Gravitational Search Algorithm

Abstract. Gravitational search algorithm (GSA) is a new member of swarm intelligence algorithms. It stems from Newtonian law of gravity and motion. The performance of synchronous GSA (S-GSA) and asynchronous GSA (A-GSA) is studied here using statistical analysis. The agents in S-GSA are updated synchronously, where the whole population is updated after each member’s performance is evaluated. On the other hand, an agent in A-GSA is updated immediately after its performance evaluation. Hence an agent in A-GSA is updated without the need to synchronize with the entire population. Asynchronous update is more attractive from the perspective of parallelization. The results show that both implementations have similar performance.

Received July 31, 2012; revised August 31, 2012; accepted September 15, 2012 ABSTRACT Gravitational search algorithm (GSA) is a recent introduced global convergence guaranteed algorithm. In this paper, a quantum-behaved gravitational search algorithm, namely called as QGSA, is proposed. In the proposed QGSA each individual mass moves in a Delta potential well in feasible search space with a center which is weighted average of all kbests. The QGSA is tested on several benchmark functions and compared with the GSA. It is shown that the quan- tum-behaved gravitational search algorithm has faster convergence speed with good precision, and thus generating a better performance.

ABSTRACT Gravitational Search Algorithm (GSA) is a metaheuristic population-based optimization algorithm inspired by the Newtonian law of gravity and law of motion. Ever since it was introduced in 2009, GSA has been employed to solve various optimization problems. Despite its superior performance, GSA has a fundamental problem. It has been revealed that the force calculation in GSA is not genuinely based on the Newtonian law of gravity. Based on the Newtonian law of gravity, force between two masses in the universe is inversely proportional to the square of the distance between them. However, in the original GSA, R is used instead of R 2 . In this paper, the performance of GSA is re-evaluated considering the square of the distance between masses, R 2 . The CEC2014 benchmark functions for real-parameter single objective optimization problems are employed in the evaluation. An important finding is that by considering the square of the distance between masses, R 2 , significant improvement over the original GSA is observed provided a large gravitational constant should be used at the beginning of the optimization process.

A B S T R A C T Nowadays, optimization problems are large-scale and complicated, so heuristic optimization algorithms have become common for solving them. Gravitational Search Algorithm (GSA) is one of the heuristic algorithms for solving optimization problems inspired by Newton’s lows of gravity and motion. Definition and calculation of masses in GSA have an impact on the performance of the algorithm. Defining appropriate functions for mass calculation improves the exploitation and exploration power of the algorithm and prevents the algorithm from getting trapped in local optima. In this paper, Sigma scaling and Boltzmann selection functions are examined for mass calculation in GSA. The proposed functions are evaluated on some standard test functions including unimodal functions and multimodal functions. The obtained results are compared with the standard GSA, genetic algorithm, particle swarm optimization algorithm, gravitational particle swarm algorithm and clustered-GSA. Experimental results show that the proposed method outperforms the state-of-the-art optimization algorithms, despite the simplicity of implementation.

2 Department of Electrical and Electronics Engineering, Gudlavalleru Engineering College, Gudlavalleru, India 3 Department of Electrical and Electronics Engineering, JNTU University, Hyderabad, India Abstract: This paper proposes a new approach for solving unit commitment problem using gravitational search algorithm (GSA). The proposed search is based on law of gravity and mass interaction applied to determine the optimal unit commitment schedule includes with minimum up/down time and spinning reserve constraints. The GSA approach is useful to decide the optimal setting of control variables of unit commitment. The performance of the proposed approach initially examined and tested on 10 unit system later extended up to 40 unit system with 24-hr horizon. The results obtained from the proposed GSA approach indicate that GSA provides effective and robust solution of unit commitment.

Department of Electrical Engineering, D.A.V.I.E.T., Jalandhar, Punjab, India 1, 2 Email:shivanimehta7@gmail.com 1 ,kgourav170@yahoo.com 2 Abstract: - An imperative condition in power system process is to meet the power demand at least fuel cost using the most favourable combination of diverse power plants. Unit Commitment is the predicament of defining the list of generating units focus to device and operating constraints. The design of unit commitment has been conversed and the result is got by hybrid gravitational search algorithm (HGSA). An algorithm based on hybrid gravitational search technique, which is aninhabitants based global search and optimization procedure has been established to resolve the unit commitment problem. The efficiency of these algorithms has been finding by compare four units and ten units of system.

