基于规则的最短路径查询算法

最短路径查询是图数据管理中非常重要的一类问题.研究了基于规则的最短路径查询,它是一类特殊的最短路径查询问题.给定起点和终点,基于规则的最短路径查询是指找到一条从起点到终点的最短路径,使得此路径经过用户指定点集中的所有点,并且某些点的访问顺序满足一定的偏序规则.该问题被证明是一个NP-hard问题.目前已有的工作侧重于空间数据集（两点之间的最短距离用欧氏距离表示）上基于规则的最短路径问题,它采用穷举的方式列出所有满足规则的路径,然后选择长度最小的路径作为问题的解.然而在实际的道路交通网中,两点之间的距离等于两点之间的最短路径的长度,它往往大于两点之间的欧氏距离;此外,采用穷举的方式会造成大量重复的计算.因此,设计了一种前向搜索算法以及一些优化技术来求解该问题.最后,在不同的真实数据集上设计了大量的实验来验证算法的有效性.实验结果表明,该算法可以快速给出问题的解,而且算法的效率在很大程度上超过了现有的算法.     

最短路径动态规划问题及C语言实现探讨

动态规划算法是一种研究多阶段决策问题的算法.用动态规划方法求最短路问题,要求所求问题具有明显的阶段。该文以动态规划理论为指导,研究了动态规划算法求解最短路径的基本原理及步骤,编写了基于动态规划算法的C语言程序,辅助完成最短路径的求解。     

基于改进型遗传算法的动态避障路径规划方法

针对遗传算法易陷入局部最优的不足,在标准遗传算法基础上加入了三个新的操作-复原、重构和录优操作,使改进后的遗传算法收敛于全局最优,并在此基础上以路边约束、动态避障和路径最短作为适应度函数,提出了动态避障的路径规划方法.通过实验仿真验证了算法的有效性、准确性和实时性,并与基于以往的遗传算法的路径规划方法进行比较,结果表明本文提出的方法在产生的路径长度和算法运行时间上都具有更优的性能.     

多维代价图模型上最优路径查询问题的研究

近年来,图数据模型被广泛地用于刻画现实世界中各种各样的实体间的复杂关系.最短路径查询是图研究领域中一类非常重要的查询并有着广泛的应用.然而,目前大多数关于最短路径的查询都是定义在单代价(权重)图模型下的.现实世界中,基于单一代价所选择的最短路径并不明智,比如路程最短的路径需要花费极高的费用.该文中,作者介绍了多维代价图模型的概念,并给出了多维代价图模型下基于函数的最优路径的定义.现有的计算最短路径的方法都利用了最短路径的子路径最优的性质:最短路径上的任意两点间的子路径是这两点的最短路径.因此,在计算最短路径的过程中,对访问过的每个顶点,只需保留起点到该点的最短路径即可.不幸的是,多维代价图模型下,当评分函数是非线性的时候,子路径最优的性质并不成立.因此,目前的方法均不能应用于多维代价图模型下基于函数的最优路径查询问题.该文给出了一个best-first search分支界限法并给出3种优化策略.进一步,给出了一个顶点过滤算法,该算法能从图中过滤掉大部分不属于最优路径的顶点.最后,用真实数据集上的实验验证了算法的有效性.     

异质信息环境下基于案例推理的应急决策方法

针对在突发事件应急决策中,信息表述为精确数、区间数、语言术语、直觉模糊数、中智数、梯形模糊中智数等多样性的特点,同时鉴于案例推理方法的简单易用,提出一种异质信息环境下基于案例推理的应急决策方法.首先,引入异质数据的距离及相似度测度,并基于偏差最大化方法计算异质信息属性权重;然后,基于综合相似度测度,采用案例推理的方法从案例库中找到与目标案例相同或者相似的历史案例,从而获得有效的解决当前突发事件的应急预案和处理措施;最后,通过一个应急突发事件案例验证所提出决策方法的可行性和有效性,同时与其他方法相比较验证其优点.     

