A Hopfield network learning method for bipartite subgraph problem

We present a gradient ascent learning method of the Hopfield neural network for bipartite subgraph problem. The method is intended to provide a near-optimum parallel algorithm for solving the bipartite subgraph problem. To do this we use the Hopfield neural network to get a near-maximum bipartite subgraph, and increase the energy by modifying weights in a gradient ascent direction of the energy to help the network escape from the state of the near-maximum bipartite subgraph to the state of the maximum bipartite subgraph or better one. A large number of instances are simulated to verify the proposed method with the simulation results showing that the solution quality is superior to that of best existing parallel algorithm. We also test the learning method on total coloring problem. The simulation results show that our method finds optimal solution in every test graph.     

A hill-jump algorithm of Hopfield neural network for shortest path problem in communication network

In this paper, we present a hill-jump algorithm of the Hopfield neural network for the shortest path problem in communication networks, where the goal is to find the shortest path from a starting node to an ending node. The method is intended to provide a near-optimum parallel algorithm for solving the shortest path problem. To do this, first the method uses the Hopfield neural network to get a path. Because the neural network always falls into a local minimum, the found path is usually not a shortest path. To search the shortest path, the method then helps the neural network jump from local minima of energy function by using another neural network built from a part of energy function of the problem. The method is tested through simulating some randomly generated communication networks, with the simulation results showing that the solution found by the proposed method is superior to that of the best existing neural network based algorithm.     

A hybrid approach based on stochastic competitive Hopfield neural network and efficient genetic algorithm for frequency assignment problem

This paper presents a hybrid efficient genetic algorithm (EGA) for the stochastic competitive Hopfield (SCH) neural network, which is named SCH–EGA. This approach aims to tackle the frequency assignment problem (FAP). The objective of the FAP in satellite communication system is to minimize the co-channel interference between satellite communication systems by rearranging the frequency assignment so that they can accommodate increasing demands. Our hybrid algorithm involves a stochastic competitive Hopfield neural network (SCHNN) which manages the problem constraints, when a genetic algorithm searches for high quality solutions with the minimum possible cost. Our hybrid algorithm, reflecting a special type of algorithm hybrid thought, owns good adaptability which cannot only deal with the FAP, but also cope with other problems including the clustering, classification, and the maximum clique problem, etc. In this paper, we first propose five optimal strategies to build an efficient genetic algorithm. Then we explore three hybridizations between SCHNN and EGA to discover the best hybrid algorithm. We believe that the comparison can also be helpful for hybridizations between neural networks and other evolutionary algorithms such as the particle swarm optimization algorithm, the artificial bee colony algorithm, etc. In the experiments, our hybrid algorithm obtains better or comparable performance than other algorithms on 5 benchmark problems and 12 large problems randomly generated. Finally, we show that our hybrid algorithm can obtain good results with a small size population.     

Parallel algorithms for finding a near-maximum independent set of acircle graph

A parallel algorithm for finding a near-maximum independent set in a circle graph is presented. An independent set in a graph is a set of vertices, no two of which are adjacent. A maximum independent set is an independent set whose cardinality is the largest among all independent sets of a graph. The algorithm is modified for predicting the secondary structure in ribonucleic acids (RNA). The proposed system, composed of an n neural network array (where n is the number of edges in the circle graph of the number of possible base pairs), not only generates a near-maximum independent set but also predicts the secondary structure of ribonucleic acids within several hundred iteration steps. The simulator discovered several solutions which are more stable structures, in a sequence of 359 bases from the potato spindle tuber viroid, than previously proposed structures.     

