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Journal articles on the topic 'Hopfield algorithm'

Author: Grafiati

Published: 4 June 2025

Last updated: 1 August 2025

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1

Yu, Bin. "A Method of Hopfield Neural Network Based Nearest Neighbor Mode Solving Logistics Distribution." Applied Mechanics and Materials 263-266 (December 2012): 2054–57. http://dx.doi.org/10.4028/www.scientific.net/amm.263-266.2054.

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To solve the problem of invalid and not optimal result for Hopfield neural network to logistics distribution, a nearest neighbor mode Hopfield neural network algorithm based on improved-loop is constructed. The solution of logistics distribution is initialized by nearest neighbor matrix, to seek optimized solution of logistics distribution with the energy function evolvement of Hopfield neural network. To verify this algorithm and the result of simulation, which is compared to other well-known algorithms, indicated that , nearest neighbor mode Hopfield neural network algorithm would avoid inva

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2

Darintsev, O. V., and A. B. Migranov. "Modification of the hopfield neural network model for solving the task of optimal task allocation in a group of mobile robots." Teoriâ i sistemy upravleniâ, no. 2 (September 24, 2024): 169–82. http://dx.doi.org/10.31857/s0002338824020145.

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In the context of group interaction among mobile robots, there arises the challenge of task distribution within the group, considering the robots' characteristics and the working environment. This study aims to modify the Hopfield neural network and develop methodologies for its application in solving the task allocation problem for an arbitrary number of tasks within a group of mobile robots. To achieve this, the Hopfield neural network is represented as a graph. An algorithm is presented, demonstrating the transition from the initial problem to the Traveling Salesman Problem (TSP). The appli

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WU, CHUNG-HSIEN, JHING-FA WANG, CHAUG-CHING HUANG, and JAU-YIEN LEE. "SPEAKER-INDEPENDENT RECOGNITION OF ISOLATED WORDS USING CONCATENATED NEURAL NETWORKS." International Journal of Pattern Recognition and Artificial Intelligence 05, no. 05 (1991): 693–714. http://dx.doi.org/10.1142/s0218001491000417.

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A speaker-independent isolated word recognizer is proposed. It is obtained by concatenating a Bayesian neural network and a Hopfield time-alignment network. In this system, the Bayesian network outputs the a posteriori probability for each speech frame, and the Hopfield network is then concatenated for time warping. A proposed splitting Learning Vector Quantization (LVQ) algorithm derived from the LBG clustering algorithm and the Kohonen LVQ algorithm is first used to train the Bayesian network. The LVQ2 algorithm is subsequently adopted as a final refinement step. A continuous mixture of Gaus

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4

Argollo de Menezes, M., and T. J. P. Penna. "Improving the Hopfield–Tank Approach for the Traveling Salesman Problem." International Journal of Modern Physics C 08, no. 05 (1997): 1095–102. http://dx.doi.org/10.1142/s0129183197000965.

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In this work we revisit the Hopfield–Tank algorithm for the traveling salesman problem (J. J. Hopfield and D. W. Tank, Biol. Cybern. 52, 141 (1985)) and report encouraging results, with a different dynamics, that makes the algorithm more efficient, finding better solutions in much less computational time.

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Priyatno, Gregorius Algananda Hartanto, and Rizki Dwi Romadhona. "Algoritma Hopfield dalam menentukan rute tercepat untuk pendistribusian telur kepada konsumen." Journal of Information System and Application Development 1, no. 2 (2023): 101–10. http://dx.doi.org/10.26905/jisad.v1i2.11066.

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ENJ Poultry Shop is a business that operates in the field of egg distribution. The main problem faced is determining delivery routes, which are still less effective. The focus of this research is optimization to determine the fastest route through implementing the Hopfield algorithm in the application. With the Hopfield algorithm, it is hoped that it can provide a solution for finding the shortest route to distribute eggs to consumers. This research is quantitative, where the analysis is carried out by comparing the results of manual calculations with the results of calculations using the appl

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Muhammad Sidik, Siti Syatirah, Nur Ezlin Zamri, Mohd Shareduwan Mohd Kasihmuddin, Habibah A. Wahab, Yueling Guo, and Mohd Asyraf Mansor. "Non-Systematic Weighted Satisfiability in Discrete Hopfield Neural Network Using Binary Artificial Bee Colony Optimization." Mathematics 10, no. 7 (2022): 1129. http://dx.doi.org/10.3390/math10071129.

