Modified Hopfield Network Research Articles

Development of a Dynamically Adaptable Routing System for Data Analytics Insights in Logistic Services

This work proposes an effective solution to the Vehicle Routing Problem, taking into account all phases of the delivery process. When compared to real-world data, the findings are encouraging and demonstrate the value of Machine Learning algorithms incorporated into the process. Several algorithms were combined along with a modified Hopfield network to deliver the optimal solution to a multiobjective issue on a platform capable of monitoring the various phases of the process. Additionally, a system providing viable insights and analytics in regard to the orders was developed. The results reveal a maximum distance saving of 25% and a maximum overall delivery time saving of 14%.

Comparison of image recognition efficiency of Bayes, correlation, and modified Hopfield network algorithms

The statistical estimates of the probability of correct recognition of the images, noisy reference by an additive handicap, for Bayes, correlation, and modified Hopfield network algorithms are compared. It is shown that, in the case of complete a priori probability concerning a handicap, the modified Hopfield network algorithm reaches the quality of the Bayes algorithm. At a deviation a priori probability on a handicap, the quality of the Bayes algorithm is worse than that of the modified Hopfield network algorithm. The correlation algorithm is worse than the modified Hopfield network algorithm, in general.

Application of a Modified Hopfield Network to the Traveling Salesman Problem

This paper presents the results of the application of the modified Hopfield network to the travelling salesman problem (TSP). A cost function of the TSP consists of four components: two terms which ensure that the salesman's tour is valid, the term which forces neurons to have the output signal equal to 0 or 1, and the total length of the salesman's tour. For two 10-city benchmarks the average tour length of obtained solutions is equal to the optimal tour length. Other works did not report such results using the classical Hopfield network. For greater numbers of cities, the solution quality is significantly better in comparison with the quality of results achieved in other works. The method of auto-tuning of the constant in the fourth component of the cost function is presented. This method ensures very good quality results for randomly generated instances of the 10-city TSP. The presented network is destined for hardware implementation.

A modified hopfield network for mobility management

AbstractThis paper presents a new approach to solving the mobile location management problem using the Paging Cells (PCs) scheme. In this approach (HNN‐BDT‐PC), a combination of the Hopfield Neural Network (HNN) and the author's Ball Dropping Technique (BDT) is used to solve the problem. To this end, the location management cost of a network is embedded in the HNN parameters, and by iteration, the mobile network gradually moves toward an optimal state. The approach is inspired by the phenomenon that results from the natural movement of balls when they are dropped onto a non‐even plate (a plate with troughs and crests). Each trough of the plate corresponds to a PC, and the network corresponds to the whole plate. The aim is to find optimal PC configuration (i.e., the troughs) of the network. Three main procedures are used in the optimization process; in each optimization cycle, the HNN is launched to move the balls around the plate, and, by analogy, to move the PCs around the network to find the best configuration. Copyright © 2007 John Wiley & Sons, Ltd.

FPGA implementation of a systems identification module based upon Hopfield networks

The aim of this contribution is to implement a hardware module that performs parametric identification of dynamical systems. The design is based upon the methodology of optimization with Hopfield neural networks, leading to an adapted version of these networks. An outstanding feature of this modified Hopfield network is the existence of weights that vary with time. Since weights can no longer be stored in read-only memories, these dynamic weights constitute a significant challenge for digital circuits, in addition to the usual issues of area occupation, fixed-point arithmetic and nonlinear functions computations. The implementation, which is accomplished on FPGA circuits, achieves modularity and flexibility, due to the usage of parametric VHDL to describe the network. In contrast to software simulations, the natural parallelism of neural networks is preserved, at a limited cost in terms of circuitry cost and processing time. The functional simulation and the synthesis show the viability of the design. In particular, the FPGA implementation exhibits a reasonably fast convergence, which is required to produce accurate parameter estimations. Current research is oriented towards integrating the estimator within an embedded adaptive controller for autonomous systems.

Neural Approach for Solving Several Types of Optimization Problems

Neural networks consist of highly interconnected and parallel nonlinear processing elements that are shown to be extremely effective in computation. This paper presents an architecture of recurrent neural net-works that can be used to solve several classes of optimization problems. More specifically, a modified Hopfield network is developed and its inter-nal parameters are computed explicitly using the valid-subspace technique. These parameters guarantee the convergence of the network to the equilibrium points, which represent a solution of the problem considered. The problems that can be treated by the proposed approach include combinatorial optimiza-tion problems, dynamic programming problems, and nonlinear optimization problems.