神经网络求解图最短路径问题的一种新方法*

本文给出一种求解图最短路径问题的实用反馈式神经网络，并证明这种网络的求解稳定性．这种网络基于最小值选择网而构成，对任意有向图和无向图均能收敛到其唯一的稳定点．由此求得图所有顶点对阃的最短路径及最短路径长度．本文结果是神经网络求解非NP—难解类优化问题的一种新尝试．     

神经网络求解图最短路径问题的一种新方法

本文给出一种求解图最短路径问题的实用反馈式神经网络，并证明这两种网络的求解稳定性，这种网络基于最小值选择网而构成，对任意有向图和无向图均能收敛到其唯一的稳定点，由此求得图所有顶点对间的最短路径及最短路径长度，本文结果是神经网络求解非ＮＰ－骓难解类优化问题的一种新尝试。     

基于维诺图和二分图的水面移动基站路径规划方法

水面传感器网络（Surface sensor networks,SSNs）具有节点稀疏布置的特点（节点间距离通常大于节点通信半径）,因此难以通过节点间的多跳路由汇聚数据,目前主要采用移动基站（Mobile sink,MS）收集网络中的数据,其中移动基站的路径规划是一个关键问题.该文提出一种基于维诺图和二分图的水面移动基站路径规划方法,首先利用维诺图理论生成数据收集“候选点”;然后以二分图描述候选点对网络中传感器节点的支配关系,并基于支配集理论求解出“最小有效支配集”,即可以收集网络中所有节点数据的最小的候选点集合;最后针对最小有效支配集形成最优路径.大量实验结果表明该方法可以有效地规划出水面传感器网络中移动基站的路径,不仅可以完成全网数据收集任务,而且具有路径长度短、能量效率高和节点能耗均衡的优点.     

一种并行模糊神经网络最短路径算法

给出了模糊网络期望最短路径问题的定义,提出一种并行模糊神经网络最短路径（PFNNSP）算法解决模糊网络最短路径问题。PFNNSP算法首先通过模糊模拟对网络中的边权进行估计,接下来脉冲波在神经元之间的并行传播,相互激活搜寻任意一对结点之间的最短路径,最后,算法回溯输出路径表示和路径长度。在随机生成的小规模数据集上的仿真实验表明,PFNNSP算法在边权服从三角模糊分布的网络中执行时间优于Dijkstra算法,在大规模路网信息数据集上的仿真实验表明,PFNNSP算法能够有效求解网络中的最短路径,并且算法在迭代次数和收敛速度上要优于Dijkstra算法和A*搜索算法。     

道路转向延迟的动态对偶图模型

传统的道路转向延迟对偶图表达法缺乏对交通网络时间依赖特性的考虑,不适合动态路径规划问题的求解。本文将时间因素引入到对偶图中,发展了一种动态对偶图模型,将交通路网表达为动态对偶网络,并为之定义了FIFO(先进先出）条件,推导了满足FIFO条件的动态行程计算方法,设计了时间依赖的标号设定最短路径算法。实验结果表明,利用该对偶图模型和动态对偶网络,能有效表达路网转向延迟,在以出行时间为标准的动态路径规划中,基于动态对偶网络的路径规划结果可节省约16%的出行时间。     

A dynamic programming approach for finding shortest chains in a fuzzy network

Graph theory has numerous applications to problems in systems analysis, operations research, transportation, and economics. In many cases, however, some aspects of a graph-theoretic problem may be uncertain. For example, the vehicle travel time or vehicle capacity on a road network may not be known exactly. In such cases, it is natural to make use of fuzzy set theory to deal with the uncertainty. Here, we are concerned with finding shortest chains in a graph with fuzzy distance for every edge. We propose a dynamic programming approach to solve the fuzzy shortest chain problem using a suitable ranking method. By using MATLAB, two illustrative examples are worked out to demonstrate the proposed algorithm.     

Excel求解最短路径问题

许多实际应用问题都与最短路径相关,解决最短路径问题通常采用图论与计算机技术结合的方法,使用Excel的工作表和自定义宏函数,采用Dijkstra算法和链表动态数据结构解决最短路径问题,并在Excel的VBA环境编程运行。     

The fuzzy shortest path length and the corresponding shortest path in a network

The fuzzy shortest path (SP) problem aims at providing decision makers with the fuzzy shortest path length (FSPL) and the SP in a network with fuzzy arc lengths. In this paper, each arc length is represented as a triangular fuzzy set and a new algorithm is proposed to deal with the fuzzy SP problem. First, we proposed a heuristic procedure to find the FSPL among all possible paths in a network. It is based on the idea that a crisp number is a minimum number if and only if any other number is larger than or equal to it. It owns a firm theoretic base in fuzzy sets theory and can be implemented effectively. Second, we propose a way to measure the similarity degree between the FSPL and each fuzzy path lengths. The path with the highest similarity degree is the SP. An illustrative example is given to demonstrate our proposed approach.     

