> IV. GSA HYBRIDIZATION AND APPLICATIONS <s> Clustering analysis is an important function of data mining. Various clustering methods are need for different domains and applications. A clustering algorithm for data mining based on swarm intelligence called Ant-Cluster is proposed in this paper. Ant-Cluster algorithm introduces the concept of multi-population of ants with different speed, and adopts fixed moving times method to deal with outliers and locked ant problem. Finally, we experiment on a telecom company's customer data set with SWARM, agent-based model simulation software, which is integrated in SIMiner, a data mining software system developed by our own studies based on swarm intelligence. The results illuminate that Ant-Cluster algorithm can get clustering results effectively without giving the number of clusters and have better performance than k-means algorithm. <s> BIB002 </s> A Review on Gravitational Search Algorithm and its Applications to Data Clustering & Classification <s> IV. GSA HYBRIDIZATION AND APPLICATIONS <s> In this paper, a tabu search based clustering approach called TS-Clustering is proposed to deal with the minimum sum-of-squares clustering problem. In the TS-Clustering algorithm, five improvement operations and three neighborhood modes are given. The improvement operation is used to enhance the clustering solution obtained in the process of iterations, and the neighborhood mode is used to create the neighborhood of tabu search. The superiority of the proposed method over some known clustering techniques is demonstrated for artificial and real life data sets. <s> BIB003 </s> A Review on Gravitational Search Algorithm and its Applications to Data Clustering & Classification <s> IV. GSA HYBRIDIZATION AND APPLICATIONS <s> Clustering the web documents is one of the most important approaches for mining and extracting knowledge from the web. Recently, one of the most attractive trends in clustering the high dimensional web pages has been tilt toward the learning and optimization approaches. In this paper, we propose novel hybrid harmony search (HS) based algorithms for clustering the web documents that finds a globally optimal partition of them into a specified number of clusters. By modeling clustering as an optimization problem, first, we propose a pure harmony search-based clustering algorithm that finds near global optimal clusters within a reasonable time. Then, we hybridize K-means and harmony clustering in two ways to achieve better clustering. Experimental results reveal that the proposed algorithms can find better clusters when compared to similar methods and also illustrate the robustness of the hybrid clustering algorithms. <s> BIB004 </s> A Review on Gravitational Search Algorithm and its Applications to Data Clustering & Classification <s> IV. GSA HYBRIDIZATION AND APPLICATIONS <s> In this paper, a new hybrid population-based algorithm (PSOGSA) is proposed with the combination of Particle Swarm Optimization (PSO) and Gravitational Search Algorithm (GSA). The main idea is to integrate the ability of exploitation in PSO with the ability of exploration in GSA to synthesize both algorithms' strength. Some benchmark test functions are used to compare the hybrid algorithm with both the standard PSO and GSA algorithms in evolving best solution. The results show the hybrid algorithm possesses a better capability to escape from local optimums with faster convergence than the standard PSO and GSA. <s> BIB005 </s> A Review on Gravitational Search Algorithm and its Applications to Data Clustering & Classification <s> IV. GSA HYBRIDIZATION AND APPLICATIONS <s> Scanning a planar array in the x-z plane directs the beam peak to any direction ofi the broadside along the same plane. Reduction of sidelobe level in concentric ring array of isotropic antennas scanned in the x-z plane result in a wide flrst null beamwidth (FNBW). In this paper, the authors propose pattern synthesis methods to reduce the sidelobe levels with flxed FNBW by making the scanned array thinned based on two difierent global optimization algorithms, namely Gravitational Search Algorithm (GSA) and modifled Particle Swarm Optimization (PSO) algorithm. The thinning percentage of the array is kept more than 45 percent and the flrst null beamwidth (FNBW) is kept equal to or less than that of a fully populated, uniformly excited and 0:5‚ spaced concentric circular ring array of same scanning angle and same number of elements and rings. <s> BIB006 </s> A Review on Gravitational Search Algorithm and its Applications to Data Clustering & Classification <s> IV. GSA HYBRIDIZATION AND APPLICATIONS <s> Partner selection with due date constraint has been proved to be NP-complete problem, and it is