应用有限元混合法分析两弹性接触体的动力响应（理论部分）

本文将动力分析中的直接积分法与有限元混合法结合起来对两弹性接触体的摩擦动力求解问题进行了理论分析,推导了有关的有限元公式,设计了计算框图,为计算程序的实现提供了理论依据。     

A note on the optimal scheduling of two parallel processors

The problem of minimizing mean flow time of two parallel processors is discussed. Prior results are briefly reviewed. A dynamic programming algorithm is presented which minimizes mean flow time for a set of n preordered jobs on two nonequivalent parallel processors. The algorithm is illustrated with an example problem. The computational experience is presented which illustrates the efficiency of the algorithm.     

基于动态模型的机场配电网潮流计算新方法

机场配电网因非常情况成为孤立电力系统后，配电系统的电压、潮流和频率等发生巨大变化，传统的潮流计算方法往往会出现收敛性差、计算结果与实际不相符的情况。提出的机场配电网动态潮流计算模型能有效解决此类问题，阐述了机场配电网动态潮流计算模型的构成原理、算法并给出相应算例。通过算例计算证明了动态潮流计算模型适用于计算机场配电网的潮流。     

A forward network simplex algorithm for solving multiperiod network flow problems

An optimization model which is frequently used to assist decision makers in the areas of resource scheduling, planning, and distribution is the minimum cost multiperiod network flow problem. This model describes network structure decision-making problems over time. Such problems arise in the areas of production/distribution systems, economic planning, communication systems, material handling systems, traffic systems, railway systems, building evacuation systems, energy systems, as well as in many others. Although existing network solution techniques are efficient, there are still limitations to the size of problems that can be solved. To date, only a few researchers have taken the multiperiod structure into consideration in devising efficient solution methods. Standard network codes are usually used because of their availability and perceived efficiency. In this paper we discuss the development, implementation, and computational testing of a new technique, the forward network simplex method, for solving linear, minimum cost, multiperiod network flow problems. The forward network simplex method is a forward algorithm which exploits the natural decomposition of multiperiod network problems by limiting its pivoting activity. A forward algorithm is an approach to solving dynamic problems by solving successively longer finite subproblems, terminating when a stopping rule can be invoked or a decision horizon found. Such procedures are available for a large number of special structure models. Here we describe the specialization of the forward simplex method of Aronson, Morton, and Thompson to solving multiperiod network network flow problems. Computational results indicate that both the solution time and pivot count are linear in the number of periods. For standard network optimization codes, which do not exploit the multiperiod structure, the pivot count is linear in the number of periods; however, the solution time is quadratic.     

Distribution network design: Selection and sizing of congested connections

This paper focuses on certain types of distribution networks in which commodity flows must go through connections that are subject to congestion. Connections serve as transshipment and/or switching points and are modeled as M/G/1 queues. The goal is to select connections, assign flows to the connections, and size their capacities, simultaneously. The capacities are controlled by both the mean and the variability of service time at each connection. We formulate this problem as a mixed integer nonlinear optimization problem for both the fixed and variable service rate cases. For the fixed service rate case, we prove that the objective function is convex and then develop an outer approximation algorithm. For the variable service rate case, both mean and second moment of service time are decision variables. We establish that the utilization rates at the homogeneous connections are identical for an optimal solution. Based on this key finding, we develop a Lagrangian relaxation algorithm. Numerical experiments are conducted to verify the quality of the solution techniques proposed. The essential contribution of this work is the explicit modeling of connection capacity (through the mean and the variability of service time) using a queueing framework. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

A robust queueing network analyzer based on indices of dispersion

We develop a robust queueing network analyzer algorithm to approximate the steady-state performance of a single-class open queueing network of single-server queues with Markovian routing. The algorithm allows nonrenewal external arrival processes, general service-time distributions and customer feedback. The algorithm is based on a decomposition approximation, where each flow is partially characterized by its rate and a continuous function that measures the stochastic variability over time. This function is a scaled version of the variance-time curve, called the index of dispersion for counts (IDC). The required IDC functions for the external arrival processes can be calculated from the model primitives or estimated from data. Approximations for the IDC functions of the internal flows are calculated by solving a set of linear equations. The theoretical basis is provided by heavy-traffic limits for the flows established in our previous papers. A robust queueing technique is used to generate approximations of the mean steady-state performance at each queue from the IDC of the total arrival flow and the service specification at that queue. The algorithm's effectiveness is supported by extensive simulation studies.     

