Variant Of Gravitational Search Algorithm Research Articles

Three-dimensional path planning with enhanced gravitational search algorithm for unmanned aerial vehicle

Abstract Path planning for the unmanned aerial vehicle (UAV) is to assist in finding the proper path, serving as a critical role in the intelligence of a UAV. In this paper, a path planning for UAV in three-dimensional environment (3D) based on enhanced gravitational search algorithm (EGSA) is put forward, taking the path length, yaw angle, pitch angle, and flight altitude as considerations of the path. Considering EGSA is easy to fall into local optimum and convergence insufficiency, two factors that are the memory of current optimal and random disturbance with chaotic levy flight are adopted during the update of particle velocity, improving the balance between exploration and exploitation for EGSA through different time-varying characteristics. With the identical cost function, EGSA is compared with seven peer algorithms, such as moth flame optimization algorithm, gravitational search algorithm, and five variants of gravitational search algorithm. The experimental results demonstrate that EGSA is superior to the seven comparison algorithms on CEC 2020 benchmark functions and the path planning method based on EGSA is more valuable than the other seven methods in diverse environments.

Elite‐of‐the‐Elites Driven Five‐Layered Gravitational Search Algorithm for Optimization

The gravitational search algorithm (GSA) is a popular optimization method inspired by celestial interactions. And the MLGSA is an outstanding variant of GSA. To improve its performance, we propose the elite‐of‐the‐elites driven five‐layered gravitational search algorithm (EFGSA). EFGSA introduces a new population layer comprising elite individuals, improving the balance between exploration and exploitation. Experimental results on the 2017 IEEE Conference on Evolutionary Computation (CEC) benchmark functions demonstrate EFGSA's superiority over the MLGSA algorithm in terms of solution quality and convergence speed. The obtained results underscore the efficacy of EFGSA in addressing optimization problems. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Locally informed gravitational search algorithm with hierarchical topological structure

Recently, gravitational search algorithm (GSA) has been successfully applied to solve various optimization problems. However, GSA tends to fall into local optimum because it ignores the environmental heterogeneity of agents. Therefore, locally informed gravitational search algorithm (LIGSA) based on neighborhood structure is proposed to balance exploration and exploitation. However, LIGSA ignores the differences in the evolutionary states between agents in the same neighborhood, and also ignores the differences in the evolutionary states between neighbors, which affects the performance of the algorithm. Therefore, a hierarchical locally informed gravitational search algorithm (HLIGSA) is proposed in this paper. This algorithm designs a hierarchical topology. In the lower layer, there are several non-overlapping neighborhoods, which constitute the whole population. Each agent in the neighborhood adaptively adjusts the gravitational constant according to its evolutionary state, so as to fully search the region of the neighborhood. The upper layer is a population composed of the best agents in each neighborhood, which performs gravity strategy or merging strategy for those neighborhoods that have lost the evolutionary capability, so as to balance the algorithm’s exploration and exploitation. The two layers work together to complete the entire search process. Experimental results show that HLIGSA outperforms many variants of GSA and many current state-of-the-art heuristic algorithms.

Quantum behaved Intelligent Variant of Gravitational Search Algorithm with Deep Neural Networks for Human Activity Recognition

Human activity recognition (HAR) encompasses the detection of daily routine activities to advance usability in detecting crime and preventing dangerous activities. The recognition of activities from videos and image sequences with higher exactitude is a major challenge due to system complexities. The efficient feature optimization approach can reduce system complexities by removing ineffective features, which also improves the activity recognition performance. This research work presents a novel quantum behaved intelligent gravitational search algorithm to optimize the features for human activity recognition. The proposed intelligent variant is termed as INQGSA, which optimizes the features by using the advantageous attributes of quantum computing (QC) and intelligent gravitational search algorithm (INGSA). In INQGSA, the intelligent factor avoids the trapping of mass agents in later iterations by using the information of the best and worst agents to update the position of agents. The addition of quantum computing based attributes (such as quantum bits, their superposition, and quantum gates, etc.) ensures a better diversity of discrete optimized features. To analyze the superiority of INQGSA, the feature optimization is also conducted with the gravitational search algorithm (GSA) and the quantum-inspired binary gravitational search algorithm (QBGSA). Finally, the optimized selected features are utilized by the deep neural networks (DNN) of ResNet-50V2 and ResNet-101V2 for the classification of activities. The activity recognition experiments are conducted on the UCF101 and HMDB51 datasets. The performance comparison of the proposed HAR system with state-of-the-art techniques signifies that the proposed system is superior and effective in detecting the different activities.

