复杂网络中最短K条路径问题的求解算法研究

以时间代价作为目标函数,针对复杂网络的优化问题进行研究,给出了目标评价函数模型的建立过程,提出了基于改进的A*算法求解复杂网络中最短K条路径问题的算法,并以城市交通为例,对算法进行了验证。实验结果表明所提出的算法可适用于一般多重图中最短K条路径问题的快速求解,具有广泛的应用价值。     

移动卫星网络中的最短路径算法研究

移动卫星网络的拓扑时变性对其最短路径求解带来新的问题。文章利用提出的移动卫星网络模型,证明了基于传统网络的最短路径算法在移动卫星网络中使用存在局限性,提出了一种适用于移动卫星网络的最短路径求解方法和优化算法,并进行了仿真验证。     

一种基于路径阻断的求解最短路径算法

全源最短路径的求解是计算机科学、交通工程、地理信息系统等学科中的一个研究热点。随着网络规模不断增大,求解全源最短路径的时间复杂度急剧上升,这制约了复杂网络相关研究与应用的快速发展,因此最短路径算法的效率问题是普遍关注并且在实际应用中迫切需要解决的问题。本文在BFS的基础上,引入路径阻断策略,利用已求得的单源最短路径节点的结果,加速全源最短路径的求解。实验结果表明该方法对大规模网络全源最短路径实现了加速计算。     

网络中最短距离的递归算法

提出了在搜索过程中采用标记最短距离,调用递归函数用回溯搜索法求解网络最短距离的算法。该算法可以方便地求解复杂网络或复杂迷宫的通道与最短距离问题,在求解结果中给出从起点到网络通道上任意点的路径标识和最短距离值等信息,在无向加权图的最短路径求解中,显示出比Dijkstra方法小的时间复杂度。该算法克服了传统回溯法求解复杂迷宫时被时间复杂度和空间复杂度困扰的难题,显示出良好的应用前景。     

基于深度强化学习的电力物资配送多目标路径优化

针对现有电力物资车辆路径问题（EVRP）优化时考虑目标函数较为单一、约束不够全面,并且传统求解算法效率不高的问题,提出一种基于深度强化学习（DRL）的电力物资配送多目标路径优化模型和求解算法。首先,充分考虑了电力物资配送区域的加油站分布情况、物资运输车辆的油耗等约束,建立了以电力物资配送路径总长度最短、成本最低、物资需求点满意度最高为目标的多目标电力物资配送模型;其次,设计了一种基于DRL的电力物资配送路径优化算法DRL-EVRP求解所提模型。DRL-EVRP使用改进的指针网络（Ptr-Net）和Q-学习（Q-learning）算法结合的深度Q-网络（DQN）来将累积增量路径长度的负值与满意度之和作为奖励函数。所提算法在进行训练学习后,可直接用于电力物资配送路径规划。仿真实验结果表明,DRL-EVRP求解得到的电力物资配送路径总长度相较于扩展C-W(ECW)节约算法、模拟退火（SA）算法更短,且运算时间在可接受范围内,因此所提算法能更加高效、快速地进行电力物资配送路径优化。     

基于加权标识S-图的最短路径研究

为解决智能交通系统中交通运输网络分析和最短路径问题,提出加权标识S-图最短路径算法。根据Petri网基本原理和加权S-图的特点,给出交通网络加权S-图的网模型。阐述加权标识S-图最短路径的基本原理、求解加权标识S-图的最短路径定理及证明。通过交通运输网络示例和实验对算法进行验证,对比分析算法性能。结果表明,加权标识S-图最短路径算法能够更有效地求解交通网络最短路径。     

基于GA的网络最短路径多目标优化算法研究

针对现有基于遗传算法(GA)优化的网络最短路径算法存在优化目标单一、遗传编码质量低、搜索策略间平衡性差、适应度分配效率与灵活性较低等问题,建立一种多目标优化最短路径自适应GA模型,提出了优先级编码和优先级索引交叉算子,引入了遗传算子参数的模糊控制机制和基于自适应加权的适应度分配方法.实验结果表明,该算法的准确性和稳定性高、复杂度合理,实现了对网络设计优化中多目标最短路径问题的高质量求解.     

基于梯形模糊中智数的最短路径求解方法

最短路径的选择是图论中的经典问题之一.复杂环境中对象之间的关系通常具有模糊性、犹豫性、不确定性和不一致性,而中智集是元素的真实程度、不确定程度及谬误程度的集合,更有能力捕捉不完全信息.基于此,基于中智集理论和图理论的中智图最短路径选择成为一个关键问题.针对边长表述为梯形模糊中智数的中智图最短路径求解问题,提出一种扩展的动态规划求解方法.利用基于梯形模糊中智数的得分函数和精确函数来比较路径长度,并给出扩展的动态规划求解最短路径方法,从而得到最短路径和最短路径长度.最后,通过两个算例验证此方法的可行性,通过与Dijkstra算法对比分析说明所提出方法的合理性和有效性,并且分析了采用不同排序方法对中智图最短路径选择的影响.     