University of Malaya, Malaysia Abstract. This paper presents a performance evaluation of a novel Vector Evaluated Gravitational Search Algorithm II (VEGSAII) for multi-objective optimization problems. The VEGSAII algorithm uses a number of populations of particles. In particular, a population of particles corresponds to one objective function to be minimized or maximized. Simultaneous minimization or maximization of every objective function is realized by exchanging a variable between populations. The results shows that the VEGSA is outperformed by other multi-objective optimization algorithms and further enhancements are needed before it can be employed in any application.

GRAVITATIONAL SEARCH ALGORITHM GSA is a heuristic optimization algorithm which has been gaining interest among the scientific community recently. GSA is a nature inspired algorithm which is based on the Newton’s law of gravity and the law of motion . GSA is grouped under the population based approach and is reported to be more intuitive. The algorithm is intended to improve the performance in the exploration and exploitation capabilities of a population based algorithm, based on gravity rules. However, recently GSA has been criticized for not genuinely based on the law of gravity [3]. GSA is reported to exclude the distance between masses in its formula, whereas mass and distance are both integral parts of the law of gravity. Despite the criticism, the algorithm is still being explored and accepted by the scientific community. GSA was introduced by Rashedi et al. in 2009 and is intended to solve optimization problems. The population-based heuristic algorithm is based on the law of gravity and mass interactions. The algorithm is comprised of collection of searcher agents that interact with each other through the gravity force. The agents are considered as objects and their performance is measured by their masses. The gravity force causes a global movement where all objects move towards other objects with heavier masses. The slow movement of heavier masses guarantees the exploitation step of the algorithm and corresponds to good solutions.

A B S T R A C T In this paper, the binary gravitational search algorithm and support vector machines have been used to diagnose epilepsy. At first, features are extracted from EEG signals by using wavelet transform and fast fractional Fourier transform. Then, the binary gravitational search algorithm is used to perform feature selection, instance selection and parameters optimization of support vector machines, and finally constructed models are used to classify normal subjects and epilepsy patients. The appropriate choice of instances, features and classifier parameters; considerably affects the recognition results. In addition, the dimension reduction of the features and instances is important in terms of required space to store data and required time to execute the classification algorithms. Feature selection, instance selection and parameters optimization of support vector machines have been implemented both simultaneously and stepwise. The performance metrics in this study are accuracy, sensitivity, specificity, number of selected features, number of selected instances and execution time. The results of experiments indicate that the simultaneous implementation of feature selection, instance selection and support vector machines parameters optimization leads to better results in terms of execution time in comparison with the stepwise implementation. In the stepwise implementation, performing instance selection process before feature selection leads to better results in terms of accuracy, sensitivity and specificity, as well as reduction of execution time. The results show that the proposed methods achieve noteworthy accuracy in comparison with other methods that were used to diagnose epilepsy.

The purpose of this project is to deploy and use the Gravitational Search Algorithm in feature selection of IDS to selectively choose significant features which represents categories of network such as DoS, Probe, U2R and R2L and enable the Intrusion Detection System (IDS) to learn the pattern in network traffic.

P.G. Student, Department of Computer Science and Engineering, MIST, Bhopal, Madhya Pradesh, India 1 Associate Professor, Department of Computer Science and Engineering, MIST, Bhopal, Madhya Pradesh, India 2 Abstract: Classification is an important problem in data mining. Under the guise of supervised learning, classification has been studied extensively by the AI community as a possible solution to the “knowledge acquisition” or “knowledge extraction” problem. Briefly, the input to a classifier is a training set of records, each of which is a tuple of attribute values tagged with a class label. A set of attribute values defines each record. Many different techniques have been proposed for classification, including Bayesian classification, neural networks, genetic algorithms and tree-structured classifiers. They have been successfully applied to wide range of application areas, such as medical diagnosis, weather prediction, credit approval, customer segmentation, and fraud detection and many more. PSOGSA based data classification can also be apply, might yield more efficient and promising results, work which possesses classification of standard data using gravitational search algorithm with optimize manner. So classification of data done by the famous widely used method Feed-forward neural network with gravitational search algorithm. Particle swarm optimization is a popular heuristic algorithm that had been applied on many optimization problems over the years including data classification problem. The modified PSO is combined with gravitational search algorithm to solve its slow Execution time in the last iterations, making the hybrid PSOGSA algorithm.