Alternated superior chaotic variants of gravitational search algorithm for optimization problems

Nature inspired algorithms like Gravitational Search Algorithm (GSA) has been able to solve complex optimization problems with a reasonable performance. But still there is problem of premature convergence to the local optimal solutions due to lack of appropriate balancing between exploration and exploitation procedures. In the literature, chaotic maps have been successful in diversifying the population to a greater level to avoid the entrapment of the solutions in local region(s), and provide better convergence speed with high precision. Recent developments in nonlinear dynamical systems, especially discrete alternated systems, have proved their worth in enhancing the functionality of the metaheuristic algorithms to a great extent (Kumar and Rani, 2019). We have integrated alternated discrete dynamical systems in superior orbit with GSA for more diversification of the population with the aim of increasing the chances for the candidate solutions to arrive at global solutions which otherwise remain stagnant in local optimal points. From the obtained results, we have verified that the proposed methods have outperformed the competing algorithms significantly as they have been able to arrive at global optimal points with much improved optimization rates. In some cases, the improvement in optimization values (mean and standard deviation) have reduced to less than twice the optimization values of the chaotic GSA.

A new intrusion detection method for cyber–physical system in emerging industrial IoT

In Industrial Internet-of-Things, data streams across heterogeneous networks which results in several cyber–physical attacks. Moreover, the security of unlabeled data is a challenging task. For the same, this paper presents a new clustering method for intrusion detection. The proposed method employs a novel variant of gravitational search algorithm to obtain optimal clusters. In the proposed variant, Kbest is modified as an exponentially decreasing function with logistic-mapping-based chaotic behavior. To validate the proposed variant, a comparative analysis on IEEE CEC2013 benchmark functions is conducted against five existing algorithms. Experimental results are investigated in terms of mean error value, Wilcoxon rank-sum test, convergence graph, box-plot, and time complexity. It has been observed that proposed variant attained best values for maximum number of times on each dimension, i.e. 10, 13, 15, and 10 on 10, 30, 50, and 90 dimensions, respectively. Further, the efficacy of the proposed clustering method is tested on five Industrial Internet-of-Things datasets. The evaluation is performed in terms of F-measure and computation time. Experiments affirm that the proposed method outperforms considered methods on 80% of the datasets in terms of F-measure and computation time for ensuring security in a real-time Industrial Internet-of-Things environment.

Multi-Pose Facial Expression Recognition Using Hybrid Deep Learning Model with Improved Variant of Gravitational Search Algorithm

The recognition of human facial expressions with the variation of poses is one of the challenging tasks in real-time applications such as human physiological interaction detection, intention analysis, marketing interest evaluation, mental disease diagnosis, etc. This research work addresses the problem of expression recognition from different facial poses at the yaw angle. The major contribution of the paper is the proposal of an autonomous pose variant facial expression recognition framework using the amalgamation of a hybrid deep learning model with an improved quantum inspired gravitational search algorithm. The hybrid deep learning model is the integration of the convolutional neural network and recurrent neural network. The applicability of the hybrid deep learning model can be considered as significant if the feature set is efficiently optimized to have the discriminative features respective to each expression class. Here, the Improved Quantum Inspired Gravitational Search Algorithm (IQI-GSA) is utilized for the selection and optimization of features. The IQI-GSA method is significant for optimizing the features compared to quantum-behaved binary gravitation search algorithm for handing the local optima and stochastic characteristics. Comparing with state-of-art techniques, the proposed framework exhibits the outperformed recognition rate for experimentation on Karolinska Directed Emotional Faces (KDEF) and Japanese Female Facial Expression (JAFFE) datasets.

