Modeling concept and numerical simulation of ultrasonic wave propagation in a moving fluid-structure domain based on a monolithic approach

In the present study, we propose a novel multiphysics model that merges two time-dependent problems – the Fluid-Structure Interaction (FSI) and the ultrasonic wave propagation in a fluid-structure domain with a one directional coupling from the FSI problem to the ultrasonic wave propagation problem. This model is referred to as the “eXtended fluid-structure interaction (eXFSI)” problem. This model comprises isothermal, incompressible Navier–Stokes equations with nonlinear elastodynamics using the Saint-Venant Kirchhoff solid model. The ultrasonic wave propagation problem comprises monolithically coupled acoustic and elastic wave equations. To ensure that the fluid and structure domains are conforming, we use the ALE technique. The solution principle for the coupled problem is to first solve the FSI problem and then to solve the wave propagation problem. Accordingly, the boundary conditions for the wave propagation problem are automatically adopted from the FSI problem at each time step. The overall problem is highly nonlinear, which is tackled via a Newton-like method. The model is verified using several alternative domain configurations. To ensure the credibility of the modeling approach, the numerical solution is contrasted against experimental data.     

Using Benders Decomposition to Implicitly Model Tour Scheduling

This paper introduces a new integrated model for the combined days-off and shift scheduling problem (the tour scheduling problem). This model generalizes the forward and backward constraints, previously introduced by Bechtold and Jacobs for the shift scheduling problem, to the tour scheduling problem. This results in a general and compact formulation that can handle several types of scheduling flexibility. We also provide a new proof of the correctness of forward and backward constraints based on Benders decomposition. The latter approach is interesting in itself because it can be used to solve the problem when extraordinary overlap of break windows or start-time bands is present. A discussion of model size for a set of hypothetical test problems is presented to show the merits of the new formulation.     

A column generation approach for an employee scheduling problem with multiple shifts and work locations

This paper is concerned with the problem of assigning employees to a number of work centres taking into account employees' expressed preferences for specific shifts, off-days, and work centres. This particular problem is faced by the Kuwait National Petroleum Corporation that hires a firm to prepare schedules for assigning employees to about 86 stations distributed all over Kuwait. The number of variables in a mixed-integer programming model formulated for this problem is overwhelming, and hence, a direct solution to even the continuous relaxation of this model for relatively large-scale instances is inconceivable. However, we demonstrate that a column generation method, which exploits the special structures of the model, can readily solve the continuous relaxation of the model. Based on this column generation construct, we develop an effective heuristic to solve the problem. Computational results indicate that the proposed approach can facilitate the generation of good-quality schedules for even large-scale problem instances in a reasonable time.     

Quality inspection scheduling for multi-unit service enterprises

The traveling salesman problem is a classic NP-hard problem used to model many production and scheduling problems. The problem becomes even more difficult when additional salesmen are added to create a multiple traveling salesman problem (MTSP). We consider a variation of this problem where one salesman visits a given set of cities in a series of short trips. This variation is faced by numerous franchise companies that use quality control inspectors to ensure properties are maintaining acceptable facility and service levels. We model an actual franchised hotel chain using traveling quality inspectors to demonstrate the technique. The model is solved using a commercially available genetic algorithm (GA) tool as well as a custom GA program. The custom GA is proven to be an effective method of solving the proposed model.     

A linear approximation model for the parameter design problem

We consider the problem of minimizing the variance of a nonlinear function of several random variables, where the decision variables are the mean values of these random variables. This problem arises in the context of robust design of manufactured products and/or manufacturing processes, where the decision variables are the set points for various design components. A nonlinear programming (NLP) model is developed to obtain approximate solutions for this problem. This model is based on a Taylor series expansion of the given function, up to its linear term. A case study pertaining to the design of a coil spring is discussed, and its corresponding NLP model is developed. Using this model, a non-inferior frontier curve is obtained that shows the trade-off between the minimum mass of the coil spring and the minimum variance of its performance characteristic. Results of applying the model to three other case studies are also presented.     

一种折衷型模糊决策模型及其应用

本文针对多属性决策问题,在现有的决策方法基础上提出了一种新的折衷型模糊决策模型,并给出了有关参数的确定方法.最后应用折衷型模糊决策模型对一类飞机选购问题进行了方案的模糊优选决策分析,取得了满意的效果.该决策模型拓展和丰富了多属性决策理论,为解决同时具有定性与定量属性指标结构的多属性决策问题提供了新的有效途径.     