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Recently, new variants of non-systematic satisfiability logic were proposed to govern Discrete Hopfield Neural Network. This new variant of satisfiability logical rule will provide flexibility and enhance the diversity of the neuron states in the Discrete Hopfield Neural Network. However, there is no systematic method to control and optimize the logical structure of non-systematic satisfiability. Additionally, the role of negative literals was neglected, reducing the expressivity of the information that the logical structure holds. This study proposed an additional optimization layer of Discre

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Xiao, Yao, Yashu Zhang, Xiangguang Dai, and Dongfang Yan. "Clustering Based on Continuous Hopfield Network." Mathematics 10, no. 6 (2022): 944. http://dx.doi.org/10.3390/math10060944.

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Clustering aims to group n data samples into k clusters. In this paper, we reformulate the clustering problem into an integer optimization problem and propose a recurrent neural network with n×k neurons to solve it. We prove the stability and convergence of the proposed recurrent neural network theoretically. Moreover, clustering experiments demonstrate that the proposed clustering algorithm based on the recurrent neural network can achieve the better clustering performance than existing clustering algorithms.

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Wang, Xun, and Jie Rong. "The Computer Network Optimization Model Based on Neural Network Algorithm Research." Advanced Materials Research 798-799 (September 2013): 545–48. http://dx.doi.org/10.4028/www.scientific.net/amr.798-799.545.

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The speed of development of the computer network is an urgent need to comprehensively improve and optimize the overall performance of the network. Neural network algorithm has a massively parallel processing and distributed information storage, Hopfield neural network showed a unique advantage in the associative memory and optimization based on the neural network algorithm for computer network optimization model of Hopfield neural network theory and reality computer network, modern optimization methods, it is combined.

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9

Benedetti, Marco, Enrico Ventura, Enzo Marinari, Giancarlo Ruocco, and Francesco Zamponi. "Supervised perceptron learning vs unsupervised Hebbian unlearning: Approaching optimal memory retrieval in Hopfield-like networks." Journal of Chemical Physics 156, no. 10 (2022): 104107. http://dx.doi.org/10.1063/5.0084219.

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The Hebbian unlearning algorithm, i.e., an unsupervised local procedure used to improve the retrieval properties in Hopfield-like neural networks, is numerically compared to a supervised algorithm to train a linear symmetric perceptron. We analyze the stability of the stored memories: basins of attraction obtained by the Hebbian unlearning technique are found to be comparable in size to those obtained in the symmetric perceptron, while the two algorithms are found to converge in the same region of Gardner’s space of interactions, having followed similar learning paths. A geometric interpretati

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Someetheram, Vikneswari, Muhammad Fadhil Marsani, Mohd Shareduwan Mohd Kasihmuddin, et al. "Random Maximum 2 Satisfiability Logic in Discrete Hopfield Neural Network Incorporating Improved Election Algorithm." Mathematics 10, no. 24 (2022): 4734. http://dx.doi.org/10.3390/math10244734.

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Real life logical rule is not always satisfiable in nature due to the redundant variable that represents the logical formulation. Thus, the intelligence system must be optimally governed to ensure the system can behave according to non-satisfiable structure that finds practical applications particularly in knowledge discovery tasks. In this paper, we a propose non-satisfiability logical rule that combines two sub-logical rules, namely Maximum 2 Satisfiability and Random 2 Satisfiability, that play a vital role in creating explainable artificial intelligence. Interestingly, the combination will

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YEUNG, DANIEL S., SHENSHAN QIU, ERIC C. C. TSANG, and XIZHAO WANG. "A GENERAL UPDATING RULE FOR DISCRETE HOPFIELD-TYPE NEURAL NETWORK WITH TIME-DELAY AND THE CORRESPONDING SEARCH ALGORITHM." International Journal of Computational Intelligence and Applications 01, no. 04 (2001): 399–412. http://dx.doi.org/10.1142/s1469026801000329.

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In this paper, the Hopfield neural network with delay (HNND) is studied from the standpoint of regarding it as an optimizing computational model. Two general updating rules for networks with delay (GURD) are given based on Hopfield-type neural networks with delay for optimization problems and characterized by dynamic thresholds. It is proved that in any sequence of updating rule modes, the GURD monotonously converges to a stable state of the network. The diagonal elements of the connection matrix are shown to have an important influence on the convergence process, and they represent the relati

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Sun, Yanxia, Zenghui Wang, and Barend Jacobus van Wyk. "Chaotic Hopfield Neural Network Swarm Optimization and Its Application." Journal of Applied Mathematics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/873670.

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A new neural network based optimization algorithm is proposed. The presented model is a discrete-time, continuous-state Hopfield neural network and the states of the model are updated synchronously. The proposed algorithm combines the advantages of traditional PSO, chaos and Hopfield neural networks: particles learn from their own experience and the experiences of surrounding particles, their search behavior is ergodic, and convergence of the swarm is guaranteed. The effectiveness of the proposed approach is demonstrated using simulations and typical optimization problems.

