José Muñoz-Pérez

COVNET: a cooperative coevolutionary model for evolving artificial neural networks

This paper presents COVNET, a new cooperative coevolutionary model for evolving artificial neural networks. This model is based on the idea of coevolving subnetworks that must cooperate to form a solution for a specific problem, instead of evolving complete networks. The combination of this subnetworks is part of a coevolutionary process. The best combinations of subnetworks must be evolved together with the coevolution of the subnetworks. Several subpopulations of subnetworks coevolve cooperatively and genetically isolated. The individual of every subpopulation are combined to form whole networks. This is a different approach from most current models of evolutionary neural networks which try to develop whole networks. COVNET places as few restrictions as possible over the network structure, allowing the model to reach a wide variety of architectures during the evolution and to be easily extensible to other kind of neural networks. The performance of the model in solving three real problems of classification is compared with a modular network, the adaptive mixture of experts and with the results presented in the bibliography. COVNET has shown better generalization and produced smaller networks than the adaptive mixture of experts and has also achieved results, at least, comparable with the results in the bibliography.

Multi-objective cooperative coevolution of artificial neural networks (multi-objective cooperative networks)

In this paper we present a cooperative coevolutive model for the evolution of neural network topology and weights, called MOBNET. MOBNET evolves subcomponents that must be combined in order to form a network, instead of whole networks. The problem of assigning credit to the subcomponents is approached as a multi-objective optimization task. The subcomponents in a cooperative coevolutive model must fulfill different criteria to be useful, these criteria usually conflict with each other. The problem of evaluating the fitness on an individual based on many criteria that must be optimized together can be approached as a multi-criteria optimization problems, so the methods from multi-objective optimization offer the most natural way to solve the problem. In this work we show how using several objectives for every subcomponent and evaluating its fitness as a multi-objective optimization problem, the performance of the model is highly competitive. MOBNET is compared with several standard methods of classification and with other neural network models in solving four real-world problems, and it shows the best overall performance of all classification methods applied. It also produces smaller networks when compared to other models. The basic idea underlying MOBNET is extensible to a more general model of coevolutionary computation, as none of its features are exclusive of neural networks design. There are many applications of cooperative coevolution that could benefit from the multi-objective optimization approach proposed in this paper.

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.

Design and analysis of maximum Hopfield networks

Since McCulloch and Pitts presented a simplified neuron model (1943), several neuron models have been proposed. Among them, the binary maximum neuron model was introduced by Takefuji et al. and successfully applied to some combinatorial optimization problems. Takefuji et al. also presented a proof for the local minimum convergence of the maximum neural network. In this paper we discuss this convergence analysis and show that this model does not guarantee the descent of a large class of energy functions. We also propose a new maximum neuron model, the optimal competitive Hopfield model (OCHOM), that always guarantees and maximizes the decrease of any Lyapunov energy function. Funabiki et al. (1997, 1998) applied the maximum neural network for the n-queens problem and showed that this model presented the best overall performance among the existing neural networks for this problem. Lee et al. (1992) applied the maximum neural network for the bipartite subgraph problem showing that the solution quality was superior to that of the best existing algorithm. However, simulation results in the n-queens problem and in the bipartite subgraph problem show that the OCHOM is much superior to the maximum neural network in terms of the solution quality and the computation time.

A principal components analysis self-organizing map

We propose a new self-organizing neural model that performs principal components analysis. It is also related to the adaptive subspace self-organizing map (ASSOM) network, but its training equations are simpler. Experimental results are reported, which show that the new model has better performance than the ASSOM network.

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.

Dispersive ordering by the spread function

In this paper, we have introduced the Q-addition of random variables and we have shown that this concept is equivalent to dispersive ordering. Also, we have introduced an ordering, weaker than dispersive ordering, based on the spread function. This allows us to compare two distributions with the same finite support and to check these ordering of distributions by the spread function.

Location of an undesirable facility in a polygonal region with forbidden zones

In this paper, we develop the problem of locating an undesirable facility in a bounded polygonal region (with forbidden polygonal zones), using Euclidean distances, under an objective function that generalizes the maximin and maxisum criteria, and includes other criteria such as the linear combinations of these criterions. We identify a finite dominating set (finite set of points to which an optimal solution must belong) for this problem and show that an optimum solution can be found in polynomial time in the number of vertices of the polygons in the model and the number of existing facilities.

Competitive location with rectilinear distances

Abstract In this paper we consider the problem of locating new facilities which will compete with the existing ones for providing goods or services to n customers. It is assumed that a customer will change his habit and use a new facility if among the new facilities there is one that is closer to him than the closest old facility. Then the problem consists in finding the location of one or several new facilities in order to maximize the sum of the weights of the customers attracted by these new facilities. The problem of locating one new facility is solved using an algorithm in time O( n 3 ). Moreover, it is proposed an algorithm in time O( n 3 ) for the case of two new facilities.

A characterization of the distribution function: the dispersion function

The dispersion function, defined as D(u) = E | X - u |, characterizes the distribution function and gives a dispersive ordering of probability distributions that presents interesting properties.