A labeling algorithm for the sensitivity ranges of the assignment problem

In view of the simplex-type algorithm, the assignment problem is inherently highly degenerate. It may be the optimal basis has changed, but the optimal assignment is unchanged when parameter variation occurs. Degeneracy then makes sensitivity analysis difficult, as well as makes the classical Type I range, which identifies the range the optimal basis unchanged, impractical. In this paper, a labeling algorithm is proposed to identify two other sensitivity ranges – Type II range and Type III range. The algorithm uses the reduced cost matrix, provided in the final results of most solution algorithms for AP, to determine the Type II range which reflects the stability of the current optimal assignment. Thus, the algorithm generates a streamlined situation from searching the optimal solution until performing the sensitivity analysis of the assignment problem. The Type III range, reflecting the flexibility of optimal decision making, can be obtained immediately after the Type II range is determined. Numerical examples are presented to demonstrate the algorithm.     

A turning restriction design problem in urban road networks

Turning restriction is one of the commonest traffic management techniques and an effective low cost traffic improvement strategy in urban road networks. However, the literature has not paid much attention to the turning restriction design problem (TRDP), which aims to determine a set of intersections where turning restrictions should be implemented. In this paper, a bi-level programming model is proposed to formulate the TRDP. The upper level problem is to minimize the total travel cost from the viewpoint of traffic managers, and the lower level problem is to depict travelers’ route choice behavior based on stochastic user equilibrium (SUE) theory. We propose a branch and bound method (BBM), based on the sensitivity analysis algorithm (SAA), to find the optimal turning restriction strategy. A branch strategy and a bound strategy are applied to accelerate the solution process of the TRDP. The computational experiments give promising results, showing that the optimal turning restriction strategy can obviously reduce system congestion and are robust to the variations of both the dispersion parameter of the SUE problem and the level of demand.     

Sensitivity Analysis Based Method for Optimal Road Network Pricing

Road pricing is an important economic measure for optimal management of transportation networks. The optimization objectives can be the total travel time or total cost incurred by all the travelers, or some other environmental objective such as minimum emission of dioxide, an so on. Suppose a certain toll is posed on some link on the network, this will give an impact on flows over the whole network and brings about a new equilibrium state. An equilibrium state is a state of traffic network at which no traveler could decrease the perceived travel cost by unilaterally changing the route. The aim of the toll setting is to achieve such an equilibrium state that a certain objective function is optimized. The problem can be formulated as a mathematical program with equilibrium constraints (MPEC). A key step for solving such a MPEC problem is the sensitivity analysis of traffic flows with respect to the change of link characteristics such as the toll prices. In this paper a sensitivity analysis based method is proposed for solving optimal road pricing problems.     

Joint optimization traffic signal control for an urban arterial road

This paper considers the optimal traffic signal setting for an urban arterial road. By introducing the concepts of synchronization rate and non-synchronization degree, a mathematical model is constructed and an optimization problem is posed. Then, a new iterative algorithm is developed to solve this optimal traffic control signal setting problem. Convergence properties for this iterative algorithm are established. Finally, a numerical example is solved to illustrate the effectiveness of the method.     

Asymptotic analysis of the effect of arrival model uncertainties in some optimal routing problems

We study the effect of arrival model uncertainties on the optimal routing in a system of parallel queues. For exponential service time distributions and Bernoulli routing, the optimal mean system delay generally depends on the interarrival time distribution. Any error in modeling the arriving process will cause a model-based optimal routing algorithm to produce a mean system delay higher than the true optimum. In this paper, we present an asymptotic analysis of the behavior of this error under heavy traffic conditions for a general renewal arrival process. An asymptotic analysis of the error in optimal mean delay due to uncertainties in the service time distribution for Poisson arrivals was reported in Ref. 6, where it was shown that, when the first moment of the service time distribution is known, this error in performance vanishes asymptotically as the traffic load approaches the system capacity. In contrast, this paper establishes the somewhat surprising result that, when only the first moment of the arrival distribution is known, the error in optimal mean delay due to uncertainties in the arrival model is unbounded as the traffic approaches the system capacity. However, when both first and second moments are known, the error vanishes asymptotically. Numerical examples corroborating the theoretical results are also presented.This work was supported by the National Science Foundation under Grants ECS-88-01912 and EID-92-12122 and by NASA under Contract NAG 2-595.The authors wish to thank an anonymous referee for pointing out Ref. 20, thus avoiding the need for an explicit proof of convexity of the cost function considered in the paper.     