difficult to solve by the traditional optimization methods. In the paper, a novel gravitational chaotic search algorithm (GCSA) is proposed, and is firstly used to solve the partner selection optimization problem. By combining the gravitational search algorithm with the chaotic local search, the hybrid algorithm can not only avoid the disadvantage of easily getting to the local optional solution in the later evolution period, but also keep the rapid convergence performance. The simulation results show that the algorithm is efficient. <s> BIB007 </s> A Review on Gravitational Search Algorithm and its Applications to Data Clustering & Classification <s> IV. GSA HYBRIDIZATION AND APPLICATIONS <s> Artificial Bee Colony (ABC) algorithm which is one of the most recently introduced optimization algorithms, simulates the intelligent foraging behavior of a honey bee swarm. Clustering analysis, used in many disciplines and applications, is an important tool and a descriptive task seeking to identify homogeneous groups of objects based on the values of their attributes. In this work, ABC is used for data clustering on benchmark problems and the performance of ABC algorithm is compared with Particle Swarm Optimization (PSO) algorithm and other nine classification techniques from the literature. Thirteen of typical test data sets from the UCI Machine Learning Repository are used to demonstrate the results of the techniques. The simulation results indicate that ABC algorithm can efficiently be used for multivariate data clustering. <s> BIB008 </s> A Review on Gravitational Search Algorithm and its Applications to Data Clustering & Classification <s> IV. GSA HYBRIDIZATION AND APPLICATIONS <s> Clustering is used to group data objects into sets of disjoint classes called clusters so that objects within the same class are highly similar to each other and dissimilar from the objects in other classes. K-harmonic means (KHM) is one of the most popular clustering techniques, and has been applied widely and works well in many fields. But this method usually runs into local optima easily. A hybrid data clustering algorithm based on an improved version of Gravitational Search Algorithm and KHM, called IGSAKHM, is proposed in this research. With merits of both algorithms, IGSAKHM not only helps the KHM clustering to escape from local optima but also overcomes the slow convergence speed of the IGSA. The proposed method is compared with some existing algorithms on seven data sets, and the obtained results indicate that IGSAKHM is superior to KHM and PSOKHM in most cases. <s> BIB009 </s> A Review on Gravitational Search Algorithm and its Applications to Data Clustering & Classification <s> IV. GSA HYBRIDIZATION AND APPLICATIONS <s> This study presents a gravitational search algorithm (GSA) for reactive power dispatch (RPD) problem. RPD is an optimisation problem that decreases grid congestion with one or more objective of minimising the active power loss for a fixed economic power schedule. The proposed algorithm is used to find the settings of control variables such as generator terminal voltages, transformer tap settings and reactive power output of the compensating devices, in order to active power losses minimisation in the transmission system. In this study, GSA is examined and tested on the standard IEEE 30-bus, 57-bus and 118-bus test systems with different test cases such as minimisation of active power losses, improvement of voltage profile and enhancement of voltage stability. To show the proposed algorithm of effectiveness and the obtained results are compared with those reported in the literature. Simulation results demonstrate the superiority and accuracy of the proposed algorithm, and considering the quality of the solution obtained, the proposed algorithm seems to be effective and robust to solve the RPD problem. <s> BIB010 </s> A Review on Gravitational Search Algorithm and its Applications to Data Clustering & Classification <s> IV. GSA HYBRIDIZATION AND APPLICATIONS <s> The work presented in this paper is concerned with the identification of switched linear systems from input-output data. The main challenge with this problem is that the data are available only as a mixture of observations generated by a finite set of different interacting linear subsystems so that one does not know a priori which subsystem has generated which data. To overcome this difficulty, we formally pose the problem of identifying each submodel as a combinatorial $\ell_0$ optimization problem. To decrease the complexity of this NP-hard problem we use a gravitational search algorithm, we present sufficient conditions for this relaxation to be exact. The whole identification procedure allows us to extract the parameter