Development of neurofuzzy architecture for solving the N-Queens problem

Neural networks are dynamic systems consisting of highly interconnected and parallel nonlinear processing elements that are shown to be extremely effective in computation. This paper presents an architecture of recurrent neural networks for solving the N-Queens problem. More specifically, a modified Hopfield network is developed and its internal parameters are explicitly computed using the valid-subspace technique. These parameters guarantee the convergence of the network to the equilibrium points, which represent a solution of the considered problem. The network is shown to be completely stable and globally convergent to the solutions of the N-Queens problem. A fuzzy logic controller is also incorporated in the network to minimize convergence time. Simulation results are presented to validate the proposed approach.

Design and analysis of an efficient neural network model for solving nonlinear optimization problems

This paper presents an efficient approach based on a recurrent neural network for solving constrained nonlinear optimization. More specifically, a modified Hopfield network is developed, and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the convergence of the network to the equilibrium points that represent an optimal feasible solution. The main advantage of the developed network is that it handles optimization and constraint terms in different stages with no interference from each other. Moreover, the proposed approach does not require specification for penalty and weighting parameters for its initialization. A study of the modified Hopfield model is also developed to analyse its stability and convergence. Simulation results are provided to demonstrate the performance of the proposed neural network.

A novel approach based on recurrent neural networks applied to nonlinear systems optimization

This paper presents an efficient approach based on recurrent neural network for solving nonlinear optimization. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid subspace technique. These parameters guarantee the convergence of the network to the equilibrium points that represent an optimal feasible solution. The main advantage of the developed network is that it treats optimization and constraint terms in different stages with no interference with each other. Moreover, the proposed approach does not require specification of penalty and weighting parameters for its initialization. A study of the modified Hopfield model is also developed to analyze its stability and convergence. Simulation results are provided to demonstrate the performance of the proposed neural network.

Possible solution of parallel FIR filter structure

In this paper, a parallel form FIR adaptive filter structure with RLS (Recursive Least Squares) type adaptive algorithm is proposed. The proposed parallel form FIR structure consists of a recursive orthogonal transform stage and sparse FIR sub filters operating in parallel. The adaptive algorithm used to update coefficient vector of the sparse filters is implemented by using modified Hopfield networks. This structure implements the RLS-type adaptive algorithm, without an explicit matrix inversion avoiding numerical instability problems. Simulation results which show the desirable features of proposed structure are given.

Resolvendo problemas de fluxo de potência ótimo DC através de uma rede de hopfield modificada

Inúmeras abordagens neurais têm sido propostas na literatura para resolver problemas de Fluxo de Potência Ótimo DC. Mais especificamente, a rede de Hopfield é o modelo de rede mais utilizado nesses tipos de problemas. A maioria destes modelos, entretanto, ignora o sistema de transmissão. Tal simplificação deixa de considerar importantes restrições de potência ativa, podendo conduzir a cálculos equivocados de despacho. Outras desvantagens encontradas até então dizem respeito a problemas de velocidade, e também à dificuldade de se garantir a factibilidade das soluções. Este artigo discute a aplicação de uma rede de Hopfield modificada para resolver eficientemente problemas de Fluxo de Potência Ótimo DC. O sistema de transmissão neste caso é representado através de equações de fluxo de carga lineares e de restrições no fluxo de potência ativa. Os parâmetros internos da rede de Hopfield modificada apresentada neste artigo são computados através da técnica de subespaço-válido de soluções, o qual garante que as soluções encontradas pela rede (pontos de equilíbrio) sejam sempre factíveis. Resultados de simulações e uma análise de situações envolvendo sistemas testes IEEE são apresentados de modo a ilustrar a eficiência da abordagem proposta.

An efficient Hopfield network to solve economic dispatch problems with transmission system representation

Economic dispatch (ED) problems have recently been solved by artificial neural network approaches. Systems based on artificial neural networks have high computational rates due to the use of a massive number of simple processing elements and the high degree of connectivity between these elements. The ability of neural networks to realize some complex non-linear function makes them attractive for system optimization. All ED models solved by neural approaches described in the literature fail to represent the transmission system. Therefore, such procedures may calculate dispatch policies, which do not take into account important active power constraints. Another drawback pointed out in the literature is that some of the neural approaches fail to converge efficiently toward feasible equilibrium points. A modified Hopfield approach designed to solve ED problems with transmission system representation is presented in this paper. The transmission system is represented through linear load flow equations and constraints on active power flows. The internal parameters of such modified Hopfield networks are computed using the valid-subspace technique. These parameters guarantee the network convergence to feasible equilibrium points, which represent the solution for the ED problem. Simulation results and a sensitivity analysis involving IEEE 14-bus test system are presented to illustrate efficiency of the proposed approach.