最短路径问题及其解法研究

最短路径问题是在给定的网络图中寻找出一务从起始点到目标点之间的最短路径。该文分别从动态规划、Dijkstra、A＊算法、遗传算法这四种算法设计方法入手,概述了各种设计方法的原理,提出了求解最短路径的算法思想,并对算法进行分析．提出了改进方法。     

基于优先队列的时变网络最短路径算法

提出了基于优先队列的时变网络最短路径算法,能克服传统最短路径算法难以对时变网络求解最短路径的缺陷。提出的时间窗选择策略能够在算法求解过程中为节点选择合适的时间窗以降低路径长度,从而求得精确解。进一步地,算法使用了优先队列组织节点集合以提高计算效率。在随机生成的网络数据以及美国道路数据上的实验表明,基于优先队列的时变网络最短路径算法与经典方法相比,不仅能够求得精确解,运算速度也有所提高。     

基于Floyd算法的多重最短路问题的改进算法

路径分析是网络分析最基本的问题,其核心是对最短路径的求解。Floyd算法是一种求取最短路的经典算法。分析发现,两点间可能存在多条权重相同的最短路径,而这一点Floyd算法没有涉及。以无向联通图为研究对象,设计了基于Floyd求解多重等价最短路算法,并分析计算了一个实际算例。计算结果表明,基于Floyd的多重等价最短路算法可以有效解决多重等价最短路问题。     

基于最小路径交叉度的域内路由保护方案

已有的路由保护方案面临下面两个问题：（1）默认路径和备份路径包含的公共边数量较高,如ECMP和LFA等;（2）为了计算两条包含公共边数量较少的路径,限制默认路径不能使用最短路径,如红绿树方案等.针对上述两个问题,首先将计算默认路径和备份路径描述为一个整数规划问题,然后提出采用启发式方法求解该问题,接着介绍了转发算法,最后通过仿真实验和真实实验对算法进行了测试.实验结果表明,该算法不仅具有较低的计算复杂度,而且可以降低默认路径和最短路径包含的公共边的数量,提升网络可用性.     

切换到高一层路网最近四个点的最短路算法

针对基于大规模图的最短路问题求解速度慢的问题,提出了一个基于路网等级的求最短路的快速近似算法。该算法首先求出高一层路网到起点的4个最近点和到终点的4个最近点及最短路径,由高一层路网形成的子图T再加上这8个最短路径形成图T',在T'上求起点到终点的最短路。这种设计使得该算法适合在超大规模图上求解,理论上也证明了精度可控,同时预处理数据也是可行的,从而使两点间最短路的求解速度大大提高。在纽约公路网上的测试结果说明了该算法的有效性和合理性。     

A new parallel and distributed shortest path algorithm forhierarchically clustered data networks

This paper presents new efficient shortest path algorithms to solve single origin shortest path problems (SOSP problems) and multiple origins shortest path problems (MOSP problems) for hierarchically clustered data networks. To solve an SOSP problem for a network with n nodes, the distributed version of our algorithm reaches the time complexity of O(log(n)), which is less than the time complexity of O(log ² (n)) achieved by the best existing algorithm. To solve an MOSP problem, our algorithm minimizes the needed computation resources, including computation processors and communication links for the computation of each shortest path so that we can achieve massive parallelization. The time complexity of our algorithm for an MOSP problem is O(m log(n)), which is much less than the time complexity of O(M log² (0)) of the best previous algorithm. Here, M is the number of the shortest paths to be computed and m is a positive number related to the network topology and the distribution of the nodes incurring communications, m is usually much smaller than M. Our experiment shows that m is almost a constant when the network size increases. Accordingly, our algorithm is significantly faster than the best previous algorithms to solve MOSP problems for large data networks     

量子密钥分发网络端端密钥协商最优路径选择算法

针对量子密钥分发(QKD)网络端端密钥协商路径选择问题,设计了一种基于改进Dijkstra算法的端端密钥协商最优路径选择算法。首先,基于有效路径策略,剔除网络中的失效链路;然后,基于最短路径策略,通过改进Dijkstra算法,得到密钥消耗最少的多条最短路径;最后,基于最优路径策略,从多条最短路径中选择一条网络服务效率最高的最优路径。分析结果表明,该算法很好地解决了最优路径不唯一、最优路径非最短、最优路径非最优等问题,可以降低QKD网络端端密钥协商时密钥消耗量,提高网络服务效率。     