Particle Swarm Optimization (PSO) and Gravitational Search Algorithm are a well-known population-based heuristic optimization techniques. PSO is inspired from a motion flock of birds searching for a food. In PSO, a bird adjusts its position according to its own ‘‘experience’’ as well as the experience of other birds. Tracking and memorizing the best position encountered build bird’s experience which will leads to optimal solution. GSA is based on the Newtonian gravity and motion laws between several masses. In GSA, the heaviest mass presents an optimum solution in the search space. Other agents inside the population are attracted to heaviest mass and will finally converge to produce best solution. Black Hole Algorithm (BH) is one of the optimization technique recently proposed for data clustering problem. BH algorithm is inspired by the natural universe phenomenon called "black hole”. In BH algorithm, the best solution is selected to be the black hole and the rest of candidates which are called stars will be drawn towards the black hole. In this paper, performance of BH algorithm will be analyzed and reviewed for continuous search space using CEC2014 benchmark dataset against Gravitational Search Algorithm (GSA) and Particle Swarm Optimization (PSO). CEC2014 benchmark dataset contains 4 unimodal, 7 multimodal and 6 hybrid functions. Several common parameters has been chosen to make an equal comparison between these algorithm such as size of population is 30, 1000 iteration, 30 dimension and 30 times of experiment.

3. Gravitational search algorithm Gravitational search algorithm is a meta heuristic optimization technique based on Newton’s law of gravity and motion. This algorithm was first developed by Rashedi et al. [22] in 2009. The working of this algorithm is greatly influenced by the motion and the mass of agents. Each agent experiences grav- itational force of attraction with other agents present in the search space. Fitness of agents in the search space is character- ized by their masses. Hence, GSA can be considered as collec- tion of different masses. Heavier mass has bigger attraction force and attracts other masses with a force proportional to the product of their masses and inversely proportional to the distance (not the square of distance) between masses.

Assistant Professor Department of Electrical Engineering GNDEC Ludhiana#3 Abstract: This paper describes gravitational search algorithm for solving the non convex Economic load Dispatch (ELD) problem. The main objective of economic load dispatch problem is to generate the required amount of power so that the total operating cost of system is minimized, while satisfying load demand and system equality and inequality Constraints. Different heuristic optimization methods have been proposed to solve this problem in previous study. So in this paper, gravitational search algorithm (GSA) based on law of gravity and mass interaction is proposed. This proposed approach has been tested on 3, 38 test systems. Simulation results of proposed approach are compared with some well-known heuristic search methods. The obtained results verify the efficiency of the proposed method with minimum computational time in solving various nonlinear functions Keyword: Economic dispatch, gravitational search algorithm, equality and inequality Constraints.

Assembly sequence planning (ASP) becomes one of the major challenges in product design and manufacturing. A good assembly sequence leads to reduced costs and duration in the manufacturing process. However, assembly sequence planning is known to be a classical NP-hard combinatorial optimization problem; assembly sequence planning with many product components becomes more difficult to solve. In this paper, an approach based on a new variant of the Gravitational Search Algorithm (GSA) called the multi-state Gravitational Search Algorithm (MSGSA) is used to solve the assembly sequence planning problem. As in the Gravitational Search Algorithm, the MSGSA incorporates Newton’s law of gravity and the law of motion to improve solutions based on precedence constraints; the best feasible sequence of assembly can then be determined. To verify the feasibility and performance of the proposed approach, a case study has been performed and a comparison has been conducted against other three approaches based on Simulated Annealing (SA), a Genetic Algorithm (GA), and Binary Particle Swarm Optimization (BPSO). The experimental results show that the proposed approach has achieved significant improvement in performance over the other methods studied.

By predicting rival’s behavior through probability distribution function, the process of finding the optimal bidding strategy for generator X with the objective function (1) with constraints (2) and (3) becomes a stochastic optimization problem which is to be solved by gravitational search algorithm which is presented in next section.

