In this paper, we propose a new task decomposition method for multilayered feedforward neural networks, namely Task Decomposition with Pattern Distributor to shorten the training time and improve the generalization accuracy of a network under training. This new method uses the combination of modules (small-size feedforward networks) in parallel and series, to produce the overall solution for a complex problem. Based on a 'divide-and-conquer' technique, the original problem is decomposed into several simpler subproblems by a pattern distributor module in the network, where each subproblem is composed of the whole input vector and a fraction of the output vector of the original problem. These sub-problems are then solved by the corresponding groups of modules, where each group of modules is connected with the pattern distributor module and the modules in each group can work in parallel. The design details and implementation of this new method are introduced in this paper. Several benchmark classification problems are used to test this new method. The analysis and experimental results show that this new method could reduce training time and improve generalization accuracy. KEYWORDS multilayered feedforward neural network

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Hierarchical Incremental Class Learning (HICL) is a new task decomposition method that addresses the pattern classification problem. The HICL is proven to be a good classifier but closer examination reveals areas for potential improvement. This paper proposes a theoretical model to evaluate the performance of HICL and presents an approach to improve the classification accuracy of HICL by applying the concept of Reduced Pattern Training (RPT). The theoretical analysis shows that HICL can achieve better classification accuracy than Output Parallelism [Guan and Li: IEEE Transaction on Neural Networks, 13 (2002), 542-550]. The procedure for RPT is described and compared with the original training procedure. The RPT reduces systematically the size of the training data set based on the order of sub-networks built. The results from four benchmark classification problems show much promise for the improved model.

This paper focuses on the bargaining behavior of supply chain members and studies the stability of the bargaining system. There are two forms of bargaining in the process of negotiation. One is separate bargaining, and the other is that the automobile manufacturers form an alliance and bargain with the supplier collectively. We explore the influence of bargaining power and adjustment speed on the stability of the dynamic system and find that both of the factors need to be small to maintain the stability of the supply chain. After comparing the two forms of bargaining in terms of profits and stable regions, we find that the collective bargaining is a pattern with the existence of risk and benefit simultaneously. In order to control chaos in collective bargaining to lower the risk, we adopt the delay feedback control method. With the introduction of the control factor, the system tends to be stable finally.