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Talaván, Pedro M., and Javier Yáñez. "A continuous Hopfield network equilibrium points algorithm." Computers & Operations Research 32, no. 8 (2005): 2179–96. http://dx.doi.org/10.1016/j.cor.2004.02.008.

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14

Wang, Rong Long, Zheng Tang, and Qi Ping Cao. "An Efficient Approximation Algorithm for Finding a Maximum Clique Using Hopfield Network Learning." Neural Computation 15, no. 7 (2003): 1605–19. http://dx.doi.org/10.1162/089976603321891828.

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In this article, we present a solution to the maximum clique problem using a gradient-ascent learning algorithm of the Hopfield neural network. This method provides a near-optimum parallel algorithm for finding a maximum clique. To do this, we use the Hopfield neural network to generate a near-maximum clique and then modify weights in a gradient-ascent direction to allow the network to escape from the state of near-maximum clique to maximum clique or better. The proposed parallel algorithm is tested on two types of random graphs and some benchmark graphs from the Center for Discrete Mathematic

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15

Chi, Zhang, Zhang Chun, Wang Yan, and Hu Hao. "Research on fire distribution algorithm based on Hopfield neural network." Journal of Physics: Conference Series 2478, no. 9 (2023): 092006. http://dx.doi.org/10.1088/1742-6596/2478/9/092006.

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Abstract the problem of air defense fire distribution in ECM command and control system is studied. Based on the mathematical model of fire distribution, the classical solution algorithm Hungarian method is introduced, and the shortcomings of Hungarian method in solving fire distribution are pointed out. According to the basic principle of Hopfield neural network model, the algorithm process of solving specific optimization problems is deduced, and the fire distribution problem is simulated. According to the simulation results, the application conclusion and improved method of Hopfield neural

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Šíma, Jiří, Pekka Orponen, and Teemu Antti-Poika. "On the Computational Complexity of Binary and Analog Symmetric Hopfield Nets." Neural Computation 12, no. 12 (2000): 2965–89. http://dx.doi.org/10.1162/089976600300014791.

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We investigate the computational properties of finite binary- and analog-state discrete-time symmetric Hopfield nets. For binary networks, we obtain a simulation of convergent asymmetric networks by symmetric networks with only a linear increase in network size and computation time. Then we analyze the convergence time of Hopfield nets in terms of the length of their bit representations. Here we construct an analog symmetric network whose convergence time exceeds the convergence time of any binary Hopfield net with the same representation length. Further, we prove that the MIN ENERGY problem f

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17

FEIGELMAN, M. V., and L. B. IOFFE. "THE AUGMENTED MODELS OF ASSOCIATIVE MEMORY ASYMMETRIC INTERACTION AND HIERARCHY OF PATTERNS." International Journal of Modern Physics B 01, no. 01 (1987): 51–68. http://dx.doi.org/10.1142/s0217979287000050.

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The asymmetric modification of the Hopfield model of the associative memory is considered. It is shown that the asymmetry does not change the main properties of the model, but leads to the internal nonthermal noise. The modification of the Hopfield algorithm is proposed which can be used for storing the correlated patterns and its storage capacity is estimated. The hierarchical memory model is proposed and studied.

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Hu, Yun, and Qianqian Duan. "Solving the TSP by the AALHNN algorithm." Mathematical Biosciences and Engineering 19, no. 4 (2022): 3427–48. http://dx.doi.org/10.3934/mbe.2022158.

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<abstract> <p>It is prone to get stuck in a local minimum when solving the Traveling Salesman Problem (TSP) by the traditional Hopfield neural network (HNN) and hard to converge to an efficient solution, resulting from the defect of the penalty method used by the HNN. In order to mend this defect, an accelerated augmented Lagrangian Hopfield neural network (AALHNN) algorithm was proposed in this paper. This algorithm gets out of the dilemma of penalty method by Lagrangian multiplier method, ensuring that the solution to the TSP is undoubtedly efficient. The second order factor adde

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Loo, Chu Kiong, Mitja Peruš, and Horst Bischof. "Associative Memory Based Image and Object Recognition by Quantum Holography." Open Systems & Information Dynamics 11, no. 03 (2004): 277–89. http://dx.doi.org/10.1023/b:opsy.0000047571.17774.8d.

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A quantum associative memory, much more natural than those of “quantum computers”, is presented. Neural-net-like processing with real-valued variables is transformed into processing with quantum waves. Successful computer simulations of image storage and retrieval are reported. Our Hopfield-like algorithm allows quantum implementation with holographic procedure using present-day quantum-optics techniques. This brings many advantages over classical Hopfield neural nets and quantum computers with logic gates.