Received: 2 August 2020; Accepted: 2 September 2020; Published: 16 September 2020



Abstract: Industry 4.0 is the fourth generation of industry which will theoretically revolutionize manufacturing methods through the integration of machine learning and artificial intelligence approaches on the factory floor to obtain robustness and speed-up process changes. In particular, the use of the digital twin in a manufacturing environment makes it possible to test such approaches in a timely manner using a realistic 3D environment that limits incurring safety issues and danger of damage to resources. To obtain superior performance in an Industry 4.0 setup, a modified version of a binary gravitational search algorithm is introduced which benefits from an exclusive or (XOR) operator and a repository to improve the exploration property of the algorithm. Mathematical analysis of the proposed optimization approach is performed which resulted in two theorems which show that the proposed modification to the velocity vector can direct particles to the best particles. The use of repository in this algorithm provides a guideline to direct the particles to the best solutions more rapidly. The proposed algorithm is evaluated on some benchmark optimization problems covering a diverse range of functions including unimodal and multimodal as well as those which suffer from multiple local minima. The proposed algorithm is compared against several existing binary optimization algorithms including existing versions of a binary gravitational search algorithm, improved binary optimization, binary particle swarm optimization, binary grey wolf optimization and binary dragonfly optimization. To show that the proposed approach is an effective method to deal with real world binary optimization problems raised in an Industry 4.0 environment, it is then applied to optimize the assembly task of an industrial robot assembling an industrial calculator. The optimal movements obtained are then implemented on a real robot. Furthermore, the digital twin of a universal robot is developed, and its path planning is done in the presence of obstacles using the proposed optimization algorithm. The obtained path is then inspected by human expert and validated. It is shown that the proposed approach can effectively solve such optimization problems which arises in Industry 4.0 environment.

4 Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow, U.K. * corresponding.liusihan1200@163.com (Sihan Liu); genyunsun@163.com (Genyun Sun) Abstract: Band selection is an important data dimensionality reduction tool in hyperspectral images (HSIs). To identify the most informative subset band from the hundreds of highly corrected bands in HSIs, a novel hyperspectral band selection method using a crossover based gravitational search algorithm (CGSA) is presented in this paper. In this method, the discriminative capability of each band subset is evaluated by a combined optimization criterion, which is constructed based on the overall classification accuracy and the size of the band subset. As the evolution of the criterion, the subset is updated using the V-shaped transfer function based CGSA. Ultimately, the band subset with the best fitness value is selected. Experiments on two public hyperspectral datasets, i.e. the Indian Pines dataset and the Pavia University dataset, have been conducted to test the performance of the proposed method. Comparing experimental results against the basic GSA and the PSOGSA (hybrid PSO and GSA) revealed that all of the three GSA variants can considerably reduce the band dimensionality of HSIs without damaging their classification accuracy. Moreover, the CGSA shows superiority on both the effectiveness and efficiency compared to the other two GSA variants.

Keywords Gravitational search algorithm, Particle swarm optimization 1. INTRODUCTION Now a day, making intelligent and smart equipment through expert systems is predominantly innovative concepts for present research [11]. Therefore exploring expert system with the help of data mining and its learning algorithms has lots of scope for research work. In machine learning, the extraction of meaningful data and classifying bulk data is comparatively better for producing precise, speedy and straight forward results and hence among several methods of expert systems, selected technique has been classification. Machine learning symbolizes transformation in the ideology that is flexible in a way that they enable the system to do the same work more productively the next time. In past years many successful intelligent retrieval applications have been developed, reaching from data mining platform that learn user reading preferences to autonomy. Intelligent retrieval system is also utilized in various fields of real life application like, statistics, artificial intelligence, biology, cognitive science, computational complexity and control theory, medical, finance, engineering, aeronautic , philosophy, information theory.

6 Conclusion In this paper, a novel thresholding method based on fuzzy entropy using gravitational search algorithm has been proposed. The performance of the proposed method has been evaluated on the six test images and compared with particle swarm optimization on vari- ous parameters such as maximum entropy, standard deviation of entropy, PSNR. In proposed method en- tropy has been used as an objective function. We per- formed the experiment for bilevel and extended to mul- tilevel thresholding. The results obtained from test im- ages demonstrated that GSA performs better than PSO in terms of entropy, PSNR, stability and computation time. The experimental results show the effectiveness of GSA.