Numerical Approach of Network Problems in Optimal Mass Transportation

In this paper, we focus on the theoretical and numerical aspects of network problems. For an illustration, we consider the urban traffic problems. And our effort is concentrated on the numerical questions to locate the optimal network in a given domain (for example a town). Mainly, our aim is to find the network so as the distance between the population position and the network is minimized. Another problem that we are interested is to give an numerical approach of the Monge and Kantorovitch problems. In the literature, many formulations (see for example [1-4]) have not yet practical applications which deal with the permutation of points. Let us mention interesting numerical works due to E. Oudet begun since at least in 2002. He used genetic algorithms to identify optimal network (see [5]). In this paper we introduce a new reformulation of the problem by introducing permutations . And some examples, based on realistic scenarios, are solved.

Dimension-down iterative algorithm for the mixed transportation network design problem

An optimal dimension-down iterative algorithm （DDIA） is proposed for solving a mixed （continuous/ discrete） transportation network design problem （MNDP）, which is generally expressed as a mathematical programming with equilibrium constraints （MPEC）. The upper level of the MNDP aims to optimize the network performance via both the expansion of existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium （UE） model. The idea of the proposed DDIA is to reduce the dimensions of the problem. A group of variables （discrete/continuous） are fixed to altemately optimize another group of variables （continuous/discrete）. Some continuous network design problems （CNDPs） and discrete network design problems （DNDPs） are solved repeatedly until the optimal solution is obtained. A numerical example is given to demonstrate the efficiency of the proposed algorithm.

Artificial Neural Networks Approach for Solving Stokes Problem

In this paper a new method based on neural network has been developed for obtaining the solution of the Stokes problem. 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 an example.

The Necessities and Problems of Multimedia and Network Teaching in Vocational College English Teaching

With the development of social economy,the multimedia and network teaching is more and more important in college English teaching,especially in vocational college.It can not only help students to give full play to their collective consciousness and make our English course be full of vitality,but also make the amount of information in class redoubled.For the multimedia and network teaching,there're some problems in English teaching.So the multimedia and network teaching has both necessities and problems.

On the Problems of Computer Network Maintenance and Security

伴随我国计算机网络事业的快速发展，我们的生活已与网络紧密相联，但随着数据网络的传播，安全问题也开始出现。网络安全所涉及到的知识面较广，其中与网络安全存在着重要关联的就是计算机网络维护工作的质量。为此，本文就通过计算机网络维护保障网络安全的具体策略展开了进一步探讨，希望能为行业发展提供一定参考。

Cognitive Radio Ad-Hoc Networks: Some New Results on Multi-Channel Hidden Terminal Problem

Recently the Cognitive Radio (CR), in particular the CR Ad-Hoc Network (CRAHN) technology appears as a burgeoning area in wireless communication that enables utilization of limited network resources in more efficient and intelligent way;studies indicate that opportunistic utilization of the available radio frequency spectrum, without interfering the licensed primary user (PU) could be made. This paper presents some simulation based performance of the Multi-Channel Hidden Terminal (MCHT) problem on CRAHNs;new observations on the effect of the number of channels on certain PU-activity metrics, e.g., delay and throughput, are described.

APPLICATION OF ARTIFICIAL NEURAL NETWORK TO INVERSE PROBLEMS OF ESTIMATING INNER ETCH OF ELASTOPLASTIC PIPE UNDER PRESSURE

To determine a variation of pipe's inner geometric shape as due to etch, the three-layered feedforward artificial neural network is used in the inverse analysis through observing the elastoplastic strains of the outer wall under the working inner pressure. Because of different kinds of inner wail radii and eccentricity. several groups of strains calculated with computational mechanics are used for the network to do learning. Numerical calculation demonstrates that this method is effective and the estimated inner wall geometric parameters have high precision.

A Water Line Network Failure Application of Network Design Problems

This study investigated a water supply recovery problem involving municipal water service piping. The problem consisted in recovering full service after network failure, in order to rapidly satisfy all urgent citywide demands. The optimal recovery solution was achieved through the application of so-called network design problems （NDPs）, which are a form of combinatorial optimization problem. However, a conventional NDP is not suitable for addressing urgent situations because （1） it does not utilize the non-failure arcs in the network, and （2） it is solely concerned with stable costs such as flow costs. Therefore, to adapt the technique to such urgent situations, the conventional NDP is here modified to deal with the specified water supply problem. In addition, a numerical illustration using the Sendai water network is presented.