Fuzzy Clustering Using A Compensated Fuzzy Hopfield Network

Hopfield neural networks are well known for cluster analysis with an unsupervised learning scheme. This class of networks is a set of heuristic procedures that suffers from several problems such as not guaranteed convergence and output depending on the sequence of input data. In this paper, a Compensated Fuzzy Hopfield Neural Network (CFHNN) is proposed which integrates a Compensated Fuzzy C-Means (CFCM) model into the learning scheme and updating strategies of the Hopfield neural network. The CFCM, modified from Penalized Fuzzy C-Means algorithm (PFCM), is embedded into a Hopfield net to avoid the NP-hard problem and to speed up the convergence rate for the clustering procedure. The proposed network also avoids determining values for the weighting factors in the energy function. In addition, its training scheme enables the network to learn more rapidly and more effectively than FCM and PFCM. In experimental results, the CFHNN method shows promising results in comparison with FCM and PFCM methods.     

Hopfield神经网络在机组组合问题中的应用

提出利用多层Hopfield神经网络求解机组组合优化问题。通过构造合适的能量函数使得单层Hopfield神经网络可以解决某一时刻的机组出力问题,与之相对应的多层神经网络可以解决任意时间段的机组出力问题。多层Hopfield神经网络的层数由所需求解问题的时间段确定。给出单层及多层神经网络的能量函数及求解算法,能量函数考虑到机组升降功率和出力上下限的约束。通过对已有文献的算例进行计算比对,所得结果和遗传算法基本一致,但Hopfield神经网络通过解微分方程组来确定最优解,计算时间相对较少。     

Theoretical limitations of a Hopfield network for crossbarswitching

It has been reported through simulations that Hopfield networks for crossbar switching almost always achieve the maximum throughput. It has therefore appeared that Hopfield networks of high-speed computation by parallel processing could possibly be used for crossbar switching. However, it has not been determined whether they can always achieve the maximum throughput. In the paper, the capabilities and limitations of a Hopfield network for crossbar switching are considered. The Hopfield network considered in the paper is generated from the most familiar and seemingly the most powerful neural representation of crossbar switching. Based on a theoretical analysis of the network dynamics, we show what switching control the Hopfield network can or cannot produce. Consequently, we are able to show that a Hopfield network cannot always achieve the maximum throughput.     

基于局部进化的Hopfield神经网络的优化计算方法

提出一种基于局部进化的Hopfield神经网络优化计算方法，该方法将遗传算法和Hopfield神经网络结合在一起，克服了Hopfield神经网络易收敛到局部最优值的缺点，以及遗传算法收敛速度慢的缺点。该方法首先由Hopfield神经网络进行状态方程的迭代计算降低网络能量，收敛后的Hopfield神经网络在局部范围内进行遗传算法寻优，以跳出可能的局部最优值陷阱，再由Hopfield神经网络进一步迭代优化。这种局部进化的Hopfield神经网络优化计算方法尤其适合于大规模的优化问题，对图像分割问题和规模较大的200城市旅行商问题的优化计算结果表明，其全局收敛率和收敛速度明显提高。     

求解最大团问题的混合修复遗传算法及其在社会网络中的应用

社会网络分析是数据挖掘中与社会生活联系最紧密的热点之一,凝聚子群分析是一种典型的社会网络子结构分析方法,其中最大团结构是关系最紧密的凝聚子群,最大团问题的研究在社会网络分析中有重要意义。针对遗传算法在求解最大团问题中运行时间长、部分基准图例求解精度不高等问题,提出了一种基于混合修复策略的遗传算法MGA。MGA算法融合度修复和随机染色体修复方法并结合随机配对的精英选择、均匀块交叉和倒位变异算子,可以有效避免算法陷入局部最优,在加快收敛速度和丰富种群多样性方面有明显效果。算法在DIMACS基准图例和典型的社会网络实例上进行了测试,实验结果表明MGA算法具有较好的求解精度和较快的收敛速度。     