An integrated fuzzy-lp approach for a supplier selection problem in supply chain management

In supply chain management process, the firm select best supplier takes the competitive advantage to other companies. Thus, supplier selection is an important issue and with the multiple criteria decision-making approach, the supplier selection problem includes both tangible and intangible factors. This paper is aimed to present an integrated fuzzy and linear programming approach to the problem. Firstly, linguistic values expressed in trapezoidal fuzzy numbers are applied to assess weights and ratings of supplier selection criteria. Then a hierarchy multiple model based on fuzzy set theory is expressed and fuzzy positive and negative ideal solutions are used to find each supplier’s closeness coefficient. Finally, a linear programming model based on the coefficients of suppliers, buyer’s budgeting, suppliers’ quality and capacity constraints is developed and order quantities assigned to each supplier according to the linear programming model. The integrated model is illustrated by an example in a textile firm.     

最短路径模型下的双目立体匹配算法研究

传统的双目立体匹配算法,是通过计算像素点间的相似程度来找出左图像素点和右图像素点的匹配关系。为了提高匹配准确度,当前策略主要是将立体匹配转化为求解能量方程最小化问题,再对全局空间的能量进行优化,如扫描线算法、动态规划算法、图割算法和置信传播算法。然而各个算法有着自身不足,若仅仅从原有的模型出发,难以克服缺点。通过对能量方程最小化问题深入研究,建立了一个最短路径模型,即将能量方程映射到有向图中,通过求解图的最短路径来解能量方程的最小化问题,详细阐述了算法原理后又从视差空间的角度描述了算法的运行图。实验证明最短路径算法克服了上述四种方法的固有缺陷,在准确度较高的同时,有较低的时间复杂度。     

Optimal route selection based on Monte Carlo method and adaptive amoeba algorithm under uncertain environment

The fuzzy optimal path under uncertainty is one of the basic network optimization problems. Considering the uncertain environment, many fuzzy numbers are used to represent the edge weights, such as interval number and triangular fuzzy number. Then, these fuzzy numbers are converted to real numbers directly. This converting makes the optimal path the shortest path selection problem. However, much information of uncertainty get lost when converting fuzzy numbers to real numbers. In order to ensure all the origan data complete, in this paper, a fuzzy optimal path solving model based on the Monte Carlo method and adaptive amoeba algorithm is proposed. In Monte Carlo process, a random number which belongs to the fuzzy number is generated. Then, Physarum polycephalum algorithm is used to solve the shortest path every time and record the result. After many times calculation, many shortest paths have been found and recorded. At last, by analysing the characters of all the results, the optimal path can be selected. Several numerical examples are given to illustrate the effectiveness of the proposed method, the results show that the proposed method can deal with the fuzzy optimal path problems effectively.     

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。     

Fuzzy heterogeneous multiattribute decision making method for outsourcing provider selection

One of the critical activities for outsourcing success is outsourcing provider selection, which may be regarded as a type of fuzzy heterogeneous multiattribute decision making (MADM) problems with fuzzy truth degrees and incomplete weight information. The aim of this paper is to develop a new fuzzy linear programming method for solving such MADM problems. In this method, the decision maker’s preferences are given through pair-wise alternatives’ comparisons with fuzzy truth degrees, which are expressed with trapezoidal fuzzy numbers (TrFNs). Real numbers, intervals, and TrFNs are used to express heterogeneous decision information. Giving the fuzzy positive and negative ideal solutions, we define TrFN-type fuzzy consistency and inconsistency indices based on the concept of the relative closeness degrees. The attribute weights are estimated through constructing a new fuzzy linear programming model, which is solved by using the developed fuzzy linear programming method with TrFNs. The relative closeness degrees of alternatives can be calculated to generate their ranking order. An example of the IT outsourcing provider selection problem is analyzed to demonstrate the implementation process and applicability of the method proposed in this paper.     

Decomposition's Dantzig–Wolfe applied to fuzzy multicommodity flow problems

We present, in this paper, a method for solving linear programming problems with fuzzy costs based on the classical method of decomposition's Dantzig–Wolfe. Methods using decomposition techniques address problems that have a special structure in the set of constraints. An example of such a problem that has this structure is the fuzzy multicommodity flow problem. This problem can be modeled by a graph whose nodes represent points of supply, demand and passage of commodities, which travel on the arcs of the network. The objective is to determine the flow of each commodity on the arcs, in order to meet demand at minimal cost while respecting the capacity constraints of the arcs and the flow conservation constraints of the nodes. Using the theory of fuzzy sets, the proposed method aims to find the optimal solution, working with the problem in the fuzzy form during the resolution procedure.