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20

Kathirvel, Vigneshwer, Mohd Asyraf Mansor, Mohd Shareduwan Mohd Kasihmuddin, and Saratha Sathasivam. "Hybrid Imperialistic Competitive Algorithm Incorporated with Hopfield Neural Network for Robust 3 Satisfiability Logic Programming." IAES International Journal of Artificial Intelligence (IJ-AI) 8, no. 2 (2019): 144. http://dx.doi.org/10.11591/ijai.v8.i2.pp144-155.

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Imperialist Competitive algorithm (ICA) is a robust training algorithm inspired by the socio-politically motivated strategy. This paper focuses on utilizing a hybridized ICA with Hopfield Neural Network on a 3-Satisfiability (3-SAT) logic programming. Eventually the performance of the proposed algorithm will be compared to other 2 algorithms, which are HNN-3SATES (ES) and HNN-3SATGA (GA). The performance shall be evaluated with the Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Sum of Squares Error (SSE), Schwarz Bayesian Criterion (SBC), Global Minima Ratio and Computation Time (CP

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Vigneshwer, Kathirvel, Asyraf Mansor Mohd., Shareduwan Mohd Kasihmuddin Mohd, and Sathasivam Saratha. "Hybrid imperialistic competitive algorithm incorporated with hopfield neural network for robust 3 satisfiability logic programming." International Journal of Artificial Intelligence (IJ-AI) 8, no. 2 (2019): 144–55. https://doi.org/10.11591/ijai.v8.i2.pp144-155.

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Imperialist Competitive algorithm (ICA) is a robust training algorithm inspired by the socio-politically motivated strategy. This paper focuses on utilizing a hybridized ICA with Hopfield Neural Network on a 3- Satisfiability (3-SAT) logic programming. Eventually the performance of the proposed algorithm will be compared to other 2 algorithms, which are HNN3SATES (ES) and HNN-3SATGA (GA). The performance shall be evaluated with the Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Sum of Squares Error (SSE), Schwarz Bayesian Criterion (SBC), Global Minima Ratio and Computation Time (CP

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Ziyadullaev, Davron, Dildora Muhamediyeva, Sholpan Ziyaeva, Umirzoq Xoliyorov, Khasanturdi Kayumov, and Otabek Ismailov. "Development of a traditional transport system based on the bee colony algorithm." E3S Web of Conferences 365 (2023): 01017. http://dx.doi.org/10.1051/e3sconf/202336501017.

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At present, a significant part of optimization problems, particularly questions of combinatorial optimization, are considered NP-complete problems. When solving optimization problems, the neural network approach increases the probability of obtaining an optimal solution. The traveling salesman problem is considered a test optimization problem. This problem was solved using the Hopfield neural network. In solving optimization problems, numerous computation processes and computation time are required. To improve performance and increase the program's speed, there are cases of inappropriate purch

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Juang, Jyh-Ching, and Guo-Shing Huang. "Application of Kalman Filter and Mean Field Annealing Algorithms in GPS-Based Attitude Determination." Journal of Navigation 51, no. 1 (1998): 117–31. http://dx.doi.org/10.1017/s0373463397007650.

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In this paper, two algorithms of Global Positioning System based attitude determination are proposed. The first algorithm extends the Kalman filter approach to determine the integer ambiguity and the orientation that is needed in a typical gps-based attitude determination problem. The second algorithm explores the mean field annealing neural network approach, which is a combination of the competitive Hopfield neural network and the stochastic simulated annealing technique, to resolve the optimal attitude problems. A test platform is set up for verifying these algorithms. The two algorithms are

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He, Mengyang, Lei Zhuang, Sijin Yang, Jianhui Zhang, and Huiping Meng. "Energy-Efficient Virtual Network Embedding Algorithm Based on Hopfield Neural Network." Wireless Communications and Mobile Computing 2021 (January 28, 2021): 1–13. http://dx.doi.org/10.1155/2021/8889923.

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To solve the energy-efficient virtual network embedding problem, this study proposes an embedding algorithm based on Hopfield neural network. An energy-efficient virtual network embedding model was established. Wavelet diffusion was performed to take the structural feature value into consideration and provide a candidate set for virtual network embedding. In addition, the Hopfield network was used in the candidate set to solve the virtual network energy-efficient embedding problem. The augmented Lagrangian multiplier method was used to transform the energy-efficient virtual network embedding c

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URAHAMA, KIICHI. "PERFORMANCE OF NEURAL ALGORITHMS FOR MAXIMUM-CUT PROBLEMS." Journal of Circuits, Systems and Computers 02, no. 04 (1992): 389–95. http://dx.doi.org/10.1142/s0218126692000246.