周期数据时段划分的双截断高斯混合模型及其EM算法

有限混合模型是多模态数据拟合和聚类的有力工具,本文针对具有多模态的周期数据提出了双截断高斯混合糢型,并推导出相应的EM算法,再通过BIC准則确定混合成分个数,该方法的优点是可以将相邻周期上距离较近的数据聚为一类.模拟研究显示,在具体参数设置下,EM算法和BIC准则是相合的。最后,该方法应用于车流量数据的时段划分,将一天划分为具有显著特征的6个时段,有助于交通部门采取相应策略,为优化交通灯信号配时提供参考依据.     

A new lattice model of two-lane traffic flow with the consideration of optimal current difference

In this paper, a new lattice model of traffic flow is proposed with the consideration of the optimal current difference for two-lane system. The linear stability condition is derived through linear stability analysis, which shows that the optimal current difference term can improve the stability of traffic flow. The mKdV equation is obtained through nonlinear analysis. Thus the space of traffic flow is divided into three regions: the stable region, the metastable region and the unstable region respectively. Moreover, numerical simulation confirms that the traffic jam can be suppressed efficiently by considering the optimal current difference effect in extended lattice model of two-lane traffic flow.     

A Combinatorial user optimal dynamic traffic assignment algorithm

This paper introduces a polynomial combinatorial optimization algorithm for the dynamic user optimal problem. The approach can efficiently solve single destination networks and can be potentially extended to heuristically solve multidestinational networks. In the model, traffic is propagated according to sound traffic flow theoretical models rather than link exit functions; thereby allowing link queue evolution to be modeled more precisely. The algorithm is designed, proven, implemented and computationally tested.     

基于交通流的多模糊时间窗车辆路径优化

研究了基于交通流的多模糊时间窗车辆路径问题,考虑了实际中不断变化的交通流以及客户具有多个模糊时间窗的情况,以最小化配送总成本和最大化客户满意度为目标,构建基于交通流的多模糊时间窗车辆路径模型。根据伊藤算法的基本原理,设计了求解该模型的改进伊藤算法,结合仿真算例进行了模拟计算,并与蚁群算法的计算结果进行了对比分析,结果表明,利用改进伊藤算法求解基于交通流的多模糊时间窗车辆路径问题,迭代次数小,效率更高,能够在较短的时间内收敛到全局最优解,可以有效的求解多模糊时间窗车辆路径问题。     

Solving the minimum toll revenue problem in real transportation networks

As a means to relieve traffic congestion, toll pricing has recently received significant attention by transportation planners. Inappropriate use of transportation networks is one of the major causes of network congestion. Toll pricing is a method of traffic management in which traffic flow is guided to proper time and path in order to reduce the total delay in the network. This article investigates a method for solving the minimum toll revenue problem in real and large-scale transportation networks. The objective of this problem is to find link tolls that simultaneously cause users to efficiently use the transportation network and to minimize the total toll revenues to be collected. Although this model is linear, excessive number of variables and constraints make it very difficult to solve for large-scale networks. In this paper, a path-generation algorithm is proposed for solving the model. Implementation of this algorithm for different networks indicates that this method can achieve the optimal solution after a few iterations and a proper CPU time.     

基于改进基线算法的线性规划灵敏度问题研究

针对基线算法由于计算方面的无记忆性而在线性规划灵敏度方面的难实现问题,提出了改进的基线算法,并分别讨论了在价值系数C、技术系数矩阵A及资源向量b等各种情况发生变化的条件下,如何采用改进的基线算法进行灵敏度分析,从而能够简便、快捷的获得新的最优解.最后通过实例进行了说明.     

A new multifractal network traffic model

In this paper, a new multifractal traffic model to capture the multifractal nature of modern Internet traffic was developed. Employing the algorithm of network traffic analysis (binomial inverse cascade process) to analyze the multifractal feature of traffic data and adopting the algorithm of network traffic synthesis (binomial cascade process) to model the network traffic, this approach gave an easy and efficient way to infer the model parameters from the measured traffic traces. Moreover, the traffic was simulated and analyzed using obtained parameters. It was found that the simulated traffic data were in a close fit to the real trace statistics. The analysis results showed that this model could capture the real network traffic very well.     

高速公路行车时间估计和最优路径

行车时间估计和最优路径选择是智能交通系统中的研究热点,特别是对于车辆导航系统更具有深远的意义.首先以传统的交通流理论为基础,采用间接模型和动力学模型进行行车时间估计,通过仿真实验比较了两模型的优劣,并使用实测数据分析得到的车流量信息对动力学模型进行改进.然后使用Dijkstra算法寻找出静态状态下的最优路径,再结合前面建立的时间估计模型,给出了适用于动态随机状态下的路径寻优算法,用于解决路段行车时间期望随出发时刻动态变化的问题.最后指出了交通实时信息对解决动态随机最优路线问题的重要性,并结合卡尔曼滤波算法对路段相关的情况作了进一步讨论.     

