Wang Rong Long, Tang Zheng, Cao Qi Ping
Faculty of Engineering, Fukui University, Fukui-shi 910-8507, Japan.
IEEE Trans Neural Netw. 2004 Nov;15(6):1458-65. doi: 10.1109/TNN.2004.836234.
In this paper, 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.
在本文中，我们提出了一种用于二分图子图问题的霍普菲尔德神经网络梯度上升学习方法。该方法旨在为解决二分图子图问题提供一种近乎最优的并行算法。为此，我们使用霍普菲尔德神经网络来获得一个近乎最大的二分图子图，并通过在能量的梯度上升方向上修改权重来增加能量，以帮助网络从近乎最大二分图子图的状态逃逸到最大二分图子图或更好状态。通过对大量实例进行模拟来验证所提出的方法，模拟结果表明该方法的求解质量优于现有的最佳并行算法。我们还在全着色问题上测试了该学习方法。模拟结果表明，我们的方法在每个测试图中都找到了最优解。