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The author previously developed a new neural algorithm effective for set-partitioning combinatorial optimization problems by extending the logistic transformation used in the Hopfield algorithm into its multivariable version. In this letter the performance of the algorithm is theoretically evaluated and it is proved that this algorithm is 1/p-approximate for p-partitioning maximum-cut problems.

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Kobayashi, Masaki. "Fast Recall for Complex-Valued Hopfield Neural Networks with Projection Rules." Computational Intelligence and Neuroscience 2017 (2017): 1–6. http://dx.doi.org/10.1155/2017/4894278.

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Many models of neural networks have been extended to complex-valued neural networks. A complex-valued Hopfield neural network (CHNN) is a complex-valued version of a Hopfield neural network. Complex-valued neurons can represent multistates, and CHNNs are available for the storage of multilevel data, such as gray-scale images. The CHNNs are often trapped into the local minima, and their noise tolerance is low. Lee improved the noise tolerance of the CHNNs by detecting and exiting the local minima. In the present work, we propose a new recall algorithm that eliminates the local minima. We show t

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Ahn, C. W., R. S. Ramakrishna, C. G. Kang, and I. C. Choi. "Shortest path routing algorithm using Hopfield neural network." Electronics Letters 37, no. 19 (2001): 1176. http://dx.doi.org/10.1049/el:20010800.

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David, Andrew J., and Bahaa E. A. Saleh. "Optical implementation of the Hopfield algorithm using correlations." Applied Optics 29, no. 8 (1990): 1063. http://dx.doi.org/10.1364/ao.29.001063.

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An, Jin Liang, Jia Gao, Jin Hui Lei, and Guo Hong Gao. "An Improved Algorithm for TSP Problem Solving with Hopfield Neural Networks." Advanced Materials Research 143-144 (October 2010): 538–42. http://dx.doi.org/10.4028/www.scientific.net/amr.143-144.538.

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Hopfield and Tank have shown that neural networks can be used to solve certain computationally hard problems, in particular they studied the Traveling Salesman Problem (TSP). In this paper,on the base of the analysis of tradiontial methord,introduced an improved algorithm for TSP Problem Solving with Hopfield Neural Networks.We found the accuracy of the results depend on the initial parameters to a large extent, discussed how to set initial parameters properly; analysed the internal relationship between the terms in energy function, and improved the energy function. Used a fixed starting point

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Azizan, Farah Liyana, Saratha Sathasivam, Nurshazneem Roslan, and Ahmad Deedat Ibrahim. "Logic mining with hybridized 3-satisfiability fuzzy logic and harmony search algorithm in Hopfield neural network for Covid-19 death cases." AIMS Mathematics 9, no. 2 (2024): 3150–73. http://dx.doi.org/10.3934/math.2024153.

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<abstract> <p>Since the beginning of the Covid-19 infections in December 2019, the virus has emerged as the most lethally contagious in world history. In this study, the Hopfield neural network and logic mining technique merged to extract data from a model to provide insight into the link between factors influencing the Covid-19 datasets. The suggested technique uses a 3-satisfiability-based reverse analysis (3SATRA) and a hybridized Hopfield neural network to identify the relationships relating to the variables in a set of Covid-19 data. The list of data is to identify the relatio

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Shi, Jun You, Hong Yan Zhai, and Chuang Sheng Su. "Optimal Layout of the Irregular Parts with Neural Networks Hybrid Algorithm." Advanced Materials Research 97-101 (March 2010): 3514–18. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.3514.

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An irregular parts optimal layout method based on artificial neural networks is proposed. The manufacturing process of parts is involved in the layout problem. Every side of shapes is expanded in consideration of the machining allowance. Self-Organizing Map (SOM) and Hopfield artificial neural network are integrated to complete the automatic layout. In the beginning, irregular parts are randomly distributed. Self-Organizing Map is used to look for the best position of the irregular parts by moving them. The overlapping area is gradually reduced to zero. Hopfield neural network is used to rotat

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Percy, R. Cheryal. "Segmentation of Remotely Sensed Images using Unsupervised ‘Sampling-Resampling’ based on Hopfield Type Neural Network." International Journal Of Engineering And Computer Science 7, no. 02 (2018): 23606–12. http://dx.doi.org/10.18535/ijecs/v7i2.14.

