无圈模糊有向网络最短路径算法

本文基于 OERI排序方法 ,使模糊数具有线性可加性 ,并通过对无圈有向网络的拓扑排序 ,使 Bell-man方程可以递推计算 ,建立在这两个基础上的标号算法是复杂度最低的算法 ,时间复杂度为 O(m)     

求最短路径树的一个新算法

本文考虑在一个具有ｎ个结点和ｍ条弧的网络中，求出从一个指定的结到其余所有结点的最短路径，或者找到一条具有负长度环路的问题，文中基于结点标号深度的概念，给出一个计算复杂性的界为Ｏ（ｎｍ）并且具有“尖利”（ｓｈａｒｐ）性质的求最短路径树的新算法。此外，我们还讨论了负长度环路的探测问题，并给出了一个具有“时间尖利”（ｔｉｍｅ－ｓｈａｒｐ）性质的检测负长度环路的方法。     

求最短路径的“改进标号法”

本给出了求赋权图中两顶点之间最短路径的“改进标号法”,该方法在效率上优于Ｄｉｊｋｓｔｒａ的标号法,并在确定最短路径的长度的同时,也确定了相应的最短路径。     

一类最速降线与最短路径问题

本结合梯度讨论了椭球面上一类最速降线问题,应用变分法及Ｍａｔｈｅｍａｔｉｃａ软件讨论了椭球面上最短路径问题;分析了二的关系,旨在加强应用数学知识的能力。     

Kth最短路径的Bellman改进算法

基于对Bellm an算法的改进,得到了求解k th最短路的新算法.改进算法的优势在于从Bellm an算法只能解决最短路问题拓展到求解k th最短路问题,而且可以考虑权重为负数的情况.与传统算法相比,新算法更易于理解.     

模糊最短路的一种算法

模糊最短路问题在许多领域有着广泛的应用,研究这一问题具有重要意义。根据多准则决策理论求非被支配路径集合,求最大效用模糊最短路以及利用模糊数排序方法求模糊最短路是常用的三种研究方法,本文利用OERI排序原理,使网络模糊边长具有线性可加性,对具有三角模糊数边权的网络给出了一种标号算法,该算法简单高效,且易于在计算机上实现,算法的时间复杂度为O(n^2)。     

罚转向网络最短路径算法及其复杂性研究

本文建立和研究了具有转向惩罚值的网络模型．论文首先引入了罚转向网络符号及规则，对所建立的罚转向网络模型的性质进行了讨论，在证明了路径与子路径关系的三个定理之后，提出了求解其最短路径的算法并证明了算法的复杂性结论，论文最后给出了一个用该算法求解项转向网络的最短路径实例．     

最短时限运输问题的推广

在目前文献所讨论的最短时限运输问题中,从一个发点到一个收点的运输时间为常数,与运输量无关.这有一定的局限性.本文从实际出发,在已有模型中加入运输量对运输时间的影响,使其更具一般性.实际上,可把时间函数推广到单调递增函数.文中给出了推广模型的多项式时间算法,它能相对快速地找到最优运输方案.     

基于改进蚁群算法的最短路径问题研究及应用

蚁群系统作为一种蚁群算法是解决最短路径问题的一种行之有效的方法.然而,它自身也存在着一些缺陷,主要针对基本蚁群算法易陷入局部最优这一缺陷对其进行改进,集中体现在初始信息素求解和信息素更新这两方面.为了进一步了解改进蚁群算法的优点,进行了实验仿真:将改进的蚁群算法应用子模拟医疗救护GIS中,利用GIS的网络分析功能对城市道路网络的最短路径选择算法进行了深入地探讨研究,并以山西省太原市的交通路线作为实例进行研究.计算机仿真结果表明,改进的蚁群算法在解决最短路径问题时较基本蚁群算法的性能好,它具有一定的理论参考价值和现实意义.     

约束四点集的最短网络问题

设Ｌ为Ｅｕｃｌｉｄｅａｎ平面上一连续曲线,在Ｌ的一侧有一个含ｎ个固定点的集合Ｎ,且点集Ｎ的凸包ＣＨ（Ｎ）与曲线ＬＩ 相交,总是是在Ｌ上找一点Ｐ,使点集Ｎ∪（Ｐ）的互联网络最短,本文在Ｌ是圆及点集Ｎ含有３个点的条件下给出了问题解。     

Shortest Path Problem on a Network with Imprecise Edge Weight

A network with its arc lengths as imprecise number, instead of a real number, namely, interval number and triangular fuzzy number is considered here. Existing ideas on addition and comparison between two imprecise numbers of same type are introduced. To obtain a fuzzy shortest path from a source vertex to all other vertices, a common algorithm is developed which works well on both types of imprecise numbers under consideration. In the proposed algorithm, a decision-maker is to negotiate with the obtained fuzzy shortest paths according to his/her view only when the means are same but the widths are different of the obtained paths. Otherwise, a fuzzy optimal path is obtained to which the decision-maker always satisfies with different grades of satisfaction. All pairs fuzzy shortest paths can be found by repeated use of the proposed algorithm.     