NETWORK ANALYSIS OF EIGENVALUE PROBLEM FOR MULTILAYER DIELECTRIC WAVEGUIDE CONSISTING OF ARBITRARY NUMBER OF LAYERS

In this paper,the eigenvalue problem of a multilayer dielectric waveguide consisting of arbitrarynumber of layers is solved by the microwave network method.A general program with the function of com-puter graphics has been developed for analyzing the dispersion characteristics and the electromagnetic fielddistributions of an N layer dielectric waveguide.As an example of practical applications,the procedure ofmode conversion and mode separation in dielectric branching waveguides is vividly demonstrated throughanalyzing the field distributions of asymmetric multilayer dielectric structures and the general rules of modeconversion are discussed.

Chaotic Neural Network Technique for "0-1" Programming Problems

0-1 programming is a special case of the integer programming, which is commonly encountered in many optimization problems. Neural network and its general energy function are presented for 0-1 optimization problem. Then, the 0-1 optimization problems are solved by a neural network model with transient chaotic dynamics (TCNN). Numerical simulations of two typical 0-1 optimization problems show that TCNN can overcome HNN's main drawbacks that it suffers from the local minimum and can search for the global optimal solutions in to solveing 0-1 optimization problems.

Assessment of a Proposed Software Design for the Solution of Multi-Phase Mechanics Problems on Networked Laptops

This paper presents the design of a computational software system that enables solutions of multi-phase and multi-scale problems in mechanics. It demonstrated how mechanicians can design “process-driven” software systems directly, and that such efforts are more suitable in solving multi-phase or multi-scale problems, rather than utilizing the “data-driven” approaches of legacy network systems. Specifically, this paper demonstrates how this approach can be used to solve problems in flexible dynamics. Then it suggests a view of mechanics algorithms as ‘state equilibrium’ enforcers residing as servers, rather than as computer programs that solve field equations. It puts forth the need for identical input/output files to ensure widespread deployment on laptops. Then it presents an assessment of the laptop platform. A software system such as the one presented here can also be used to supply virtual environments, animations and entertainment/education software with physics.

Unsupervised neural network model optimized with evolutionary computations for solving variants of nonlinear MHD Jeffery-Hamel problem

A heuristic technique is developed for a nonlinear magnetohydrodynamics （MHD） Jeffery-Hamel problem with the help of the feed-forward artificial neural net- work （ANN） optimized with the genetic algorithm （GA） and the sequential quadratic programming （SQP） method. The twodimensional （2D） MHD Jeffery-Hamel problem is transformed into a higher order boundary value problem （BVP） of ordinary differential equations （ODEs）. The mathematical model of the transformed BVP is formulated with the ANN in an unsupervised manner. The training of the weights of the ANN is carried out with the evolutionary calculation based on the GA hybridized with the SQP method for the rapid local convergence. The proposed scheme is evaluated on the variants of the Jeffery-Hamel flow by varying the Reynold number, the Hartmann number, and the an- gles of the walls. A large number of simulations are performed with an extensive analysis to validate the accuracy, convergence, and effectiveness of the scheme. The comparison of the standard numerical solution and the analytic solution establishes the correctness of the proposed designed methodologies.

The Budget Constrained Multi-product Newsboy Problem with Reactive Production:A Problem from Entrepreneurial Network Construction

This paper develops an extended newsboy model and presents a formula- tion for this model. This new model has solved the budget contained multi-product newsboy problem with the reactive production. This model can be used to describe the status of entrepreneurial network construction. We use the Lagrange multiplier procedure to deal with our problem, but it is too complicated to get the exact solu-tion. So we introduce the homotopy method to deal with it. We give the flow chart to describe how to get the solution via the homotopy method. We also illustrate our model in both the classical procedure and the homotopy method. Comparing the two methods, we can see that the homotopy method is more exact and efficient.

Using Heuristics to the Controller Placement Problem in Software-Defined Multihop Wireless Networking

Solving the controller placement problem (CPP) in an SDN architecture with multiple controllers has a significant impact on control overhead in the network, especially in multihop wireless networks (MWNs). The generated control overhead consists of controller-device and inter-controller communications to discover the network topology, exchange configurations, and set up and modify flow tables in the control plane. However, due to the high complexity of the proposed optimization model to the CPP, heuristic algorithms have been reported to find near-optimal solutions faster for large-scale wired networks. In this paper, the objective is to extend those existing heuristic algorithms to solve a proposed optimization model to the CPP in software-defined multihop wireless networking (SDMWN).Our results demonstrate that using ranking degrees assigned to the possible controller placements, including the average distance to other devices as a degree or the connectivity degree of each placement, the extended heuristic algorithms are able to achieve the optimal solution in small-scale networks in terms of the generated control overhead and the number of controllers selected in the network. As a result, using extended heuristic algorithms, the average number of hops among devices and their assigned controllers as well as among controllers will be reduced. Moreover, these algorithms are able tolower the control overhead in large-scale networks and select fewer controllers compared to an extended algorithm that solves the CPP in SDMWN based on a randomly selected controller placement approach.