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In this paper we propose a technique for performing unsupervised segmentation for satellite images using a ’sampling – resampling’ based on Hopfield type Neural Network. The multi band values of the satellite images are grouped into clusters that are modeled using Gaussians. The parameters of Gaussian mixture models are learnt using Hopfield Type Neural Network. The purpose of this work is to show the effectiveness of the results obtained by using Hopfield type Neural Network rather than Bayesian parameter estimation. Each spatial position in the considered image is represented by neuron that

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Wei, Na, Zhe Cheng, and Xiao Meng Wu. "Study of Reconfiguration Algorithm in Distribution System Based on Hopfield Network." Applied Mechanics and Materials 241-244 (December 2012): 1900–1903. http://dx.doi.org/10.4028/www.scientific.net/amm.241-244.1900.

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In accordance with the characteristic of radial running an algorithm for distribution network reconfiguration based on Hopfield neural network is put forward. The in-degree of each node is determined by Hopfield neural network, it is determined whether the lines run according to the in-degree of the nodes, and the state of each loop switch is determined according to whether the lines run, and thus the distribution network reconfiguration scheme is determined finally. The energy function of the neural network and its solution method are presented. In the energy function are considered the radia

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Ren, Kun, and Jihong Qu. "Identification of Shaft Centerline Orbit for Wind Power Units Based on Hopfield Neural Network Improved by Simulated Annealing." Mathematical Problems in Engineering 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/571354.

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In the maintenance system of wind power units, shaft centerline orbit is an important feature to diagnosis the status of the unit. This paper presents the diagnosis of the orbit as follows: acquire characters of orbit by the affine invariant moments, take this as the characteristic parameters of neural networks to construct the identification model, utilize Simulated Annealing (SA) Algorithm to optimize the weights matrix of Hopfield neural network, and then some typical faults were selected as examples to identify. Experiment’s results show that SA-Hopfield identification model performed bett

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Bagheri, F., N. Ghafarnia, and F. Bahrami. "Electrocardiogram (ECG) Signal Modeling and Noise Reduction Using Hopfield Neural Networks." Engineering, Technology & Applied Science Research 3, no. 1 (2013): 345–48. http://dx.doi.org/10.48084/etasr.243.

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The Electrocardiogram (ECG) signal is one of the diagnosing approaches to detect heart disease. In this study the Hopfield Neural Network (HNN) is applied and proposed for ECG signal modeling and noise reduction. The Hopfield Neural Network (HNN) is a recurrent neural network that stores the information in a dynamic stable pattern. This algorithm retrieves a pattern stored in memory in response to the presentation of an incomplete or noisy version of that pattern. Computer simulation results show that this method can successfully model the ECG signal and remove high-frequency noise.

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Liu, Song, Xinhua Gao, Liu Chen, et al. "Multi-Traveler Salesman Problem for Unmanned Vehicles: Optimization through Improved Hopfield Neural Network." Sustainability 15, no. 20 (2023): 15118. http://dx.doi.org/10.3390/su152015118.

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In response to the COVID-19 pandemic, communities utilize unmanned vehicles to minimize person-to-person contact and lower the risk of infection. This paper addresses the critical considerations of these unmanned vehicles’ maximum load capacity and service time, formulating them as constraints within a multi-traveling salesman problem (MTSP). We propose a comprehensive optimization approach that combines a genetic simulated annealing algorithm with clustering techniques and an improved Hopfield neural network (IHNN). First, the MTSP is decomposed into multiple independent TSPs using the fuzzy

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Shehab, Abdulhabib Alzaeemi, Sathasivam Saratha, and Velavan Muraly. "Hybrid Genetic Algorithm Model in Neuro Symbolic Integration." International Journal of Engineering and Advanced Technology (IJEAT) 9, no. 4 (2020): 2144–49. https://doi.org/10.35940/ijeat.D8761.049420.

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The development of artificial neural network and logic programming plays an important part in neural network studies. Genetic Algorithm (GA) is one of the escorted randomly searching technicality that uses evolutional concepts of the natural election as a stimulus to solve the computational problems. The essential purposes behind the studies of the evolutional system is for developing adaptive search techniques which are robust. In this paper, GA is merged with agent based modeling (ABM) by using specified proceedings to optimise the states of neurons and energy function in the Hopfield neural

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Abubakar, Hamza, Shamsul Rijal Muhammad Sabri, Sagir Abdu Masanawa, and Surajo Yusuf. "Modified election algorithm in hopfield neural network for optimal random k satisfiability representation." International Journal for Simulation and Multidisciplinary Design Optimization 11 (2020): 16. http://dx.doi.org/10.1051/smdo/2020008.