Examining Optimal Criterion Weights in Mixed Integer Programming Approaches to the Multiple-group Classification Problem

Several mixed integer programming approaches to the multiple-group statistical classification problem are examined. Many papers have investigated conditions under which a degenerate solution occurs in linear programming approaches to the two-group discriminant problem. Very little research has been conducted in the multiple-group case. We investigate conditions under which a degenerate solution can occur in mixed integer programming approaches to the multiple-group classification problem. A multiple-group ‘minimize the sum of deviations’ model is presented. This model is similar in structure to the general single function classification model. Also, a two-goal approach to the multiple-group classification problem is discussed.     

Maximum Likelihood Estimation of the Markov-Switching GARCH Model Based on a General Collapsing Procedure

The Markov-switching GARCH model allows for a GARCH structure with time-varying parameters. This flexibility is unfortunately undermined by a path dependence problem which complicates the parameter estimation process. This problem led to the development of computationally intensive estimation methods and to simpler techniques based on an approximation of the model, known as collapsing procedures. This article develops an original algorithm to conduct maximum likelihood inference in the Markov-switching GARCH model, generalizing and improving previously proposed collapsing approaches. A new relationship between particle filtering and collapsing procedures is established which reveals that this algorithm corresponds to a deterministic particle filter. Simulation and empirical studies show that the proposed method allows for a fast and accurate estimation of the model.     

Solving the logit-based stochastic user equilibrium problem with elastic demand based on the extended traffic network model

This paper proposes a novel extended traffic network model to solve the logit-based stochastic user equilibrium (SUE) problem with elastic demand. In this model, an extended traffic network is established by properly adding dummy nodes and links to the original traffic network. Based on the extended traffic network, the logit-based SUE problem with elastic demand is transformed to the SUE problem with fixed demand. Such problem is then further converted to a linearly constrained convex programming and addressed by a predictor–corrector interior point algorithm with polynomial complexity. A numerical example is provided to compare the proposed model with the method of successive averages (MSA). The numerical results indicate that the proposed model is more efficient and has a better convergence than the MSA.     

Fixed zeros in the model matching problem for systems over semirings

This paper studies “fixed zeros” of solutions to the model matching problem for systems over semirings. Such systems have been used to model queueing systems, communication networks, and manufacturing systems. The main contribution of this paper is the discovery of two fixed zero structures, which possess a connection with the extended zero semimodules of solutions to the model matching problem. Intuitively, the fixed zeros provides an essential component that is obtained from the solutions to the model matching problem. For discrete event dynamic systems modeled in max-plus algebra, a common Petri net component constructed from the solutions to the model matching problem can be discovered from the fixed zero structure.     

Trust-region problems with linear inequality constraints: exact SDP relaxation,global optimality and robust optimization

The trust-region problem, which minimizes a nonconvex quadratic function over a ball, is a key subproblem in trust-region methods for solving nonlinear optimization problems. It enjoys many attractive properties such as an exact semi-definite linear programming relaxation (SDP-relaxation) and strong duality. Unfortunately, such properties do not, in general, hold for an extended trust-region problem having extra linear constraints. This paper shows that two useful and powerful features of the classical trust-region problem continue to hold for an extended trust-region problem with linear inequality constraints under a new dimension condition. First, we establish that the class of extended trust-region problems has an exact SDP-relaxation, which holds without the Slater constraint qualification. This is achieved by proving that a system of quadratic and affine functions involved in the model satisfies a range-convexity whenever the dimension condition is fulfilled. Second, we show that the dimension condition together with the Slater condition ensures that a set of combined first and second-order Lagrange multiplier conditions is necessary and sufficient for global optimality of the extended trust-region problem and consequently for strong duality. Through simple examples we also provide an insightful account of our development from SDP-relaxation to strong duality. Finally, we show that the dimension condition is easily satisfied for the extended trust-region model that arises from the reformulation of a robust least squares problem (LSP) as well as a robust second order cone programming model problem (SOCP) as an equivalent semi-definite linear programming problem. This leads us to conclude that, under mild assumptions, solving a robust LSP or SOCP under matrix-norm uncertainty or polyhedral uncertainty is equivalent to solving a semi-definite linear programming problem and so, their solutions can be validated in polynomial time.     