Graph Collapsing in Shortest Path Auction Algorithms

In this paper we consider the problem of finding a shortest path from a source node to a fixed target node (SSP) or to all the nodes (SPT) on a directed graph. A family of algorithms which derives from the known auction algorithm is introduced. The key feature of these algorithms is based on topological transformations operated on the graphs that replace an optimal sub-path with a single arc of the same length (graph collapsing concept). The same idea is applied both to the standard auction algorithm and to a modified version of the algorithm. In the last mentioned case a good saving in computation cost is obtained as shown by the reported numerical examples.     

一种最短路问题的遗传算法求解

针对最短路径问题,在分析传统遗传算法不足的基础上提出了变长染色体遗传算法(ClvGA),详细论叙了其编码、基因插入(删除、变异)算子的设计,最后通过两个网络对ClvGA进行了实验仿真,结果表明:该方法在最短路径问题上表现出较好的鲁棒性.     

Resource Constrained Shortest Path Problems in Path Planning for Fleet Management

In the management and control of a vehicle fleet on a road network, the problem arises of finding the best route in relation to the mission of the fleet and to the typology of freight or users. Sometimes the route has to be adapted not only to current traffic conditions, but also to the physical, geometric and functional attributes of the roads, related to their urban location and environmental characteristics. This problem is approached here through an extension of the classic Shortest Path problem, named Resource Constrained Shortest Path problem (RCSP), where the resources are related to the road link attributes, assumed as relevant to the specific planning problem. A classification scheme of these attributes is first proposed and RCSP is described and reviewed. Next, a General Resource Constrained Shortest Path problem (GRCSP) is defined, which can be found in all cases where it is necessary to plan, statically or dynamically, the path of a vehicle and to respect a set of constraints expressed in terms of parameters and indices associated with the roads on the network. For this general problem a model has been formulated and a Branch and Cut solution approach is proposed. Computational results obtained on test and real networks during the experimentation of a fleet with low emission vehicles are also given. This revised version was published online in August 2006 with corrections to the Cover Date.     

非平衡交通分配的拟Frank-Wolfe迭代算法

提出了基于最短路动态生成的一种新的非平衡交通分配迭代算法.在每轮迭代中,将按全有全无方法在当前最短路上分配的交通量与前一轮迭代所得到的交通量加权组合,而各O-D对的加权系数则依据Logit原则来确定.和Frank-Wolfe算法不同,不必通过一维搜索确定加权系数.同时又避免了Logit方法要求枚举所有路径的困难.本文还证明了算法的收敛性,而计算实例显示,由本算法所得结果与平衡交通分配非常接近,因而它是一个高效而可靠的交通分配算法,适用于大、中型道路交通网络的交通分配计算.     

On the Generalized Elementary Shortest Path Problem: A heuristic approach

We introduce the generalized elementary shortest path problem (GESPP) where in addition to the features of the shortest path problem, nodes belong to predefined non-disjoint clusters. Each cluster is associated to a profit to the cost function, obtained if at least one element in the cluster appears in the path. Several applications can be considered as school bus routing, pricing problems, or telecommunication network design. Thus, depending on the case, clusters could be interpreted as groups of nodes with linking features as, for example, being easily reachable from each other, or some kind of coverage guarantee. We compare the GESPP to similar problems in the literature and we propose a two-phase heuristic algorithm for graphs including negative cycles. Tests on random instances with up to 100 nodes show an average gap of 0.3% to the best known solutions computed in 2.8s in average.     

Shortest Path Auction Algorithm Without Contractions Using Virtual Source Concept

In this paper, the problem of finding a shortest path tree rooted at a given source node on a directed graph (SPT) is considered. A new efficient algorithm based on a primal-dual approach is presented, which improves both the convergence and the complexity of the best known auction-like algorithm. It uses the virtual source (VS) concept based on the following consideration: when a node i is visited for the first time by any algorithm which preserves verified the dual admissibility conditions, then the shortest path (SP) from the source node to i is found. Therefore, the SP from the source to the remaining nodes may be computed by considering i as a virtual source.We propose a very efficient implementation of an auction-like algorithm that uses this concept and enables us to obtain a computational cost of O(n ²), where n is the number of nodes.Numerical experimentsare reported showing that the new method outdoes previously proposed auction-like algorithms and is highly competitive with other state-of-art SP approaches.     

负权最短路问题的新算法

Bellman-Ford算法自1958年以来一直是负权最短路问题的公认的最好算法之一．1970年,Yen对其进行了改进,理论上可以节省一半的计算量．本文得到了一种比Bellman-Ford算法更加优越的算法．尽管在理论上新算法无法保证完全超越于Yen的改进算法,但在许多情况下需要更少的计算量．     

具有最大能量的最短路

本文讨论一类新的赋权图 ,称为双权图 ,G=( V,E;w,c) ,w称为权函数 ,c为容量函数 .并给出了 G中两顶点 u与 v之间具有最大能量的最短路的算法 .