vectors (associated with the different subsystems) one after another without any prior clustering of the data according to their respective generating submodels. Some simulation results are included to support the potentialities of the proposed method. <s> BIB011 </s> A Review on Gravitational Search Algorithm and its Applications to Data Clustering & Classification <s> IV. GSA HYBRIDIZATION AND APPLICATIONS <s> Path planning of Uninhabited Aerial Vehicle (UAV) is a complicated global optimum problem. In the paper, an improved Gravitational Search Algorithm (GSA) was proposed to solve the path planning problem. Gravitational Search Algorithm (GSA) is a newly presented under the inspiration of the Newtonian gravity, and it is easy to fall local best. On the basis of introducing the idea of memory and social information of Particle Swarm Optimization (PSO), a novel moving strategy in the searching space was designed, which can improve the quality of the optimal solution. Subsequently, a weighted value was assigned to inertia mass of every agent in each iteration process to accelerate the convergence speed of the search. Particle position was updated according to the selection rules of survival of the fittest. In this way, the population is always moving in the direction of the optimal solution. The feasibility and effectiveness of our improved GSA approach was verified by comparative experimental results with PSO, basic GSA and two other GSA models. <s> BIB012
The hybridization of an algorithm pretends the algorithm more powerful and enhances the capabilities of an algorithm. Due to hybridization, coverage area of algorithms exacerbates and it can wrap more problems. The GSA is also hybridizes with conventional and swarm based algorithms to enhance its capabilities. To solve permutation flow shop problem (PFSSP) Xiangtao Li  et al. has proposed -SIGSA‖ a new hybrid algorithm based on the GSA and SA. To design the proposed algorithm for PFSSP there were two challenges, firstly how to make GSA applicable for PFSSP and second trap in local minima problem. BIB005 has proposed a new hybrid algorithm PSOGSA which is based on the PSO and GSA for function optimization problems. The proposed algorithm is used the global best i.e. -gbest‖ concept of PSO in GSA to find out best current position among all current positions. The performance of PSOGSA evaluates with twenty three benchmarks functions and compares with Std. PSO & Std. GSA in which PSOGSA performs very well with most of functions as compare to Std.PSO & Std.GSA and provides faster convergence speed. To improve side lobe levels in concentric ring array A. Chatterjeeet et al. BIB006 has applied the GSA for synthesis of thinned scanned concentric ring array antenna. The performance of GSA evaluates with fitness value & computational time and compare with Modified PSO in which GSA provides better results than Modified PSO. The ability to solve the optimization problems with minimizes discrete time objective function Radu-Emil Precup et al.  has proposed a new version of GSA for tuning the fuzzy control systems. The new version of GSA is derived from the original GSA by modification in deprecation equation and adding constraint regarding system in original GSA. The proposed algorithm provides significant improvement in performance indices and covers large number of control plants but the algorithm could not promised global optimum and minimum sensitivity. To solve the partner selection problem with due date constraint Jianhua Xiao et al. BIB007 has proposed a new  . In novel adaptive gravitational search algorithm two deprecation laws are defined for gravitational coefficient which is derived from adaptive PSO. The adaptive GSA provides reduced time constant sensitivity with a new formulation of Takagi-Sugeno Proportional Integrated Fuzzy Controllers (T-S PI-FCs). The back propagation algorithm for neural network sometime provides local minimum convergence rather than global minimum. So, to overcome local minimum convergence problem of back propagation in neural network Lucian-Ovidiu Fedorovici et al.  has applied GSA with back propagation to train the convolution neural network for OCR applications because GSA has ability to provided near global optimum solution and evaluated the performance of embedded GSA in convolution neural network with back propagation technique to classical back propagation algorithm. The embedded GSA provides better result as compares to classical BP in terms of convergence and recognitions rates. To determine the behavior of GSA with nonlinear problems S. Duman et al. BIB010 has applied the GSA algorithm to find the optimal solution for -reactive power dispatch problem‖. complexity, optimality and