Strategic Manipulation Approach for Solving Negotiated Transfer Pricing Problem

This paper suggests an approach for solving the transfer pricing problem, where negotiation between divisions is carried out considering the manipulation game theory model for a multidivisional firm. The manipulation equilibrium point is conceptualized under the Machiavellian social theory, represented by three concepts: views, tactics and immorality. In this approach, we are considering a non-cooperative model for the transfer pricing problem: a game model involving manipulating and manipulated players engaged cooperatively in a Nash game, restricted by a Stackelberg game. The cooperation is represented by the Nash bargaining solution. The transfer pricing problem is conceptualized as a strong Stackelberg game involving manipulating and manipulated divisions. This structure established conditions of unequal relative power among divisions, where high-power divisions tend to be abusive and less powerful divisions have a tendency to behave compliantly. For computation purposes, we transform the Stackelberg game model into a Nash game, where every division is able of manipulative behavior to some degree: the Nash game relaxes the interpretation of the manipulation game and the equilibrium selection for the transfer pricing problem. The manipulation dynamics and rationality proposed for the transfer pricing problem correspond to many real-world negotiation situations. We present an example, that illustrates how manipulation can be employed to solve the transfer pricing problem in a multidivisional firm.     

Improved optimization modelling for the closest string and related problems

We present a new integer linear programming model for the closest string problem. This model requires considerably less variables and constraints than the popular binary linear programming model used for this purpose. Due to the reduced size it is easier to handle rounding errors when an LP relaxation technique is used to solve the problem.     

Simultaneous Optimization in Process Quality Control via Prediction-interval Constrained Programming

A challenging problem in process control is the selection of input levels which will produce desirable output quality. This problem is complicated by the unsure relationships of cause and effect and by the trade-offs between meeting conflicting output specifications. This paper proposes a new approach, which incorporates prediction-interval constraints into a goal-programming model. A process-control problem, originally solved by the desirability-function approach, is solved using this new model. Comparisons between the two approaches are discussed.     

Determination of unknown functions in a mathematical model of ductal carcinoma in situ

This study deals with the numerical investigation of a mathematical model of breast cancer at the initial growth stage known as ductal carcinoma in situ. This model considered as an inverse problem and the uniqueness of solution of this inverse problem is proved. To solve this problem, a computational approach is developed based on an iterative procedure and space marching and mollification methods. The stability and convergence results are given to support the method theoretically. Two test problems are considered to demonstrate the efficiency and ability of the proposed numerical approach.     

基于情景分析的应急疏散车辆配置模型

在情景模式影响疏散点疏散人员数量及疏散最晚完成时间限制的条件下,研究了避难所应急疏散车辆配置计划及各种情景模式下的车辆出车任务安排,以疏散车辆出车安排为下层模型,以期望疏散总时间最小化车辆配置计划为上层模型建立了车辆配置及出车任务安排的双层规划模型。设计了结合CPLEX内置算法的模拟退火算法,最后用算例进行了仿真研究。     

Fixed poles in the model matching problem for systems over semirings

In this paper, solution existence conditions for the model matching problem are studied for systems over semirings, which are used in many applications, such as queueing systems, communication networks, and manufacturing systems. The main contribution is the discovery of fixed pole structure in solutions to the model matching problem. This fixed pole structure provides essential information contained in all the solutions to the model matching problem. For a discrete-event dynamic system example, a common Petri net component in the solutions of the model matching problem can be discovered from the fixed pole structure.     

基于模糊收益率的组合投资模型

本文考虑了收益率为模糊数的投资组合选择问题,利用模型约束简化方差约束,建立了投资组合选择的模糊线性规划模型,然后引进模糊期望把模糊线性规划问题化为普通参数线性规划问题,最后给出了一个数值算例.     

Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework

This paper is concerned with a continuous-time mean-variance portfolio selection model that is formulated as a bicriteria optimization problem. The objective is to maximize the expected terminal return and minimize the variance of the terminal wealth. By putting weights on the two criteria one obtains a single objective stochastic control problem which is however not in the standard form due to the variance term involved. It is shown that this nonstandard problem can be ``embedded' into a class of auxiliary stochastic linear-quadratic (LQ) problems. The stochastic LQ control model proves to be an appropriate and effective framework to study the mean-variance problem in light of the recent development on general stochastic LQ problems with indefinite control weighting matrices. This gives rise to the efficient frontier in a closed form for the original portfolio selection problem. Accepted 24 November 1999     

带平衡约束的离散网络平衡设计问题的遗传算法

本文研究了带平衡约束的离散网络设计问题及其求解算法.模型中上层是一个离散网络设计的数学规划模型,采用遗传算法来求解.下层是采用变分不等式描述的用户平衡配流问题,利用对角化方法直接求解.通过实例对算法进行验证,结果表明该算法是有效的.