Deep neural networks-based classification optimization by reducing the feature dimensionality with the variants of gravitational search algorithm

The optimization of the problems significantly improves the solution of the complex problems. The reduction in the feature dimensionality is enormously salient to reduce the redundant features and improve the system accuracy. In this paper, an amalgamation of different concepts is proposed to optimize the features and improve the system classification. The experiment is performed on the facial expression detection application by proposing the amalgamation of deep neural network models with the variants of the gravitational search algorithm. Facial expressions are the movement of the facial components such as lips, nose, eyes that are considered as the features to classify human emotions into different classes. The initial feature extraction is performed with the local binary pattern. The extracted feature set is optimized with the variants of gravitational search algorithm (GSA) as standard gravitational search algorithm (SGSA), binary gravitational search algorithm (BGSA) and fast discrete gravitational search algorithm (FDGSA). The deep neural network models of deep convolutional neural network (DCNN) and extended deep convolutional neural network (EDCNN) are employed for the classification of emotions from imagery datasets of JAFFE and KDEF. The fixed pose images of both the datasets are acquired and comparison based on average recognition accuracy is performed. The comparative analysis of the mentioned techniques and state-of-the-art techniques illustrates the superior recognition accuracy of the FDGSA with the EDCNN technique.

An ensemble approach of improved quantum inspired gravitational search algorithm and hybrid deep neural networks for computational optimization

In this paper, an autonomous ensemble approach of improved quantum inspired gravitational search algorithm (IQI-GSA) and hybrid deep neural networks (HDNN) is proposed for the optimization of computational problems. The IQI-GSA is a combinational variant of gravitational search algorithm (GSA) and quantum computing (QC). The improved variant enhances the diversity of mass collection for retaining the stochastic attributes and handling the local trapping of mass agents. Further, the hybrid deep neural network encompasses the convolutional and recurrent neural networks (HDCR-NN) which analyze the relational & temporal dependencies among the different computational components for optimization. The proposed ensemble approach is evaluated for the application of facial expression recognition by experimentation on Karolinska Directed Emotional Faces (KDEF) and Japanese Female Facial Expression (JAFFE) datasets. The experimentation evaluations evidently exhibit the outperformed recognition rate of the proposed ensemble approach in comparison with state-of-the-art techniques.

Path Planning for Unmanned Aerial Vehicle Using a Mix-Strategy-Based Gravitational Search Algorithm

Path planning is a global optimization problem aims to program the optimal flight path for Unmanned Aerial Vehicle (UAV) that has short length and suffers from low threat. In this paper, we present a Mixed-Strategy based Gravitational Search Algorithm (MSGSA) for the path planning. In MSGSA, an adaptive adjustment strategy for the gravitational constant attenuation factor alpha ( $\alpha$ ) is presented firstly, in which the value of $\alpha $ is adjusted based on the evolutionary state of the particles. This helps to adaptively balance the exploration and exploitation of the algorithm. In addition, to further alleviate the premature convergence problem, a Cauchy mutation strategy is developed for MSGSA. In this strategy, only when the global best particle cannot be further improved for several times the mutation is executed. In the MSGSA based path planning procedure, we construct an objective function using the flight length cost, threat area cost, and turning angle constraint to decrease the flight risk and obtain the smoother path. For performance evaluation, the MSGSA is applied to two typical simulated flight missions with complex flight environments, including user-defined forbidden flying areas, Radar, missile, artillery and anti-aircraft gun. The obtained flight paths are compared with that of the standard Gravitational Search Algorithm (GSA) and two improved variants of GSA, i.e. gbest -guided GSA (GGSA), and hybrid Particle Swarm Optimization and GSA (PSOGSA). The experimental results demonstrate the superiority of the MSGSA based method in terms of the solution quality, robustness, as well as the constraint-handling ability.

Gravitational search algorithm: a comprehensive analysis of recent variants

Gravitational search algorithm is a nature-inspired algorithm based on the mathematical modelling of the Newton’s law of gravity and motion. In a decade, researchers have presented many variants of gravitational search algorithm by modifying its parameters to efficiently solve complex optimization problems. This paper conducts a comparative analysis among ten variants of gravitational search algorithm which modify three parameters, namely Kbest, velocity, and position. Experiments are conducted on two sets of benchmark categories, namely standard functions and CEC2015 functions, including problems belonging to different categories such as unimodal, multimodal, and unconstrained optimization functions. The performance comparison is evaluated and statistically validated in terms of mean fitness value and convergence graph. In experiments, IGSA has achieved better precision with balanced trade-off between exploration and exploitation. Moreover, triple negative breast cancer dataset has been considered to analysis the performance of GSA variants for the nuclei segmentation. The variants performance has been analysed in terms of both qualitative and quantitive with aggregated Jaccard index as performance measure. Experiments affirm that IGSA-based method has outperformed other methods.

