一类广义变分不等式问题的神经网络模型

基于解的充分必要条件,提出一类广义变分不等式问题的神经网络模型.通过构造Lyapunov函数,在适当的条件下证明了新模型是Lyapunov稳定的,并且全局收敛和指数收敛于原问题的解.数值试验表明,该神经网络模型是有效的和可行的.     

基于GA-Chebyshev神经网络的分数阶Bagley-Torvik方程数值解法

本文基于现有的切比雪夫神经网络,提出了一种利用遗传算法优化切比雪夫神经网络求解分数阶Bagley-Torvik方程数值解的新方法,结合多点处的泰勒公式原理,给出数值解的一般形式,将原问题转化为求解无约束最小化问题.与现有数值方法的数值结果进行比较表明了本文方法的可行性和有效性,为分数阶微分方程中类似问题的求解提供了新的思路.     

基于组合神经网络的时间分数阶扩散方程计算方法

该文首次采用一种组合神经网络的方法，求解了一维时间分数阶扩散方程.组合神经网络是由径向基函数（RBF）神经网络与幂激励前向神经网络相结合所构造出的一种新型网络结构.首先，利用该网络结构构造出符合时间分数阶扩散方程条件的数值求解格式，同时设置误差函数，使原问题转化为求解误差函数极小值问题；然后，结合神经网络模型中的梯度下降学习算法进行循环迭代，从而获得神经网络的最优权值以及各项最优参数，最终得到问题的数值解.数值算例验证了该方法的可行性、有效性和数值精度.该文工作为时间分数阶扩散方程的求解开辟了一条新的途径.     

An optimal solution technique for the joint replenishment problem with storage and transport capacities and budget constraints

The joint replenishment problem, which is concerned with the problem of coordinating the replenishment of a group of items that may be ordered jointly, has been studied extensively and many heuristic solution procedures have been presented in the literature. To obtain the minimum of the total cost, the main complexity lies in determining the appropriate lower bound of the basic cycle time. Also there is a lack of a global optimal solution technique of the problem. This paper presents its extended model to include some practical issues and develops a simple procedure to calculate the appropriate lower bound of the basic cycle time. By a comparative study of a numerical example, it demonstrates the inabilities of the available lower bound formulae in the literature. It also develops a generalized global optimal solution algorithm of the extended model and illustrates this with a numerical example. Then a comparative study of the results of seven numerical examples is carried out to highlight the global optimality of the solution technique.     

一个解决线性互补问题的新型神经网络

本文构造了一个新型的解决线性互补问题的神经网络,不同于那些运用罚函数和拉格朗日函数的神经网络,它的结构简单,易于计算,我们证明了该神经网络的全局收敛性和稳定性,并给出数值实验检验其有效性。     

New approach to applying neural network in nonlinear dynamic model

In this work, radial basis function neural network (RBF-NN) is applied to emulate an extended Kalman filter (EKF) in a data assimilation scenario. The dynamical model studied here is based on the one-dimensional shallow water equation DYNAMO-1D. This code is simple when compared with an operational primitive equation models for numerical weather prediction. Although simple, the DYNAMO-1D is rich for representing some atmospheric motions, such as Rossby and gravity waves. It has been shown in the literature that the ability of the EKF to track nonlinear models depends on the frequency and accuracy of the observations and model errors. In some cases, just fourth-order moment EKF works well, but will be unwieldy when applied to high-dimensional state space. Artificial Neural Network (ANN) is an alternative solution for this computational complexity problem, once the ANN is trained offline with a high order Kalman filter, even though this Kalman filter has high computational cost (which is not a problem during ANN training phase). The results achieved in this work encourage us to apply this technique on operational model. However, it is not yet possible to assure convergence in high dimensional problems.     

The fractional minimal cost flow problem on network

A problem and a new algorithm are given for the linear fractional minimal cost flow problem on network. Using a new check number and combining the characteristic of network to extend the traditional theories of minimum cost flow problem, discussed the relation between it and its dual problem. Optimality conditions are derived and a Network Simplex Algorithm is proposed that leads to optimal solution assuming certain properties. Finally, an numerical example test is also developed.     

Implicit algorithms for solving the Cauchy problem for the equations of the dynamics of mechanical systems

It is shown that in the numerical solution of the Cauchy problem for systems of second-order ordinary differential equations, when solved for the highest-order derivative, it is possible to construct simple and economical implicit computational algorithms for step-by-step integration without using laborious iterative procedures based on processes of the Newton-Raphson iterative type. The initial problem must first be transformed to a new argument — the length of its integral curve. Such a transformation is carried out using an equation relating the initial parameter of the problem to the length of the integral curve. The linear acceleration method is used as an example to demonstrate the procedure of constructing an implicit algorithm using simple iterations for the numerical solution of the transformed Cauchy problem. Propositions concerning the computational properties of the iterative process are formulated and proved. Explicit estimates are given for an integration stepsize that guarantees the convergence of the simple iterations. The efficacy of the proposed procedure is demonstrated by the numerical solution of three problems. A comparative analysis is carried out of the numerical solutions obtained with and without parametrization of the initial problems in these three settings. As a qualitative test the problem of the celestial mechanics of the “Pleiades” is considered. The second example is devoted to modelling the non-linear dynamics of an elastic flexible rod fixed at one end as a cantilever and coiled in its initial (static) state into a ring by a bending moment. The third example demonstrates the numerical solution of the problem of the “unfolding” of a mechanical system consisting of three flexible rods with given control input.     

