时间依赖无向中国邮路问题的分支限界算法

时间依赖网络相比传统网络模型有更广泛的应用领域,比如会交网络和通信网络都可以抽象成为时间依赖的网络模型。当模型中弧的访问代价为时间依赖的变量时,中国邮路问题的求解将变得非常困难。首先分析了传统的中国邮路问题求解算法,如奇偶图上作业法和Edmonds& Johnson算法,以及不能有效求解时间依赖中国邮路问题的根本原因;其次给出了一般时变无向中国邮路问题的特性,并在此基础上设计了该问题的分支限界最优化算法;然后针对FIFO(First In First Out)这一类特殊时变网络,设计了新的剪枝条件,从而得到了更有效求解FIFO网络的时变无向中国邮路问题的分支限界最优化算法;最后对算法进行了实验,算法实验结果正确。     

时间窗-时间依赖中国邮路问题的图转换算法

研究时间依赖网络上带时间窗的中国邮路问题（TDCPPTW）,该问题是对中国邮路问题的扩展,它考虑了时间因素,在实时软件测试等当前许多具有时间依赖性质的热门问题中更具优势。首先提出了一个新的图转换算法;然后,从理论上证明了该转换算法能够在伪多项式时间内将TDCPPTW转换为相应的广义乡村邮路问题（GRPP）;最后,建立了一个0/1线性整数规划模型用于求解转换后的问题,并对随机生成的12个实例进行了求解实验。     

时间依赖网络中国邮路问题

中国邮路问题是图论中的经典问题,得到了深入的研究和广泛应用。近年来,由于计算机网络与通信、智能交通系统等复杂应用领域的需求,时间依赖网络问题的研究具有更为重要的现实应用意义。本文首次提出了时间依赖网络中的中国邮路问题,建立了该问题的整数线性规划模型,并对该模型的上界进行了分析,最后给出了网络应用实例。     

时变网络中国邮路问题的时间自动机模型

基于时间自动机理论,提出了时间窗、时间依赖服务代价以及时间依赖旅行时间这3类时变网络中国邮路问题的统一建模的语义模型和求解方法.首先,将中国邮路问题可行解条件和时变参数与时间自动机联系起来,建立了3类问题的统一时间自动机系统(timed automata system,简称TAS)模型;然后,将时变网络中国邮路问题归结为TAS模型上的一系列可达性判定问题,并利用形式化验证算法给出了有效的求解方法.由于TAS模型中存在O(|A|+|AR|+1)个时间自动机,限制了问题求解规模.为此,通过扩展时间自动机语义,提出了TAS模型中的时间自动机合并策略,进而将TAS模型转换为一个广义时间自动机(GTA)模型.基于GTA模型,利用UPPAAL工具对9组、共54个随机算例进行实验.实验结果表明,该方法在求解精度上明显优于运筹学领域的方法.     

时间依赖网络中非FIFO弧的转化研究

经典最短路算法不能有效地解决时间依赖网络的最短路问题.时间依赖网络中的非FIFO弧的存在是导致经典的最短路算法失效的原因.本文对非FIFO弧的权函数为非连续(存在有限个非连续点)或者离散情况下转化为FIFO弧进行了研究,在允许等待的前提条件下,提出了解决此类问题的方法.建立在经典Dijkstra算法基础上,本文提出了时间依赖网络最短路算法.     

基于中国邮路算法及UIO序列的状态机测试序列生成

状态测试的首要问题就是从大量的状态组合中挑选针对典型的错误能够最为有效和最为优化的测试序列。A.V.Aho等人提出了使用中国邮路算法及UIO序列进行生成测试序列的方法,但并没有考虑UIO序列的加入对状态迁移造成的影响,因此不能够对测试序列进行全局优化。该文对上述算法进行改进,并使用遗传算法解决了中国邮路NP-Complete问题。     

一种改进的量子进化算法及其在乡村邮路问题的应用

针对基本量子进化算法易陷于局部最优解的缺陷,提出一种改进的量子进化算法(QEA)。结合乡村邮路问题,对算法进行了测试,结果表明,改进算法在全局寻优能力和种群多样性方面比基本量子进化算法有所改进,是求解乡村邮路问题的一种有效算法。     

最小时间路径算法的改进及在路径优化中的应用*

由于城市交通网络中路径行程时间是随着时间的变化而变化的,求解最小时间路径比较困难,为此提出把交通网络抽象为时间依赖的网络模型的解决方法。对时间依赖网络模型和理论基础进行分析,指出文献［1］描述的最小时间路径算法存在的不足,即不能正确记录路径;通过引入一个记录路径的数组来对此算法进行改进,改进后的算法不仅解决了原算法存在的问题,而且可以满足n∶1的最短路径搜索,扩展了原算法的应用范围。最后用实验验证了改进算法的正确性和有效性。     