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Election algorithm (EA) is a novel metaheuristics optimization model motivated by phenomena of the socio-political mechanism of presidential election conducted in many countries. The capability and robustness EA in finding an optimal solution to optimization has been proven by various researchers. In this paper, modified version of EA has been utilized in accelerating the searching capacity of Hopfield neural network (HNN) learning phase for optimal random-kSAT logical representation (HNN-R2SATEA). The utility of the proposed approach has been contrasted with the current standard exhaustive se

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Karoun, Rabia Chaimaà, Adel Ouannas, Mohammed Al Horani, and Giuseppe Grassi. "The Effect of Caputo Fractional Variable Difference Operator on a Discrete-Time Hopfield Neural Network with Non-Commensurate Order." Fractal and Fractional 6, no. 10 (2022): 575. http://dx.doi.org/10.3390/fractalfract6100575.

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In this work, we recall some definitions on fractional calculus with discrete-time. Then, we introduce a discrete-time Hopfield neural network (D.T.H.N.N) with non-commensurate fractional variable-order (V.O) for three neurons. After that, phase-plot portraits, bifurcation and Lyapunov exponents diagrams are employed to verify that the proposed discrete time Hopfield neural network with non-commensurate fractional variable order has chaotic behavior. Furthermore, we use the 0-1 test and C0 complexity algorithm to confirm and prove the results obtained about the presence of chaos. Finally, simu

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Heggarty, K. J., and R. C. Chevallier. "Optical implementation of an improved Hopfield-like retrieval algorithm." Optics Communications 88, no. 2-3 (1992): 91–95. http://dx.doi.org/10.1016/0030-4018(92)90491-9.

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Zhang, Haitao, and Shuangqi Yang. "Image Encryption Based on Hopfield Neural Network and Bidirectional Flipping." Computational Intelligence and Neuroscience 2022 (February 11, 2022): 1–7. http://dx.doi.org/10.1155/2022/7941448.

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Many encryption systems face two problems: the key has nothing to do with the plaintext; only a single chaotic sequence is adopted during the encryption. To solve the problems, this paper proposes an image encryption method based on Hopfield neural network and bidirectional flipping. Firstly, the plaintext image was segmented into blocks, the resulting image matrix was block scrambled, and each block was bidirectionally flipped to complete the scrambling process. After that, the plaintext image was processed by the hash algorithm to obtain the initial values and control parameters of the chaot

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Chen, Ju, Yuan Gao, Mohd Shareduwan Mohd Kasihmuddin, et al. "MTS-PRO2SAT: Hybrid Mutation Tabu Search Algorithm in Optimizing Probabilistic 2 Satisfiability in Discrete Hopfield Neural Network." Mathematics 12, no. 5 (2024): 721. http://dx.doi.org/10.3390/math12050721.

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The primary objective of introducing metaheuristic algorithms into traditional systematic logic is to minimize the cost function. However, there is a lack of research on the impact of introducing metaheuristic algorithms on the cost function under different proportions of positive literals. In order to fill in this gap and improve the efficiency of the metaheuristic algorithm in systematic logic, we proposed a metaheuristic algorithm based on mutation tabu search and embedded it in probabilistic satisfiability logic in discrete Hopfield neural networks. Based on the traditional tabu search alg

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Liu, Song, Di Liu, and Meilong Le. "Multi-UAV Delivery Path Optimization Based on Fuzzy C-Means Clustering Algorithm Based on Annealing Genetic Algorithm and Improved Hopfield Neural Network." World Electric Vehicle Journal 16, no. 3 (2025): 157. https://doi.org/10.3390/wevj16030157.

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This study develops an MTSP model for multi-UAV delivery optimization from a central hub, proposing a hybrid algorithm that integrates genetic simulated annealing-enhanced clustering with an improved Hopfield neural network to minimize the total flight distance. The proposed methodology initially employs an enhanced fuzzy C-means clustering technique integrated with genetic simulated annealing (GSA) to effectively partition the MTSP formulation into multiple discrete traveling salesman problem (TSP) instances. The subsequent phase implements an enhanced Hopfield neural network (HNN) architectu

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Zhang, Na. "Psychological Stress Identification and Evaluation Method Based on Mobile Human-Computer Interaction Equipment." Applied Bionics and Biomechanics 2022 (April 25, 2022): 1–13. http://dx.doi.org/10.1155/2022/6039789.

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Since the 1980s, the research of artificial neural networks in the field of artificial intelligence has become more and more common. It accepts nonlinear parallel processing, has strong learning and flexibility, and can be used for influencing factor analysis. The ideal power values and triggers are obtained in the Hopfield network model using genetic algorithm, which best avoids the drawbacks of the Hopfield network model instillation learning method. Through the BP of mobile human-computer interaction equipment, hereditary, genetic algorithms, and Hi-PLS regression method in the artificial n

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Zhang, Na. "Psychological Stress Identification and Evaluation Method Based on Mobile Human-Computer Interaction Equipment." Applied Bionics and Biomechanics 2022 (April 25, 2022): 1–13. http://dx.doi.org/10.1155/2022/6039789.

