神经网络的隐层数和隐层节点数决定了网络规模，并对网络性能造成较大影响。在满足网络所需最少隐层节点数的前提下，利用剪枝算法删除某些冗余节点，减少隐层节点数，得到更加精简的网络结构。基于惩罚函数的剪枝算法是在目标函数后加入一个惩罚函数项，该惩罚函数项是一个变量为网络权值的函数。由于惩罚函数中的网络权值变量可以附加一个可调参数，将单一惩罚函数项泛化为一类随参数规律变化的新的惩罚函数，初始惩罚函数可看作泛化后惩罚函数的参数取定值的特殊情况。实验利用基于标准BP神经网络的XOR数据进行测试，得到隐层节点剪枝效果和网络权值随惩罚函数的泛化而发生变化，并从数据分析中得出具有更好剪枝效果及更优网络结构的惩罚函数泛化参数。

The number of hidden layer and hidden layer node in neural network determines the size of the network and has a great influence on the performance of the network. Therefore,when the network contains the least hidden layer node number,pruning algorithm can be used to delete some redundant node, then the network is more simple. The pruning algorithm adds a penalty function to the target function, and the penalty function regards the weights of network as variable. It adds a variable parameter to the weights of network,so the simple penalty function can be generalized to a kind of new penalty function that changes as the parameter. The initial function can be treated as a special condition after the generalization of penalty function. Experiment tests the XOR data based on the BP neural network and sums up the effect of the generalization of penalty function on the pruning of the hidden layer node with neural network and the structure of the neural network. Then the parameters w

采用一种新型的多学科设计方法———目标解析分流法进行重水潜器的概念设计。首先利用半经验法建立重水潜器的集成系统模型，并进行目标层解分析（ATC）优化模型；再应用增广拉格朗日惩罚函数松弛化方法，通过改进内外层嵌套式求解策略，减少内层循环病态子问题的求解计算时间，在内层循环得到收敛的同时，外层循环更新惩罚权重来获得可行解；随后改变惩罚函数权重，对比分析各种惩罚函数对求解效率的影响。由实验可得，应用增广拉格朗日惩罚函数松弛化求解的方法，保持计算精度的同时也提高了计算效率。最终获得的系统最优解与多维的一次设计优化问题所得到的最优解非常接近，证明了多学科设计优化能充分利用不同学科之间的相互作用所产生的协同效应，从而获得系统整体的最优解。

A new multidisciplinary design optimization,analytical target cascading(ATC)method,was adopted to carry out con-ceptual design of heavier-than-water(HTW)AUV.Firstly,a semi-empirical method was applied to establish an integrated sys-tem model for HTW as well as ATC optimization model.Secondly,the augmented Lagrangian penalty function relaxation method was applied by improving the inner and outer layers nested solving strategy,reducing computation time for solving the problem in the inner loop,and updating the weight of the outer loop to obtain a feasible solution.Then the penalty function weight was changed to analyze the affect for solving efficiency brought by various penalty functions.It can be extracted that the augmented Lagrangian penalty function relaxation method can reduce the number of iteration and keep the accuracy.The system optimal solu-tion obtained is close to the one calculated by multidimensional all-in-one design,which proves that multidisciplinary design op

主要考虑了生长曲线模型中的参数矩阵的估计.首先基于Potthoff-Roy变换后的生长曲线模型,采用不同的惩罚函数:Hard Thresholding函数,LASSO,ENET,改进LASSO,SACD给出了参数矩阵的惩罚最小二乘估计.接着对不做变换的生长曲线模型,直接定义其惩罚最小二乘估计,基于Nelder-Mead法给出了估计的数值解算法.最后对提出的参数估计方法进行了数据模拟.结果表明自适应LASSO在估计方面效果比较好.

This paper studied the estimation of parameter matrix in the growth curve model.Based on the Potthoff-Roy transform of the growth curve model,and by using different penalty functions:Hard Thresholding function,LASSO, ENET,LASSO,SACD,the penalized least estimation of parameter matrix was given.Then the penalized least squares estima-tion was defined directly on the growth curve model.The numerical solution algorithm for the estimation was proposed based on the Nelder-Mead method.Finally,the methods for the parameter estimation were simulated.The results show that the a-daptive LASSO is better in the estimation results.

通过构造罚方程的思想提出一个求解绝对值线性互补问题的罚函数方法,证明了当惩罚因子趋于正无穷时,所提出了罚函数方法的解收敛于绝对值线性互补问题的解,并且收敛速率是指数次.

We propose a penalty function method to a kind of absolute value linear complementarity prob-lem(ALCP) inRnbased on approximating the ALCP by a nonlinear equation.We prove that the solution to our method converges to that of the ALCP at an exponential rate when the penalty parameter tends to infinity.

基于排队理论研究了混流制造系统服务率优化问题。建立了混流制造系统的开放式排队网络模型;以每一个工作单元单位时间内服务费用与产品逗留损失费用之和的期望值为目标函数,以工作单元加工每一类产品的服务强度为约束条件,建立了期望费用模型;针对所建立的混流制造系统服务率优化数学模型的复杂性,构造惩罚函数对原目标函数加以修正,将原约束问题转化为无约束问题,利用坐标轮换法、黄金分割法、进退法等最优化方法以及MATLAB程序对每一个工作单元的惩罚函数进行了求解,得到了其加工每一类产品的最优服务率。算例计算结果表明了该方法的有效性和可行性。

The mixed-model manufacturing system service rate optimization problem is studied based on queuing theory in this paper.A mixed-model manufacturing system is modeled to be an open type queuing network model.After that, the sum per unit time of the work unit service cost and products staying cost is considered as the objective function and the traffic intensities when work unit is producing every class of product as the constraint condition.Since the model is difficult to be solved, by im-porting the punishment function, the initial constrained problem is transformed to be non-constrained problem.The trans-formed objective function is solved by the optimization methods such as cyclic coordinate method, golden section method, ad-vance and retreat method and the MATLAB procedure to obtain the optimal service rate for every class product .A numerical example shows that the method is effective and feasible.