Parameter tuning for meta-heuristics

These days meta-heuristic algorithms are gaining lot of popularity. The performance of the meta-heuristics depends upon the suitable selection of user dependent parameters. Finding the most suitable values for the parameters (fine tuning) is a challenging problem. This paper proposes a generalized strategy to find the most suitable value of any parameter for a meta-heuristic algorithm. The approach is based on the relation between algorithm’s performance and functional landscape. The proposed approach is evaluated by applying it to a recent meta-heuristic algorithm, Gravitational Search Algorithm (GSA). The parameter α which plays a vital role in the convergence of GSA search process, is fine tuned using the proposed strategy. Obtained values of α, change the nature of gravitational coefficient G from monotonic to non-monotonic for a cluster free diversified search. The proposed strategy is tested over CEC-2015 test suite. Various statistical tests have been applied to compare the obtained results with recent variants of GSA and other state-of-the-art meta-heuristics. Results confirm that the parameters obtained using proposed approach significantly improve the results.

Evaluation of fuzzy based HS and GSA on reloading cycle length optimization of PWR nuclear power plant

Nowadays, nuclear power is a portion of the response to energy demand growth in the world. Therefore, the optimal use of this energy is a major challenge for the scientists. One of the ways to increase energy extraction from nuclear power plant (NPP) is enhancement of refueling cycle length (RCL) by in-core loading pattern optimization (LPO). In this paper, the Gravitational Search Algorithm (GSA) and Harmony Search Algorithm (HS) are selected as metaheuristic algorithms for in-core LPO. The GSA and HS have been inspired by the gravity law and music improvisation process, respectively. Hence, for enhancing the performance of the GSA and HS in the optimization process of in-core loading pattern, a new variant of GSA and HS, i.e. Fuzzy Gravitational Search Algorithm (FGSA) and Fuzzy Harmony Search (FHS), have been implemented. In this way, at first, the performance of FGSA and FHS are compared with the GSA and HS algorithms on Drop Wave Function. Then, these algorithms have been developed for loading pattern optimization of WWER1000 reactor core. The results show that FHS has promising performance for the LPO problem. The RCL, using the FHS is increased from 287 to 292 days and it is demonstrated that in the case, FHS have better results in comparison to other algorithms. Finally, a reactor core pattern with five extra operating days in 1000 MWe with significant economic advantages has been proposed.

An automatic nuclei segmentation method using intelligent gravitational search algorithm based superpixel clustering

Abstract A reliable nuclei segmentation is still an open-ended problem, especially in the breast cancer histology images. For the same, this paper proposes an intelligent gravitational search algorithm based superpixel clustering method for automatic nuclei segmentation. In the proposed method, a novel variant of gravitational search algorithm, intelligent gravitational search algorithm, is employed to obtain the optimal cluster centroids. The experimental and statistical results evince that the proposed variant surpasses existing meta-heuristic algorithms on 47 benchmark functions belonging to different problem categories i.e., unimodal, multimodal, and real-parameter single objective optimization problems of CEC, 2013. Further, the segmentation accuracy of the proposed method is examined on H&E stained estrogen receptor positive (ER+) breast cancer images. Experiments affirm that the proposed method is comparatively an efficacious and accurate method for segmenting the nuclei within breast cancer histology images.

An image segmentation method using logarithmic kbest gravitational search algorithm based superpixel clustering

Image segmentation partitions an image into coherent and non-overlapping regions. Due to variations of visual patterns in images, it is a challenging problem. This paper introduces a new superpixel-based clustering method to efficiently perform the image segmentation. In the proposed method, initially superpixels from an image are obtained. The superpixels are further clustered into the required number of regions by a newly proposed variant of gravitational search algorithm namely; logarithmic kbest gravitational search algorithm. Experiments are conducted on the Berkeley Segmentation Dataset and Benchmark (BSDS500). It is affirmed from both visual and numerical analyses that the proposed method is efficacious and accurate in segmenting an image than the other considered segmentation methods.