时间依赖的网络中最小时间路径算法

时间依赖的网络与传统网络模型相比更具有现实意义，具有广泛的应用领域，交通网络和通信网络可以抽象为时间依赖的网络模型，当模型中弧的工度是时间依赖的变量，最短路径问题的求解变得非常困难，早期的研究者通过具体的网络实例认识到传统最短路径算法在这种情况下是不正确的，因此给出限制性条件使得传统最短路径算法是有效的。该文从最短路径算法的理论基础入手，从理论上证明了传统最短路径算法，如Dijkstra算法和标号设置算法，在时间依赖的网络上不能有效地求解最短路径问题，并且，在没有任何限制性条件下，给出了时间依赖的网络模型，理论基础，求解最小时间路径的优化条件和SPTDN算法，从理论上证明了SPTDN算法的正确性，算法的实验结果是正确的，最后给出了时间依赖的网络应用实例。     

动态容量网络中的最小最大时间流问题

动态(时间依赖的)容量网络与传统静态网络相比更具现实意义,在交通网络、物流网络和通信网络中都有着广泛的应用。在时间依赖网络最短路算法的基础上,研究具有实际背景的动态容量网络的最小最大时间流问题,给出求动态容量网络的最小最大时间流的多项式算法和算法的应用实例,其时间复杂度为O(mMv)。     

中国邮递员问题的动态规划算法研究

在动态规划的决策过程思想基础上，针对无向中国邮递员问题，提出了一个新的搜索算法CPDPA(Chinese postman decision process algorithm)，首次实现了中国邮递员问题的动态规划求解．针对中国邮递员问题不能直接应用于决策思想，提出了弧点转换算法CEPA(convert edge to Doint algorithm)，建立了该问题适用于决策的模型．进而针对这一模型，提出了多阶段决策过程模型转换算法MDPMCA(multistep decision process model convert algorithm)，转换所得模型符合多阶段决策过程需求，可用CPDPA算法求解中国邮递员问题．对每一算法都给出了其网络应用实例．对算法的正确性和理论性做出了证明，并对最优性原理在中国邮递员问题上做了一定扩展．     

The time-dependent rural postman problem: polyhedral results

The Chinese postman problem is a famous and classical problem in graph theory. This paper introduces a new variant of this problem, namely, the time-dependent rural postman problem, which is motivated by applications, involving scheduling with time-dependent processing time. We present an arc-path formulation for the problem with a constraint set that is divided into two parts. The first part is linear and has a strong combinatorial structure, which defines the polytope of the arc-path alternation sequence (APAS), while the second part is nonlinear and is closely related to time-dependent travel time. First, we investigate the facial structure of the APAS polytope and present several facet inequalities. Second, considering the travel and service time functions as piecewise functions, we linearize the nonlinear inequalities and propose several strong, valid inequalities. Finally, we propose a cutting plane algorithm and report numerical results on several randomly generated instances.     

Computational experiments with algorithms for a class of routing problems

The vehicle routing problem, a generalization of the infamous traveling salesman problem, is a well-known distribution management problem that has been the focus of much research attention. On the other hand, generalizations of arc routing problems, such as the Chinese postman problem, have been comparatively neglected. In a recent paper, we studied a class of capacitated arc routing problems from primarily a theoretical point of view. In this paper, we focus on the development and testing of algorithms for solving the capacitated Chinese postman problem. Extensive computational results are presented and analyzed.     

A heuristic for the periodic rural postman problem

The periodic rural postman problem (PRPP) is variant of the classical rural postman problem whose applications arise in garbage collection and street sweeping. In the PRPP each required arc/edge of a graph must be visited a given number of times over an m-day planning period in such a way that service days are equally spaced. The PRPP amounts to select a service day combination for each required arc/edge and to determine a postman tour for each day of the planning period. The objective is to minimize the total distance travelled. In this paper a simple but effective heuristic for the undirected PRPP is presented. Extensive computational results indicate that the algorithm is capable of providing high quality solutions. To our knowledge this is the first methodological paper devoted to a periodic arc routing problem.     

New heuristic algorithms for the windy rural postman problem

In this paper we deal with the windy rural postman problem. This problem generalizes several important arc routing problems and has interesting real-life applications. Here, we present several heuristics whose study has lead to the design of a scatter search algorithm for the windy rural postman problem. Extensive computational experiments over different sets of instances, with sizes up to 988 nodes and 3952 edges, are also presented.     

Approximate solutions for the maximum benefit chinese postman problem

The Maximum Benefit Chinese Postman Problem (MBCPP) is an interesting and practical generalization of the classical Chinese Postman Problem, which has many real-world applications. Each arc on the MBCPP network is associated with a service cost for the traversal with service, a deadhead cost for the traversal with no service, and a set of benefits. Each time an arc is traversed, a benefit is generated. The objective of the MBCPP is to find a postman tour traversing a selected set of arcs with the total net benefit maximized. Such a generalization reflects real-world situations more closely. The MBCPP has been shown to be more complicated than the Rural Postman Problem, which is an NP-hard problem. Therefore, it is difficult to find polynomial-time bounded algorithms to solve the problem exactly. In this paper, we first review an existing exact solution procedure, and introduce several heuristic algorithms including the Branch-Scan algorithm, the Connection algorithm with various connection strategies, and the Directed Tree algorithm, to solve the MBCPP approximately. We also apply one-opt, two-opt, component exchange, and component-drop procedures to improve the solutions. The proposed algorithms are tested and compared. Extensive computational results are provided and analysed.