Discrete Structural Optimization bu Neural Networks and Its Programming

20世纪80年代中期，Hopfield证明了一些离散优化问题可以在人工神经网络上编程求解，使二次能量函数最小化。Hopfield神经网络的基本概念是输入输出神经元模型和最速下降法的结合，基于Hopfield神经网络的概念，我们提出了一种优化方法NEURO-OPTIMIZER，它可以很好地解决一般的非线性离散优化问题。神经优化器需要一些算法来摆脱能量函数的局部极小值。本文介绍了模拟退火方法，离散变量用神经元数值表示，神经元状态取二进制值1或0。本文通过稳定性分析研究了不规则离散变量的数字表示，并提出了一种映射技术作为不规则离散变量的冗余表示。结构优化的数值例子来说明神经优化器的适用性。

In the middle 1980's Hopfield showed that some discrete optimization problem can be programd and solved on artificial neural networks minimizing the quadratic energy function. The basic concept of the Hopfield neural networks is a combination of the input-output neuron model and the steepest descent method.Based on the concept of the Hopfield neural networks we propose an optimization method named NEURO-OPTIMIZER which is expected to be able to attain good solutions for general nonlinear discrete optimization problems. The NEURO-OPTIMIZER needs some algorithm to escape from local minima of the energy function. The simulated annealing method is introduced here.The discrete variable is represented numerically by neurons in the NEURO-OPTIMIZER.The neuron state takes binary values of one or zero. In this study the number representation for irregularly discrete variable is investigated by a stability analysis, and a mapping technique is proposed as a redundant representation for irregularly discrete variables. Numerical examples for structural optimization are provided to illustrate the applicability of the NEURO-OPTIMIZER.