Reconstruction of 3D curves and surfaces using new variants of gravitational search algorithm

The problem of reconstruction of 3D curves and surfaces is modelled as a nonlinear optimization problem in which the objective function to be minimized is the error function between given data points and data points on the generated curve/surface.Although any optimization algorithm can be used to solve this problem, but due to the inherent complexities in the optimization model, heuristic algorithms are best suited. In this paper, a recently proposed nature motivated optimization technique, namely Gravitational Search Algorithm and its three variants are used to solve reconstruction problem. The approach is illustrated with the help of two examples- a helix and a dumbbell. The results are demonstrated and it is concluded that the approach is very promising in the area.

An optimum multi-level image thresholding segmentation using non-local means 2D histogram and exponential Kbest gravitational search algorithm

Multi-level image thresholding segmentation divides an image into multiple non-overlapping regions. This paper presents a novel two-dimensional (2D) histogram-based segmentation method to improve the efficiency of multi-level image thresholding segmentation. In the proposed method, a new non-local means 2D histogram and a novel variant of gravitational search algorithm (exponential Kbest gravitational search algorithm) have been used to find the optimal thresholds. Further, for the optimization, a 2D Rényi entropy has been redefined for multi-level thresholding. The proposed method has been tested on the Berkeley Segmentation Dataset and Benchmark (BSDS300) in terms of both subjective and objective assessments. The experimental results affirm that the proposed method outperforms the other 2D histogram-based image thresholding segmentation methods on majority of performance parameters.

A comprehensive survey on gravitational search algorithm

Abstract Gravitational Search Algorithm (GSA) is an optimization method inspired by the theory of Newtonian gravity in physics. Till now, many variants of GSA have been introduced, most of them are motivated by gravity-related theories such as relativity and astronomy. On the one hand, to solve different kinds of optimization problems, modified versions of GSA have been presented such as continuous (real), binary, discrete, multimodal, constraint, single-objective, and multi-objective GSA. On the other hand, to tackle the difficulties in real-world problems, the efficiency of GSA has been improved using specialized operators, hybridization, local search, and designing the self-adaptive algorithms. Researchers have utilized GSA to solve various engineering optimization problems in diverse fields of applications ranging from electrical engineering to bioinformatics. Here, we discussed a comprehensive investigation of GSA and a brief review of GSA developments in solving different engineering problems to build up a global picture and to open the mind to explore possible applications. We also made a number of suggestions that can be undertaken to help move the area forward.

A stability constrained adaptive alpha for gravitational search algorithm

Gravitational search algorithm (GSA), a recent meta-heuristic algorithm inspired by Newton's law of gravity and mass interactions, shows good performance in various optimization problems. In GSA, the gravitational constant attenuation factor alpha (α) plays a vital role in convergence and the balance between exploration and exploitation. However, in GSA and most of its variants, all agents share the same α value without considering their evolutionary states, which has inevitably caused the premature convergence and imbalance of exploration and exploitation. In order to alleviate these drawbacks, in this paper, we propose a new variant of GSA, namely stability constrained adaptive alpha for GSA (SCAA). In SCAA, each agent's evolutionary state is estimated, which is then combined with the variation of the agent's position and fitness feedback to adaptively adjust the value of α. Moreover, to preserve agents’ stable trajectories and improve convergence precision, a boundary constraint is derived from the stability conditions of GSA to restrict the value of α in each iteration. The performance of SCAA has been evaluated by comparing with the original GSA and four alpha adjusting algorithms on 13 conventional functions and 15 complex CEC2015 functions. The experimental results have demonstrated that SCAA has significantly better searching performance than its peers do.

Improved Variants of Gravitational Search Algorithm Based on “Best-so-Far” Updating Mechanism

Gravitational Search Algorithm is a memory-less nature inspired optimization technique which keeps a record of the position of the “best- so- far” particle during the current as well as populations during previous iterations. The “best-so-far” particle or Lbest particle may not be the same as the best particle of the current population. With an objective to enhance the exploration of GSA, in this paper, three natural updating mechanisms of “best-so-far” particle are used to design three new variants of GSA, called IGSA-1, IGSA-2 and IGSA-3. The experiments are performed on a set of 23 benchmarks problems, divided into three category of problems. Based on the numerical analysis of results it is concluded that the overall performance of IGSA-1 is better than others on scalable unimodal function for 30 dimensional problems and low dimensional multimodal functions, whereas the performance of IGSA-3 is better than others on scalable multimodal functions having 30 dimension.