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Since the 1980s, the research of artificial neural networks in the field of artificial intelligence has become more and more common. It accepts nonlinear parallel processing, has strong learning and flexibility, and can be used for influencing factor analysis. The ideal power values and triggers are obtained in the Hopfield network model using genetic algorithm, which best avoids the drawbacks of the Hopfield network model instillation learning method. Through the BP of mobile human-computer interaction equipment, hereditary, genetic algorithms, and Hi-PLS regression method in the artificial n

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Yu, Zheqi, Adnan Zahid, Shuja Ansari, et al. "Hardware-Based Hopfield Neuromorphic Computing for Fall Detection." Sensors 20, no. 24 (2020): 7226. http://dx.doi.org/10.3390/s20247226.

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With the popularity of smart wearable systems, sensor signal processing poses more challenges to machine learning in embedded scenarios. For example, traditional machine-learning methods for data classification, especially in real time, are computationally intensive. The deployment of Artificial Intelligence algorithms on embedded hardware for fast data classification and accurate fall detection poses a huge challenge in achieving power-efficient embedded systems. Therefore, by exploiting the associative memory feature of Hopfield Neural Network, a hardware module has been designed to simulate

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Kai, Cui. "An ad-hoc network routing algorithm based on improved neural network under the influence of COVID-19." Journal of Intelligent & Fuzzy Systems 39, no. 6 (2020): 8767–74. http://dx.doi.org/10.3233/jifs-189273.

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Under the influence of COVID-19, an efficient Ad-hoc network routing algorithm is required in the process of epidemic prevention and control. Artificial neural network has become an effective method to solve large-scale optimization problems. It has been proved that the appropriate neural network can get the exact solution of the problem in real time. Based on the continuous Hopfield neural network (CHNN), this paper focuses on the study of the best algorithm path for QoS routing in Ad-hoc networks. In this paper, a new Hopfield neural network model is proposed to solve the minimum cost proble

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LIU, SHAO-HAN, and JZAU-SHENG LIN. "A COMPENSATED FUZZY HOPFIELD NEURAL NETWORK FOR CODEBOOK DESIGN IN VECTOR QUANTIZATION." International Journal of Pattern Recognition and Artificial Intelligence 14, no. 08 (2000): 1067–79. http://dx.doi.org/10.1142/s0218001400000647.

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In this paper, a new Hopfield-model net called Compensated Fuzzy Hopfield Neural Network (CFHNN) is proposed for vector quantization in image compression. In CFHNN, the compensated fuzzy c-means algorithm, modified from penalized fuzzy c-means, is embedded into Hopfield neural network so that the parallel implementation for codebook design is feasible. The vector quantization can be cast as an optimal problem that may also be regarded as a minimization of a criterion defined as a function of the average distortion between training vector and codevector. The CFHNN is trained to classify the div

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Cheng, Guo Zhong, Wei Feng, Fang Song Cui, and Shi Lu Zhang. "Neural Network Algorithm for Solving Large Scale Travelling Salesman Problems." Advanced Materials Research 542-543 (June 2012): 1398–402. http://dx.doi.org/10.4028/www.scientific.net/amr.542-543.1398.

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This study improves the neural network algorithm that was presented by J.J.Hopfield for solving TSP(travelling salesman problem) and gets an effective algorithm whose time complexity is O(n*n), so we can solve quickly TSP more than 500 cities in microcomputer. The paper considers the algorithm based on the replacement function of the V Value. The improved algorithm can greatly reduces the time and space complexities of Hopfield method. The TSP examples show that the proposed algorithm could efficiently find a satisfactory solution and has a fast convergence speed.

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Roslan, Muhammad Aqmar Fiqhi, Nur Ezlin Zamri, Mohd Asyraf Mansor, and Mohd Shareduwan Mohd Kasihmuddin. "Major 3 Satisfiability logic in Discrete Hopfield Neural Network integrated with multi-objective Election Algorithm." AIMS Mathematics 8, no. 9 (2023): 22447–82. http://dx.doi.org/10.3934/math.20231145.

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<abstract> <p>Discrete Hopfield Neural Network is widely used in solving various optimization problems and logic mining. Boolean algebras are used to govern the Discrete Hopfield Neural Network to produce final neuron states that possess a global minimum energy solution. Non-systematic satisfiability logic is popular due to the flexibility that it provides to the logical structure compared to systematic satisfiability. Hence, this study proposed a non-systematic majority logic named Major 3 Satisfiability logic that will be embedded in the Discrete Hopfield Neural Network. The mode

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