convergence in hybrid system identification Hamed Sadeghiet et al. BIB011 has proposed a new version of GSA based on GSA & idea of sparse optimization from the field of sparse signal recovery to identification of switched linear system from inputoutput data and parameter extraction for sub models. The proposed algorithm provides better performance. To enhance the global search strategy for path planning problem in UAV, LI Pei et al. BIB012 has applied the hybridize GSA plus PSO algorithm for this problem and compared the performance of proposed algorithm with original GSA & PSO in which proposed algorithm provides better performance than others. The application of GSA in clustering and classification discuss in separate section. 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. entities into disjoint clusters such that entities of each cluster are similar. Clustering techniques have been employed in many areas such as pattern recognition BIB003  , information retrieval BIB004  , data mining   , and many more. Large number of nature inspired algorithms is applied on the data clustering problem such as ABC BIB008 , PSO BIB002 , KMH  , ACO BIB001 , K-means  , BB-BC  etc. There does not exists a single algorithm that is adequate to solve all of requisite for clustering problems due to diversity of clustering problems, different data type and intention of clustering. This paper also enlightens the application of GSA for data clustering problems. Abdolreza Hatamlou et al.  has proposed a gravitational search algorithm for data clustering applications and compared the performance of proposed algorithm with PSO, GA and K-means. Proposed algorithm provides the viable and robust result for data clustering as compares the PSO, GA and K-means using sum of intra cluster distance and standard deviation parameters. This algorithm provides the good searching ability to find global optimum but in the last iterations the performance of algorithm suffers due to slow searching speed. To improve the searching ability of GSA, Abdolreza Hatamlou and Salwani Abdullah et al.  have proposed a hybrid algorithm GSA-KM based on the GSA & K-means for clustering problem because k-means is simple and fast algorithm. The hybrid algorithm provides better performance in comparison of original GSA by two ways. First, the numbers of steps require for iteration & evaluate the objective function to find global optimum was reduced, its increased execution speed of hybrid algorithm. Second, due to the use of kmeans with GSA, a good candidate solution is generated for initial population so that near global optimum searched in more promising search space and provided a better quality solution as compared to original GSA. To reduce the slow convergence speed of GSA, Minghao Yin et al. BIB009 has proposed new algorithm IGSAKHM based on the IGSA and K-harmonic means for clustering problem. KHM is easily sucked in local optima but fast convergence speed as compare to GSA. On the other hand IGSA has ability to find near global optimum solution easily but suffered with slow convergence rate. The performance of IGSAKMH evaluates with F measure, run time, mean and standard deviation parameters and compares with KMH and PSOKMH in which IGSAKMH provides better performance with F measure, mean & standard deviation than others but execution time of IGSAKMH algorithm longer than the KMH. So, the application where run time is critical parameter, IGSAKMH will not work efficiently. To reduce convergence in local optima of K-Means algorithm, Abdolreza Hatamlou et al.  has proposed a new hybrid algorithm GSA-HS based on GSA and Heuristic search technique. In the proposed algorithm, initial population is generated by the GSA after that heuristic search technique is applied to exploration of population. The performance of GSA-HS evaluate with two parameters i.e. sum of intra cluster distance and center of corresponding cluster including four bench mark datasets and compare with K-Means & PSO in which GSA-HS provides better results than others. To improve the -fuzzy space partition‖ & identification of ‗premises parameter‖ Chaoshun Li et al.  has developed a new hybrid GSA based on hyper plane clustering algorithm (GSAHCA) for identification of T-S fuzzy model. The GSA is used to identify the consequence and premises parameters which are used to build T-S fuzzy model. The performance of GSAHCA evaluates with some non linear system using real system sampled data sets in which GSAHCA provides better performance. The GSAHCA also compares with FCRM for identify model accuracy in which GSAHCA provides better result than FCRM. 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    BIB009 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.