Improving BP neural network with simulated annealing algorithm can overcome the defect of falling into local optimal point easily, and further improve the network performance.

用模拟退火算法改进BP神经网络，克服了BP神经网络极易陷入局部最优点的缺点，进一步提高了网络的性能。

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We prove that when the homotopy map is a regular map, the K-K-T point obtained from this homotopy method must be a local optimal solution by choosing proper homotopy equation.

证明了同伦映射为正则映射的条件下，选取合适的同伦方程，用此同伦方法得到的K-K-T点一定是问题局部最优解。

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In the process of optimization, the method has the ability of escaping from the local minimized point and arriving at the global optimal point by setting an escaping coefficient.

通过设定逃逸系数，算法在寻优过程中具有了能够跳出局部极小点到达全局最优点的能力。

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