A Feed-Forward Neural Network for Solving Stokes Problem

The current research attempts to offer a novel method for solving the Stokes problem based on the use of feed-forward neural networks. We transform the mixed Stokes problem into three independent Poisson problems which by solving them the solution of the Stokes problem is obtained. The results obtained by this method, has been compared with the existing numerical method and with the exact solution of the problem. It can be observed that the current new approximation has higher accuracy. The number of model parameters required is less than conventional methods. The proposed new method is illustrated by two examples.     

An eigenvalue problem arising in a patch formation model

A simple numerical scheme has been developed for the solution of the eigenvalue problem arising in a patch formation model given by Del Grosso et al. [1]. The scheme is based on finding bounds which separate the eigenvalues. The exact eigenvalues are obtained by solving an algebraic equation given by the corresponding regular Frobenius series solution. At the same time eigenfunctions may also be obtained from this series solution.     

Einige laminare Grenzschichtströmungen,berechnet mittels einer neuen Reihenmethode

Summary A new and formally exact series solution of the general laminar boundary layer problem for arbitrary outer pressure distribution [1] is discussed briefly. The main part of the paper is concerned with the application of this solution to the numerical evaluation of instructive examples of boundary layer flows. Application of this new and rigorous series method requires only a short and simple numerical calculation, involving the application of tables of certain universal functions.      

Permutation-induced acyclic networks for the job shop scheduling problem

In the literature of the combinatorial optimization problems, it is a commonplace to find more than one mathematical model for the same problem. The significance of a model may be measured in terms of the efficiency of the solution algorithms that can be built upon it. The purpose of this article is to present a new network model for the well known combinatorial optimization problem – the job shop scheduling problem. The new network model has similar structure as the disjunctive graph model except that it uses permutations of jobs as decision variables instead of the binary decision variables associated with the disjunctive arcs. To assess the significance of the new model, the performances of exact branch-and-bound algorithmic implementations that are based on both the new model and the disjunctive graph model are compared.     

An extended algorithm for separated continuous linear programs

Separated continuous linear programs (SCLP) are a class of continuous linear programs which, among other things, can serve as a useful model for dynamic network problems where storage is permitted at the nodes. Recent work on SCLP has produced a detailed duality theory, conditions under which an optimal solution exists with a finite number of breakpoints, a purification algorithm, as well as a convergent algorithm for solving SCLP under certain assumptions on the problem data. This paper combines much of this work to develop a possible approach for solving a wider range of SCLP problems, namely those with fairly general costs. The techniques required to implement the algorithm are no more than standard (finite-dimensional) linear programming and line searching, and the resulting algorithm is simplex-like in nature. We conclude the paper with the numerical results obtained by using a simple implementation of the algorithm to solve a small problem. Received: May 1994 / Accepted: March 2002?Published online June 25, 2002     

求解系统可靠性优化中指派问题的启发式算法

本文回顾了系统可靠性优化中部件指派问题的研究,针对该类问题特点提出了一个新的启发式算法,该算法基于概率重要度来指派部件可靠度。文章最后给出了算例分析,并将算法结果与已有的算法和枚举法求得的最优解进行了比较。新的算法简单,而且效率非常高,可以在很短的计算时间内得到较好的求解效果,有效提高了复杂系统和大规模系统可靠性优化的计算效率。     

粘性阻尼线性振动系统的复模态特征值问题的一种新的矩阵摄动分析解法

本文提出了对粘性阻尼线性振动系统的复模态二次广义特征值问题进行高效近似求解的一种新的矩阵摄动分析方法,即先将阻尼矩阵分解为比例阻尼部分和非比例阻尼部分之和,并求得系统的比例阻尼实模态特征解;然后以此为初始值,将阻尼矩阵的非比例部分作为对其比例部分的小量修改,利用摄动分析方法简捷地得到系统的复模态特征值问题的近似解.这一新方法适用于振系阻尼分布不十分偏离比例阻尼情况的问题,因此对大阻尼(非过阻尼)振动系统也有效.这是它优于以前提出的基于无阻尼实模态特征解的类似摄动分析方法的重要特点.文中建立了复模态特征值和特征向量的二阶摄动解式,并通过算例证实了其有效性.此外还讨论了利用比例阻尼假定估计阻尼系统固有振动的复特征值的可行性.     