Production-allocation scheduling and capacity expansion using network flows under uncertainty

This paper extends Connors and Zangwill's work in network flows under uncertainty to the convex costs case. In this paper the extended network flow under uncertainty algorithm is applied to compute N-period production and delivery schedules of a single commodity in a two-echelon production-inventory system with convex costs and low demand items. Given an initial production capacity for N periods, the optimal production and delivery schedules for the entire N periods are characterized by the flows through paths of minimal expected discounted cost in the network As a by-product of this algorithm the multi-period stochastic version of the parametric budget problem for the two-echelon production-inventory system is solved.     

Algorithms for the minimax transportation problem

In this paper, we consider a variant of the classical transportation problem as well as of the bottleneck transportation problem, which we call the minimax transportation problem. The problem considered is to determine a feasible flow x_ij from a set of origins I to a set of destinations J for which max_(i,j)εIxJ{c_ijx_ij} is minimum. In this paper, we develop a parametric algorithm and a primal-dual algorithm to solve this problem. The parametric algorithm solves a transportation problem with parametric upper bounds and the primal-dual algorithm solves a sequence of related maximum flow problems. The primal-dual algorithm is shown to be polynomially bounded. Numerical investigations with both the algorithms are described in detail. The primal-dual algorithm is found to be computationally superior to the parametric algorithm and it can solve problems up to 1000 origins, 1000 destinations and 10,000 arcs in less than 1 minute on a DEC 10 computer system. The optimum solution of the minimax transportation problem may be noninteger. We also suggest a polynomial algorithm to convert this solution into an integer optimum solution.     

Time minimizing flows in directed networks

An important class of network flow problems is that class for which the objective is to minimize the cost of the most expensive unit of flow while obtaining a desired total flow through the network. Two special cases of this problem have been solved, namely, the bottleneck assignment problem and time-minimizing transportation problem. This paper addresses the more general case which we shall refer to as the time-minimizing network flow problem. Associated with each arc is an arc capacity (static) and a transferral time. The objective is to find a maximal flow for which the length (in time) of the longest path carrying flow is minimized. The character of the problem is discussed and a solution algorithm is presented.     

Mathematical control theory solution of an interactive accounting flows model

In this paper we have applied the mathematical control theory to the accounting network flows, where the flow rates are constrained by linear inequalities. The optimal control policy is of the “generalized bang-bang” variety which is obtained by solving at each instant in time a linear programming problem whose objective function parameters are determined by the “switching function” which is derived from the Hamiltonian function. The interpretation of the adjoint variables of the control problem and the dual evaluators of the linear programming problem demonstrates an interesting interaction of the cross section phase of the problem, which is characterized by linear programming, and the dynamic phase of the problem, which is characterized by control theory.     

Computational techniques for optimizing systems with standby redundancy

Three methods are used to solve the following problem: For P, a positive constant, maximize (P. Reliability-cost) of a system with standby redundancy. The results show that a method which rounds a noninteger solution to the nearest integer solution can lead to tremendous mistakes. However, neither a well known dynamic programming algorithm nor a previously developed branch and bound technique are able to solve large size problems. The solution of problems of large dimension thus requires the use of the noninteger solution of the first method to limit the number of possible solutions when using either the dynamic programming algorithm or a modified branch and bound technique. With this assistance, the branch and bound technique is able to solve large problems in a short amount of computational time.     

基于禁忌退火算法的巡航导弹航迹规划

针对巡航导弹航迹规划这个复杂的优化问题,一个禁忌退火混合优化算法被提出.首先,该算法是以基本模拟退火算法为基础.其次,为了加快该模拟退火算法的收敛速度,在恶化解的接受判断过程中,增加了一定动态的约束条件.最后,为了使最优解能够跳出局部最优的陷阱,使用了一个动态的禁忌表.仿真结果验证了该禁忌退火混合优化算法能够取得目标函数更优的航迹规划路径,从而有效提高巡航导弹的作战效能.     

基于动网格的翼型设计优化

针对传统基于代理模型的翼型优化的缺陷,提出采用基于动网格的翼型优化;针对基本Hicks-Henne方法后缘不光滑情况进行了改进;采用自编程序实现动网格生成,通过集成商业软件Pointwise和CFD计算软件Fluent完成边界条件生成和流场解算,并实现上述程序和软件间的数据交互和自动化,整个优化流程在iSIGHT平台下执行,优化算例表明基于动网格的翼型优化方法能大幅提高翼型性能,节省大量的重复性操作,增加优化结果的鲁棒性和可信度,是翼型优化中的一种有效方法。     

An improved adaptive differential evolution algorithm for single unmanned aerial vehicle multitasking

Single unmanned aerial vehicle (UAV) multitasking plays an important role in multiple UAVs cooperative control, which is as well as the most complicated and hardest part. This paper establishes a three-dimensional topographical map, and an improved adaptive differential evolution (IADE) algorithm is proposed for single UAV multitasking. As an optimized problem, the efficiency of using standard differential evolution to obtain the global optimal solution is very low to avoid this problem. Therefore, the algorithm adopts the mutation factor and crossover factor into dynamic adaptive functions, which makes the crossover factor and variation factor can be adjusted with the number of population iteration and individual fitness value, letting the algorithm exploration and development more reasonable. The experimental results implicate that the IADE algorithm has better performance, higher convergence and efficiency to solve the multitasking problem compared with other algorithms.     