RECURRENT NEURAL NETWORK MODEL BASED ON PROJECTIVE OPERATOR AND ITS APPLICATION TO OPTIMIZATION PROBLEMS

The recurrent neural network （RNN） model based on projective operator was studied. Different from the former study, the value region of projective operator in the neural network in this paper is a general closed convex subset of n-dimensional Euclidean space and it is not a compact convex set in general, that is, the value region of projective operator is probably unbounded. It was proved that the network has a global solution and its solution trajectory converges to some equilibrium set whenever objective function satisfies some conditions. After that, the model was applied to continuously differentiable optimization and nonlinear or implicit complementarity problems. In addition, simulation experiments confirm the efficiency of the RNN.

Components Assignment Problem for Multi-Source Multi-Sink Flow Networks with Reliability and Budget Constraints

System reliability optimization problem of multi-source multi-sink flow network is defined by searching the optimal components that maximize the reliability and minimize the total assignment cost. Therefore, a genetic-based approach is proposed to solve the components assignment problem under budget constraint. The mathematical model of the optimization problem is presented and solved by the proposed genetic-based approach. The proposed approach is based on determining the optimal set of lower boundary points that maximize the system reliability such that the total assignment cost does not exceed the specified budget. Finally, to evaluate our approach, we applied it to various network examples with different numbers of available components;two-source two-sink network and three-source two-sink network.

2-median location improvement problems under weighted l_1 norm and l_∞ norm on trees

This paper focuses on the 2-median location improvement problem on tree networks and the problem is to modify the weights of edges at the minimum cost such that the overall sum of the weighted distance of the vertices to the respective closest one of two prescribed vertices in the modified network is upper bounded by a given value.l1 norm and l∞norm are used to measure the total modification cost. These two problems have a strong practical application background and important theoretical research value. It is shown that such problems can be transformed into a series of sum-type and bottleneck-type continuous knapsack problems respectively.Based on the property of the optimal solution two O n2 algorithms for solving the two problems are proposed where n is the number of vertices on the tree.

Neural Network inverse Adaptive Controller Based on Davidon Least Square

General neural network inverse adaptive controller has two flaws: the first is the slow convergence speed; the second is the invalidation to the non-minimum phase system. These defects limit the scope in which the neural network inverse adaptive controller is used. We employ Davidon least squares in training the multi-layer feedforward neural network used in approximating the inverse model of plant to expedite the convergence, and then through constructing the pseudo-plant, a neural network inverse adaptive controller is put forward which is still effective to the nonlinear non-minimum phase system. The simulation results show the validity of this scheme.

Optimal paths planning in dynamic transportation networks with random link travel times

A theoretical study was conducted on finding optimal paths in transportation networks where link travel times were stochastic and time-dependent(STD). The methodology of relative robust optimization was applied as measures for comparing time-varying, random path travel times for a priori optimization. In accordance with the situation in real world, a stochastic consistent condition was provided for the STD networks and under this condition, a mathematical proof was given that the STD robust optimal path problem can be simplified into a minimum problem in specific time-dependent networks. A label setting algorithm was designed and tested to find travelers' robust optimal path in a sampled STD network with computation complexity of O(n2+n·m). The validity of the robust approach and the designed algorithm were confirmed in the computational tests. Compared with conventional probability approach, the proposed approach is simple and efficient, and also has a good application prospect in navigation system.

Fuzzy-support vector machine geotechnical risk analysis method based on Bayesian network

Machine learning method has been widely used in various geotechnical engineering risk analysis in recent years. However, the overfitting problem often occurs due to the small number of samples obtained in history. This paper proposes the FuzzySVM(support vector machine) geotechnical engineering risk analysis method based on the Bayesian network. The proposed method utilizes the fuzzy set theory to build a Bayesian network to reflect prior knowledge, and utilizes the SVM to build a Bayesian network to reflect historical samples. Then a Bayesian network for evaluation is built in Bayesian estimation method by combining prior knowledge with historical samples. Taking seismic damage evaluation of slopes as an example, the steps of the method are stated in detail. The proposed method is used to evaluate the seismic damage of 96 slopes along roads in the area affected by the Wenchuan earthquake. The evaluation results show that the method can solve the overfitting problem, which often occurs if the machine learning methods are used to evaluate risk of geotechnical engineering, and the performance of the method is much better than that of the previous machine learning methods. Moreover,the proposed method can also effectively evaluate various geotechnical engineering risks in the absence of some influencing factors.