An optimization model and a solution algorithm for the many-to-many car pooling problem

Car pooling is one method that can be easily instituted and can help to resolve a variety of problems that continue to plague urban areas, ranging from energy demands and traffic congestion to environmental pollution. Although car pooling is becoming more common, in practice, participant matching results are still being obtained by an inefficient manual approach, which may possibly result in an inferior solution. In the past, when car pooling studies have been done the problem has been treated as either a to-work problem (from different origins to the same destination) or return-from-work problem (from the same origin to different destinations). However, in this study we employ a time-space network flow technique to develop a model for the many-to-many car pooling problem with multiple vehicle types and person types. The model is formulated as an integer multiple commodity network flow problem. Since real problem sizes can be huge, it could be difficult to find optimal solutions within a reasonable period of time. Therefore, we develop a solution algorithm based on Lagrangian relaxation, a subgradient method, and a heuristic for the upper bound solution, to solve the model. To test how well the model and the solution algorithm can be applied to real world, we randomly generated several examples based upon data reported from a past study carried out in northern Taiwan, on which we performed numerical tests. The test results show the effectiveness of the proposed model and solution algorithm.     

The QNET method for two-moment analysis of open queueing networks

Consider an open network of single-server stations, each with a first-in-first-out discipline. The network may be populated by various customer types, each with its own routing and service requirements. Routing may be either deterministic or stochastic, and the interarrival and service time distributions may be arbitrary. In this paper a general method for steady-state performance analysis is described and illustrated. This analytical method, called QNET, uses both first and second moment information, and it is motivated by heavy traffic theory. However, our numerical examples show that QNET compares favorably with W. Whitt's Queueing Network Analyzer (QNA) and with other approximation schemes, even under conditions of light or moderate loading. In the QNET method one first replaces the original queueing network by what we call an approximating Brownian system model, and then one computes the stationary distribution of the Brownian model. The second step amounts to solving a certain highly structured partial differential equation problem; a promising general approach to the numerical solution of that PDE problem is described by Harrison and Dai [8] in a companion paper. Thus far the numerical solution technique has been implemented only for two-station networks, and it is clear that the computational burden will grow rapidly as the number of stations increases. Thus we also describe and investigate a cruder approach to two-moment network analysis, called ΠNET, which is based on a product form approximation, or decomposition approximation, to the stationary distribution of the Brownian system model. In very broad terms, ΠNET is comparable to QNA in its level of sophistication, whereas QNET captures more subtle system interactions. In our numerical examples the performance of ΠNET and QNA is similar; the performance of QNET is generally better, sometimes much better.     

Optimal egress time calculation and path generation for large evacuation networks

Finding the optimal clearance time and deciding the path and schedule of evacuation for large networks have traditionally been computationally intensive. In this paper, we propose a new method for finding the solution for this dynamic network flow problem with considerably lower computation time. Using a three phase solution method, we provide solutions for required clearance time for complete evacuation, minimum number of evacuation paths required for evacuation in least possible time and the starting schedules on those paths. First, a lower bound on the clearance time is calculated using minimum cost dynamic network flow model on a modified network graph representing the transportation network. Next, a solution pool of feasible paths between all O-D pairs is generated. Using the input from the first two models, a flow assignment model is developed to select the best paths from the pool and assign flow and decide schedule for evacuation with lowest clearance time possible. All the proposed models are mixed integer linear programing models and formulation is done for System Optimum (SO) scenario where the emphasis is on complete network evacuation in minimum possible clearance time without any preset priority. We demonstrate that the model can handle large size networks with low computation time. A numerical example illustrates the applicability and effectiveness of the proposed approach for evacuation.     

强部分逆网络流问题

Abstract. In this paper,a new model for inverse network flow problems,robust partial inverseproblem is presented. For a given partial solution,the robust partial inverse problem is to modify the coefficients optimally such that all full solutions containing the partial solution becomeoptimal under new coefficients. It has been shown that the robust partial inverse spanning treeproblem can be formulated as a combinatorial linear program,while the robust partial inverseminimum cut problem and the robust partial inverse assignment problem can be solved by combinatorial strongly polynomial algorithms.     

Sparsity-promoting distributed charging control for plug-in electric vehicles over distribution networks

Uncoordinated charging of plug-in electric vehicles brings a new challenge on the operation of a power system as it causes power flow fluctuations and even unacceptable load peaks. To ensure the stability of power network, plug-in charging needs to be scheduled against the base load properly. In this paper, we propose a sparsity-promoting charging control model to address this issue. In the model, the satisfaction of customers is improved through sparsity-promoting charging where the numbers of charging time slots are optimized. Dynamic feeder overload constraints are imposed in the model to avoid any unacceptable load peaks, and thus ensure the network stability. Then, a distributed solution strategy is developed to solve the problem based on the alternating direction method of multipliers (ADMM) since most of power networks are managed typically in a distributed manner. During solving process, Lagrangian duality is used to transform the original problem into an equivalent dual problem, which can be decomposed into a set of homogeneous small-scaled sub-problems. Particularly, each sub-problem either has a closed-form solution or can be solved locally by an accelerated dual gradient method. The global convergence of the proposed algorithm is also established. Finally, numerical simulations are presented to illustrate our proposed method. In contrast to traditional charging models, our sparsity-promoting charging model not only ensures the stability of power network, but also improves the satisfaction of customers.