Client‐contractor bargaining on net present value in project scheduling with limited resources

The client‐contractor bargaining problem addressed here is in the context of a multi‐mode resource constrained project scheduling problem with discounted cash flows, which is formulated as a progress payments model. In this model, the contractor receives payments from the client at predetermined regular time intervals. The last payment is paid at the first predetermined payment point right after project completion. The second payment model considered in this paper is the one with payments at activity completions. The project is represented on an Activity‐on‐Node (AON) project network. Activity durations are assumed to be deterministic. The project duration is bounded from above by a deadline imposed by the client, which constitutes a hard constraint. The bargaining objective is to maximize the bargaining objective function comprised of the objectives of both the client and the contractor. The bargaining objective function is expected to reflect the two‐party nature of the problem environment and seeks a compromise between the client and the contractor. The bargaining power concept is introduced into the problem by the bargaining power weights used in the bargaining objective function. Simulated annealing algorithm and genetic algorithm approaches are proposed as solution procedures. The proposed solution methods are tested with respect to solution quality and solution times. Sensitivity analyses are conducted among different parameters used in the model, namely the profit margin, the discount rate, and the bargaining power weights. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

A hybrid algorithm for the one machine sequencing problem to minimize total tardiness

In a recent paper, Hamilton Emmons has established theorems relating to the order in which pairs of jobs are to be processed in an optimal schedule to minimize the total tardiness of performing n jobs on one machine. Using these theorems, the algorithm of this paper determines the precedence relationships among pairs of jobs (whenever possible) and eliminates the first and the last few jobs in an optimal sequence. The remaining jobs are then ordered by incorporating the precedence relationships in a dynamic programming framework. Propositions are proved which considerably reduce the total computation involved in the dynamic programming phase. Computational results indicate that the solution time goes up less than linearly with the size (n) of the problem. The median solution time for solving 50 job problems was 0.36 second on UNIVAC 1108 computer.     

全隐LU-SGS算法在高超声速热化学非平衡流刚性问题中的应用

在高超声速热化学非平衡流动计算中,当地气体能量松弛时间、化学反应特征时间与流动时间推进步长量级差异过大会带来严重数值刚性问题,且在高雷诺数条件下,壁面、拐角等强干扰区网格加密使得该问题加剧,导致初始最大CFL数极小,收敛速度缓慢.原始LU-SGS算法仅考虑化学反应源项和对流项的隐式处理,通过推导黏性项Jacobian矩...     

A network isolation algorithm

A set of edges D called an isolation set, is said to isolate a set of nodes R from an undirected network if every chain between the nodes in R contains at least one edge from the set D. Associated with each edge of the network is a positive cost. The isolation problem is concerned with finding an isolation set such that the sum of its edge costs is a minimum. This paper formulates the problem of determining the minimal cost isolation as a 0–1 integer linear programming problem. An algorithm is presented which applies a branch and bound enumerative scheme to a decomposed linear program whose dual subproblems are minimal cost network flow problems. Computational results are given. The problem is also formulated as a special quadratic assignment problem and an algorithm is presented that finds a local optimal solution. This local solution is used for an initial bound.     

双原子分子气体的定常隐式全流域多尺度算法

巨大的计算资源需求极大地阻碍了统一气体动理学格式的应用。采用宏观预估技术,基于Boltzmann-Rykov模型方程发展全流域适用的保守恒定常隐式算法,协同求解宏观方程和微观方程以加速收敛。在单元界面,通过模型方程特征差分解构造简单高效的多尺度数值通量,并结合非均匀非结构速度空间和速度空间自适应技术进一步降低计算需求、提升计算效率。超声速和高超声速平板绕流和圆球绕流的数值结果验证了算法的准确性与高效性。结果表明,算法能够准确求解二维和三维双原子气体多尺度流动问题,且相比于显式离散统一气体动理学格式可加速一个量级。     

A new storage reduction technique for the solution of the group problem

This paper shows that by making use of an unusual property of the decision table associated with the dynamic programming solution to the goup problem, it is possible to dispense with table storage as such, and instead overlay values for both the objective and history functions. Furthermore, this storage reduction is accomplished with no loss in computational efficiency. An algorithm is presented which makes use of this technique and incorporates various additional efficiencies. The reduction in storage achieved for problems from the literature is shown.