An ant colony optimization algorithm for the bi-objective shortest path problem

Multi-objective shortest path problem (MOSP) is an extension of a traditional single objective shortest path problem that seeks for the efficient paths satisfying several conflicting objectives between two nodes of a network. MOSP is one of the most important problems in network optimization with wide applications in telecommunication industries, transportation and project management. This research presents an algorithm based on multi-objective ant colony optimization (ACO) to solve the bi-objective shortest path problem. To analyze the efficiency of the algorithm and check for the quality of solutions, experimental analyses are conducted. Two sets of small and large sized problems that generated randomly are solved. Results on the set problems are compared with those of label correcting solutions that is the most known efficient algorithm for solving MOSP. To compare the Pareto optimal frontiers produced by the suggested ACO algorithm and the label correcting algorithm, some performance measures are employed that consider and compare the distance, uniformity distribution and extension of the Pareto frontiers. The results on the set of instance problems show that the suggested algorithm produces good quality non-dominated solutions and time saving in computation of large-scale bi-objective shortest path problems.     

Parallel Algorithms for Dynamic Shortest Path Problems

The development of intelligent transportation systems (ITS) and the resulting need for the solution of a variety of dynamic traffic network models and management problems require faster‐than‐real‐time computation of shortest path problems in dynamic networks. Recently, a sequential algorithm was developed to compute shortest paths in discrete time dynamic networks from all nodes and all departure times to one destination node. The algorithm is known as algorithm DOT and has an optimal worst‐case running‐time complexity. This implies that no algorithm with a better worst‐case computational complexity can be discovered. Consequently, in order to derive algorithms to solve all‐to‐one shortest path problems in dynamic networks, one would need to explore avenues other than the design of sequential solution algorithms only. The use of commercially‐available high‐performance computing platforms to develop parallel implementations of sequential algorithms is an example of such avenue. This paper reports on the design, implementation, and computational testing of parallel dynamic shortest path algorithms. We develop two shared‐memory and two message‐passing dynamic shortest path algorithm implementations, which are derived from algorithm DOT using the following parallelization strategies: decomposition by destination and decomposition by transportation network topology. The algorithms are coded using two types of parallel computing environments: a message‐passing environment based on the parallel virtual machine (PVM) library and a multi‐threading environment based on the SUN Microsystems Multi‐Threads (MT) library. We also develop a time‐based parallel version of algorithm DOT for the case of minimum time paths in FIFO networks, and a theoretical parallelization of algorithm DOT on an ‘ideal’ theoretical parallel machine. Performances of the implementations are analyzed and evaluated using large transportation networks, and two types of parallel computing platforms: a distributed network of Unix workstations and a SUN shared‐memory machine containing eight processors. Satisfactory speed‐ups in the running time of sequential algorithms are achieved, in particular for shared‐memory machines. Numerical results indicate that shared‐memory computers constitute the most appropriate type of parallel computing platforms for the computation of dynamic shortest paths for real‐time ITS applications.     

最短路算法在生产最优化中的应用

给出了一种基于Djikstra最短路算法的实现,该算法实现可以求得有限权图中任一点到其他所有点的最短路径及相应的距离,并清晰完整地表现求解过程及所得结果。生产领域中的一些多阶段优化决策问题可以转化为最短路径问题,由所给出的算法实现来解决这些多阶段优化问题,可以一次求得各不同阶段内的最优策略。以求解设备更新问题和原料选用问题为例,显示了这一算法实现可以完全而简捷地解决多阶段优化决策问题的特点,是最短路算法在生产过程最优化领域的有效运用。     

Fault-tolerant routing over shortest node-disjoint paths in hypercubes

This paper presented a routing algorithm that finds n disjoint shortest paths from the source node s to target node d in the n-dimensional hypercube. Fault-tolerant routing over all shortest node-disjoint paths has been investigated to overcome the failure encountered during routing in hypercube networks. In this paper, we proposed an efficient approach to provide fault-tolerant routing which has been investigated on hypercube networks. The proposed approach is based on all shortest node-disjoint paths concept in order to find a fault-free shortest path among several paths provided. The proposed algorithm is a simple uniform distributed algorithm that can tolerate a large number of process failures, while delivering all n messages over optimal-length disjoint paths. However, no distributed algorithm uses acknowledgement messages (acks) for fault tolerance. So, for dealing the faults, acknowledgement messages (acks) are included in the proposed algorithm for routing messages over node-disjoint paths in a hypercube network.