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 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.
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