基于多维模糊关联规则的道路交通阻断分析方法

交通阻断成因复杂,与气象环境、道路线形、车辆状态以及交通环境等多因素相关。由于缺乏对造成交通阻断相关因素间潜在关联的研究,交通阻断管控一直是公路管理,特别是高速公路管理的难点。本文提出了一种基于多维模糊关联规则的道路交通阻断分析方法,发掘交通阻断的潜在规律和各因素间的关联关系。首先在国家现有相关划分体系和大量交通阻断(事件)案例的基础上,根据道路管理实际需求,建立了交通阻断多维属性模型,然后利用基于FCM的模糊关联规则,挖掘阻断因素的多维属性的依存关系,得到面向道路交通阻断分析的多维模糊关联规则。通过研究成果的实践应用,证明关联规则可以为道路交通阻断预防和管理提供有效支持,在道路交通阻断分析领域有着良好的应用前景。     

A memetic algorithm for the orienteering problem with hotel selection

In this paper, a memetic algorithm is developed to solve the orienteering problem with hotel selection (OPHS). The algorithm consists of two levels: a genetic component mainly focuses on finding a good sequence of intermediate hotels, whereas six local search moves embedded in a variable neighborhood structure deal with the selection and sequencing of vertices between the hotels. A set of 176 new and larger benchmark instances of OPHS are created based on optimal solutions of regular orienteering problems. Our algorithm is applied on these new instances as well as on 224 benchmark instances from the literature. The results are compared with the known optimal solutions and with the only other existing algorithm for this problem. The results clearly show that our memetic algorithm outperforms the existing algorithm in terms of solution quality and computational time. A sensitivity analysis shows the significant impact of the number of possible sequences of hotels on the difficulty of an OPHS instance.     

A semismooth Newton method for traffic equilibrium problem with a general nonadditive route cost

Computing traffic equilibria with a general nonadditive route cost disutility function is considered in this paper. Following the user equilibrium (UE) condition, that is, no driver can unilaterally change route to achieve less travel costs, the traffic equilibrium problem (TEP) can be formulated as a nonlinear complementary problem (NCP). In this paper, we propose a semismooth Newton method with a penalized Fischer–Burmeister (PFB) NCP function to solve the NCP formulation of the TEP, and also, we investigate the properties of the proposed method. Numerical results are provided and compared with the classical TEP with additive route cost functions. The results show the algorithm can achieved substantially better performance than the existing approaches. A sensitivity analysis is also conducted to examine the parameter of the proposed nonadditive route cost function.     

Joint determination of optimal safety stocks and production policy for an imperfect production system

In this article, we develop an imperfect economic manufacturing quantity (EMQ) model for an unreliable production system subject to process deterioration, machine breakdown and repair and buffer stock. The basic model is developed under general process shift, machine breakdown and repair time distributions. We suggest a computational algorithm for determination of the optimal safety stock and production run time which minimize the expected cost per unit time in the steady state. For a numerical example, we illustrate the outcome of the proposed model and perform a sensitivity analysis with respect to the model-parameters which have direct influence on the optimal decisions.     

Computation of the optimal tolls on the traffic network

The present paper is devoted to the computation of optimal tolls on a traffic network that is described as fuzzy bilevel optimization problem. As a fuzzy bilevel optimization problem we consider bilinear optimization problem with crisp upper level and fuzzy lower level. An effective algorithm for computation optimal tolls for the upper level decision-maker is developed under assumption that the lower level decision-maker chooses the optimal solution as well. The algorithm is based on the membership function approach. This algorithm provides us with a global optimal solution of the fuzzy bilevel optimization problem.     

Performance of CSMA in multi-channel wireless networks

We analyze the performance of CSMA in multi-channel wireless networks, accounting for the random nature of traffic. Specifically, we assess the ability of CSMA to fully utilize the radio resources and in turn to stabilize the network in a dynamic setting with flow arrivals and departures. We prove that CSMA is optimal in the ad-hoc mode, when each flow goes through a unique dedicated wireless link from a transmitter to a receiver. It is generally suboptimal in infrastructure mode, when all data flows originate from or are destined to the same set of access points, due to the inherent bias of CSMA against downlink traffic. We propose a slight modification of CSMA that we refer to as flow-aware CSMA, which corrects this bias and makes the algorithm optimal in all cases. The analysis is based on some time-scale separation assumption which is proved valid in the limit of large flow sizes.     

一种改进的公交网络最优路径算法

通过对公交网络模型进行分析,考虑公交线路票价变化,按照出行时间最短同时保证换乘次数较少的原则,对现有解决公交网络最短路问题的算法进行改进.应用了将公交线路抽象为顶点,建立邻接矩阵的方法处理换乘问题.通过实际问题计算验证了算法的有效性.