基于局部有限搜索的无向图近似最大团快速求解算法

无向图最大团求解是一个著名的NP-完全问题,解决该问题的经典算法基本上都采用完全精确搜索策略。鉴于NP-完全问题本身所固有的复杂性,这些算法或许仅适用于某些特殊的小规模图,对于具有大规模顶点和边的复杂图还是显得无力,难以适用。针对完全精确搜索策略下的无向图最大团求解算法的大部分时间都用于对图进行额外而无效的查找的问题,采用分划递归技术将图划分为邻接子图和悬挂子图,然后对邻接子图进行递归求解,而对悬挂子图则通过设置搜索范围控制函数进行局部有限搜索。在DIMACS数据集上将所提算法与当前主要的最大团求解算法进行对比实验,结果表明,文中提出的局部有限搜索求解策略能在75%的基准数据上获得最大团,剩下不能得到最大团的数据实际上也可以获得接近于最大团的近似最大团,但算法的平均求解时间仅为目前最大团精确求解算法的20%左右。因此,在很多最大团非精确要求的场景中,所提算法具有极高的应用价值。     

基于遗忘进化规划的Hopfield网学习算法

本文提出了一个基于遗忘进化规划的Hopfield网学习算法.通过遗忘部分个体,算法能避免局部最小.给定不动点、极限环或迭代序列,通过解不等式,算法能同时获得Hopfield网的拓扑结构和权值.该算法克服了进化Hopfield网学习的局限性.它还能找到多个优化解.实验也证明了该算法的有效性.     

使用模糊竞争Hopfield网络进行图像分割

针对传统自组织竞争学习方法的不足,将模糊竞争学习引入竞争Hopfield网络中,由此设计了一个用于图像分割的模糊竞争Hopfield网络,通过将图像空间映射到灰度特征空间,实现灰度特征集的模糊聚类,进而实现图像分割.实验结果表明:对于二值分割,与Ostu方法相比,此算法在分割效果和对噪声的自适应能力方面具有明显的优点.对于多类分割,此算法比目前的FCM(fuzzy C mean)算法的处理速度要快.     

Microcode optimization with neural networks

Microcode optimization is an NP-complete combinatorial optimization problem. This paper proposes a new method based on the Hopfield neural network for optimizing the wordwidth in the control memory of a microprogrammed digital computer. We present two methodologies, viz., the maximum clique approach, and a cost function based method to minimize an objective function. The maximum clique approach albeit being near O(1) in complexity, is limited in its use for small problem sizes, since it only partitions the data based on the compatibility between the microoperations, and does not minimize the cost function. We thereby use this approach to condition the data initially (to form compatibility classes), and then use the proposed second method to optimize the cost function. The latter method is then able to discover better solutions than other schemes for the benchmark data set.     

一种Hopfield神经网络能量函数改进下的作业车间调度*

由于作业车间调度问题的目标函数目前还无法用换位矩阵的元素以数学公式的形式表示,因此无法保证求出全局最优解。文中首先对换位矩阵表示方法进行了改进,给出新的带有目标函数的能量函数表达式,然后提出改进的Hopfield神经网络作业车间调度方法,并将模拟退火应用于Hopfield神经网络求解,避免了陷入局部极值。仿真结果表明,该方法具有全局搜索能力,并能够保证神经网络的稳态输出为全局最优或近似全局最优。     

Approximating the maximum weight clique using replicator dynamics

Given an undirected graph with weights on the vertices, the maximum weight clique problem (MWCP) is to find a subset of mutually adjacent vertices (a clique) having the largest total weight. This is a generalization of the problem of finding the maximum cardinality clique of an unweighted graph, which is the special case of the MWCP when all vertex weights are equal. The problem is NP-hard for arbitrary graphs, and so is the problem of approximating it within a constant factor. We present a parallel, distributed heuristic for approximating the MWCP based on dynamics principles. It centers around a continuous characterization of the MWCP (a purely combinatorial problem), and lets it be formulated in terms of continuous quadratic programming. One drawback is the presence of spurious solutions, and we present their characterizations. To avoid them we introduce a regularized continuous formulation of the MWCP and show how it completely solves the problem. The formulation naturally maps onto a parallel, distributed computational network whose dynamical behavior is governed by the replicator equations. These are dynamical systems introduced in evolutionary game theory and population genetics to model evolutionary processes on a macroscopic scale. We present theoretical results which guarantee that the solutions provided by our clique finding replicator network are actually those sought. Experimental results confirm the effectiveness of the proposed approach.     

