Enrique Mérida-Casermeiro

An Efficient Multivalued Hopfield Network for the Traveling Salesman Problem

In this Letter we show that discrete multivalued Hopfield-type neural networks enable a relatively easy formulation of the Traveling Salesman Problem compared to the traditional Hopfield model. Thus, with the multivalued representation the network can be easily confined to feasible solutions, avoiding the need to tune any parameter. An investigation into the performance of the network has led us to define updating rules based on simple effective heuristic algorithms, a technique that can not be usually incorporated into standard Hopfield models. Simulation results for Euclidean Traveling Salesman Problems taken from the data library TSPLIB [11] indicate that this multivalued neural approach is superior to the best neural network currently reported for this problem.

Modelling competitive Hopfield networks for the maximum clique problem

The maximum clique problem (MCP) is a classic graph optimization problem with many real-world applications. This problem is NP-complete and computationally intractable even to approximate with certain absolute performance bounds. In this paper, we present the design of a new discrete competitive Hopfield neural network for finding near-optimum solutions for the MCP. Other competitive Hopfield-style networks have been proposed to solve the MCP. However, recent results have shown that these models can sometimes lead to inaccurate results and oscillatory behaviors in the convergence process. Thus, the network sometimes does not converge to cliques of the considered graph, where this error usually increases with the size and the density of the graph. In contrast, we propose in this paper appropriate dynamics for a binary competitive Hop-field network in order to always generate local/global minimum points corresponding to maximal/maximun cliques of the considered graph. Moreover, an optimal modelling of the network is developed, resulting in a fast two-level winner-take-all scheme. Extensive simulation runs show that our network performs better than the other competitive neural approaches in terms of the solution quality and the computation time.

A neural implementation of multi-adjoint logic programming ☆

We present a neural net based implementation of propositional [0; 1]-valued multiadjoint logic programming. The implementation needs some preprocessing of the initial program to transform it in a homogeneous program; then, transformation rules carry programs into neural networks, where truth-values of rules relate to output of neurons, truth-values of facts represent input, and network functions are determined by a set of general operators; the output of the net being the values of propositional variables under its minimal model.

Graph partitioning via recurrent multivalued neural networks

In this work, the well-known Graph Partitioning (GP) problem for undirected weighted graphs has been studied from two points of view: maximizing (MaxCut) or minimizing (MinCut) the cost of the cut induced in the graph by the partition. An unified model, based on a neural technique for optimization problems, has been applied to these two concrete problems. A detailed description of the model is presented, and the technique to minimize an energy function, that measures the goodness of solutions, is fully described. Some techniques to escape from local optima are presented as well. It has proved to be a very competitive and efficient algorithm, in terms of quality of solutions and computational time, when compared to the state-of-the-art methods. Some simulation results are presented in this paper, to show the comparative efficiency of the methods.

Improving Neural Networks for Mechanism Kinematic Chain Isomorphism Identification

Detection of isomorphism among kinematic chains is essential in mechanical design, but difficult and computationally expensive. It has been shown that both traditional methods and previously presented neural networks still have a lot to be desired in aspects such as simplifying procedure of identification and adapting automatic computation. Therefore, a new algorithm based on a competitive Hopfield network is developed for automatic computation in the kinematic chain isomorphism problem. The neural approach provides directly interpretable solutions and does not demand tuning of parameters. We have tested the algorithm by solving problems reported in the recent mechanical literature. Simulation results show the effectiveness of the network that rapidly identifies isomorphic kinematic chains.

A New Multivalued Neural Network for Isomorphism Identification of Kinematic Chains

A lot of methods have been proposed for the kinematic chain isomorphism problem. However, the tool is still needed in building intelligent systems for product design and manufacturing. In this paper, we design a novel multivalued neural network that enables a simplified formulation of the graph isomorphism problem. In order to improve the performance of the model, an additional constraint on the degree of paired vertices is imposed. The resulting discrete neural algorithm converges rapidly under any set of initial conditions and does not need parameter tuning. Simulation results show that the proposed multivalued neural network performs better than other recently presented approaches.

An N-parallel multivalued network: applications to the travelling salesman problem

In a competitive neural network, a process unit (node) in the competitive layer is completely described by the vector of weight from the input node to it. Each such weight vector becomes the centroid of a cluster of inputs since the principal function of a competitive learning network is discovers cluster of overlapping input. In this paper we propose a competitive neural network where each process unit has a couple of weight vectors (dipoles) that becomes a line segment as representation of a cluster. A weight update is formulated such that the dipole associated with each process unit is as near as possible to all the input samples for which the node is the winner of the competition. This network allows the formation of groups or categories by means of unsupervised learning, where each class or category is identified by a line segment instead of a centroid. The line segment leads to a better representation of a group or class that a centroid that gives us only the position of the cluster. The network has been applied to the formation of groups or categories using the data IRIS, where the unsupervised learning algorithms reach between 12 and 17 incorrect classifications. However, while many partitional clustering algorithms and competitive neural networks are only suitable for detecting hyperspherical-shaped clusters, the proposed network gets only 5 incorrect classifications and is also suitable for detecting hyperspherical-shaped clusters.

Image compression by vector quantization with recurrent discrete networks

In this work we propose a recurrent multivalued network, generalizing Hopfields model, which can be interpreted as a vector quantifier. We explain the model and establish a relation between vector quantization and sum-of-squares clustering. To test the efficiency of this model as vector quantifier, we apply this new technique to image compression. Two well-known images are used as benchmark, allowing us to compare our model to standard competitive learning. In our simulations, our new technique clearly outperforms the classical algorithm for vector quantization, achieving not only a better distortion rate, but even reducing drastically the computational time.

Evaluation of trade-offs between two data sources for the accurate estimation of origin–destination matrices

In this paper, we evaluate the trade-offs between loop detector data and floating car data (FCD) for the real-time estimation of origin–destination (OD) matrices in small networks. The proposed methodology is based on a bi-level optimisation using fuzzy logic theory. Here we demonstrate that it provides accurate results with low computational cost, while presenting several advantages over other existing algorithms (especially in terms of data requirements, computational complexity, and quality of adjustment). The methodology is illustrated with three examples covering two different locations in the city of Zurich, Switzerland. Results are used to evaluate the trade-offs between loop detector coverage and the penetration rate of FCD, and to determine minimum values for ensuring a given accuracy level on the estimated OD matrices. In general, the resulting error in OD estimation is affected by the data redundancy in the network.

K-pages graph drawing with multivalued neural networks

In this paper, the K-pages graph layout problem is solved by a new neural model. This model consists of two neural networks performing jointly in order to minimize the same energy function. The neural technique applied to this problem allows to reduce the energy function by changing outputs from both networks -outputs of first network representing location of nodes in the nodes line, while the outputs of the second one meaning the page where the edges are drawn. A detailed description of the model is presented, and the technique to minimize an energy function is fully described. It has proved to be a very competitive and efficient algorithm, in terms of quality of solutions and computational time, when compared to the state-of-the-art heuristic methods specifically designed for this problem. Some simulation results are presented in this paper, to show the comparative efficiency of the methods.