Uma abordagem usando redes neurais artificiais para resolução de problemas de otimização restrita

Sistemas baseados em redes neurais artificiais fornecem altas taxas de computação devido ao uso de um número massivo de elementos processadores simples. Redes neurais com conexões realimentadas fornecem um modelo computacional capaz de resolver uma rica classe de problemas de otimização. Este artigo apresenta uma nova abordagem para resolver problemas de otimização restrita utilizando redes neurais artificiais. Mais especificamente, uma rede de Hopfield modificada é desenvolvida cujos parâmetros internos são calculados usando a técnica de subespaço válido de soluções. A partir da obtenção destes parâmetros a rede tende a convergir aos pontos de equilíbrio que representam as possíveis soluções para o problema. Exemplos de simulação são apresentados para justificar a validade da abordagem proposta.

A Modified Hopfield Neural Network for the Minimum Vertex Cover Problem

The minimum vertex cover(MVC) problem is a classic graph optimization problem. It is well known that it is NP-Complete problem. In this paper, a modified Hopfield neural network is presented for the minimum vertex cover problem. In the modified Hopfield neural network, a correction term is introduced into the motion equation. With this correction term, the modified Hopfield network can find optimal or near-optimal solutions for the minimum vertex cover problem in higher probability. Extensive simulations are performed, and the results show that the modified Hopfield neural network works much better than other existing algorithms for this problem on both random graphs and DIMACS benchmark graphs.

Object recognition and articulated object learning by accumulative Hopfield matching

In this paper, a novel object recognition method based on attributed relational graph matching is proposed, which is called accumulative Hopfield matching. We first divide the scene graph into many sub-graphs, and a modified Hopfield network is then constructed to obtain the sub-graph isomorphism between each sub-scene graph and model graph. The final result is deduced by accumulating the solutions of all small sub-networks. Comparing to the traditional Hopfield network, the proposed system has the advantage of finding homomorphic mappings between two graphs. Furthermore, the system can be applied for articulated object recognition and visual model learning, which is considered as a difficult topic till now. The proposed method has been evaluated with real images.

Neural networks in mechanics of structures and materials – new results and prospects of applications

Basic ideas of back-propagation neural networks (BPNNs) are presented in short. Then BPNN applications in analysis of the following problems are discussed: (1) bending analysis of elastoplastic beams, (2) elastoplastic plane stress problem, (3) estimation of fundamental vibration periods of real buildings, (4) detection of damage in a steel beam, (5) identification of loads applied to an elastoplastic beam. Regularization neural network is briefly discussed and its application to estimation of concrete fatigue durability it shown. A modified Hopfield network is used to the analysis of an elastic angular plate with unilateral constraints. In the end some conclusions and prospects of neurocomputing applications are pointed out.

A novel approach for solving constrained nonlinear optimization problems using neurofuzzy systems.

A neural network model for solving constrained nonlinear optimization problems with bounded variables is presented in this paper. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the convergence of the network to the equilibrium points. The network is shown to be completely stable and globally convergent to the solutions of constrained nonlinear optimization problems. A fuzzy logic controller is incorporated in the network to minimize convergence time. Simulation results are presented to validate the proposed approach.

The convergence properties of a clipped Hopfield network and its application in the design of keystream generator

We first present a modified Hopfield network, the clipped Hopfield network, with synaptic weights assigned to three values {-1,0,+1}. We give the necessary conditions under which a set of 2n binary vectors can be stored as stable points of the network. We show that in the parallel updating mode, for most of the state vectors, the network will always converge to these 2n stable points. We further demonstrate that these 2n stable points can be divided into two groups, the alpha group and the beta group, each with n stable points. It is shown that the basins of attraction of the stable points in the alpha group are evenly distributed, and the basins of attraction of the stable points in the beta group are also evenly distributed. By ways of application, we show that this class of Hopfield network can be used to build a cryptographically secure keystream generator.

An efficient model of neural networks for dynamic programming

Systems based on artificial neural networks have high computational rates owing to the use of a massive number of simple processing elements and the high degree of connectivity between these elements. Neural networks with feedback connections provide a computing model capable of solving a large class of optimization problems. This paper presents a novel approach for solving dynamic programming problems using artificial neural networks. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the convergence of the network to the equilibrium points. Simulated examples are presented and compared with other neural networks. The results demonstrate that the proposed method gives a significant improvement.

Modeling and analysis of artificial neural networks applied in operations research

Artificial neural networks are dynamic systems consisting of highly interconnected and parallel nonlinear processing elements. Systems based on artificial neural networks have high computational rates due to the use of a massive number of these computational elements. Neural networks with feedback connections provide a computing model capable of solving a rich class of optimization problems. In this paper, a modified Hopfield network is developed for solving problems related to operations research. The internal parameters of the network are obtained using the valid-subspace technique. Simulated examples are presented as an illustration of the proposed approach.