基于神经网络量子算法的多用户检测器

利用遗传量子算法和Hopfield神经网络,提出了一种融合两种算法优点的神经网络量子算法,并将其应用到CDMA通信系统的多用户检测问题中。所提算法把神经网络嵌入到遗传量子算法的每一代中,可进一步提高量子种群的适应度函数值。通过混合神经网络到GQA中,还可加快GQA的收敛速度进而减少算法的计算复杂度。另外,GQA所提供的良好初值改善了HNN的性能,嵌入的HNN也提高了GQA的性能。仿真结果证明了该方法的抗多址干扰能力和抗远近效应能力都优于传统检测器和一些应用智能算法的多用户检测器。     

Neural network for optimal steiner tree computation

Hopfield neural network model for finding the shortest path between two nodes in a graph was proposed recently in some literatures. In this paper, we present a modified version of Hopfield model to a more general problem of searching an optimal tree (least total cost tree) from a source node to a number of destination nodes in a graph. This problem is called Steiner tree in graph theory, where it is proved to be a NP-complete. Through computer simulations, it is shown that the proposed model could always find an optimal or near-optimal valid solution in various graphs.     

Mapping graphs Of parallel programs onto graphs of distributed computer systems by recurrent neural networks

A problem of mapping graphs of parallel programs onto graphs of distributed computer systems by recurrent neural network is formulated. Parameter values providing absence of incorrect solutions are experimentally determined. Because of introduction of penalty coefficient into Lyapunov function for the program graph edges non-coincided with the system graph edges, optimal solutions are found for mapping a “line”-graph onto a two-dimensional torus. For increasing probability of finding optimal mapping, a method for splitting the mapping is proposed. The method essence is a reducing solution matrix to a block-diagonal form. The Wang recurrent neural network is used to exclude incorrect solutions of the problem of mapping the line-graph onto a three-dimensional torus. This network converges quicker than the Hopfield one.     

Guaranteed convergence in a class of Hopfield networks

A class of symmetric Hopfield networks with nonpositive synapses and zero threshold is analyzed in detail. It is shown that all stationary points have a one-to-one correspondence with the minimal vertex covers of certain undirected graphs, that the sequential Hopfield algorithm as applied to this class of networks converges in at most 2n steps (n being the number of neurons), and that the parallel Hopfield algorithm either converges in one step or enters a two-cycle in one step. The necessary and sufficient condition on the initial iterate for the parallel algorithm to converge in one step are given. A modified parallel algorithm which is guaranteed to converge in [3n/2] steps ([x] being the integer part of x) for an n-neuron network of this particular class is also given. By way of application, it is shown that this class naturally solves the vertex cover problem. Simulations confirm that the solution provided by this method is better than those provided by other known methods.     

Optimization of stochastic networks using simulated annealing for the storage and recalling of compressed images using SOM

In this paper we are studying the optimization of Stochastic Hopfield neural network and the hybrid SOM–Hopfield neural network for the storage and recalling of fingerprint images. The feature extraction of these images has been performed using FFT, DWT and SOM. The feature vectors are stored in the Hopfield network with Hebbian learning and modified Pseudoinverse learning rules. The study explores the tolerance of Hopfield neural networks for reducing the effect of spurious minima in the recalling process by employing the Simulated annealing process. It is observed from the simulations that the capabilities of the Hopfield network can be sufficiently enhanced by making modifications in the feature extraction of the input data. DWT and SOM together can be used to significantly enhance the recall efficiency. The probability of error in recall in the form of spurious minima is minimized by adopting simulated annealing process in the pattern recalling process.