基于最小费用最大流问题的“排序”算法

由于现有的求解最小费用最大流问题的方法都存在其局限性,为了更好地解决实际问题,在已有最短路算法以及最小费用算法的基础上作了改进,给出了一种求解基于最大流的最小费用问题的算法.文中针对小规模网络给出求两点之间最小费用的一种简单易行的方法,此外该算法可以在一个图上完成,这样可以节省许多画图时间,增强了算法的直观性和可控性.并且构建石油运输的网络模型,结合最小费用最大流算法,给出该模型从产地到销地的最优运输方案,最后通过具体的模型实例验证了该方法的效率和实用性.     

点和边有容量约束的网络最小费用最大流算法*

分析了目前网络最小费用最大流算法存在的问题,提出网络最小费用最大流新算法。概括出条件约束下的网络最小费用最大流问题的两目标优化数学模型,针对点和边有容量约束的网络最小费用最大流问题特点,定义了有向路径、有向路径单位流费用和残量网络的概念。依据可行流分解定理,以邻接矩阵为网络数据存储结构,使用数据结构中的遍历方法,实现了网络最小费用最大流新算法。该算法在不破坏平面性条件下,可以求解点和边有容量约束的网络最小费用最大流。最后,通过实例进行了算法测试和比较。算法测试表明：点和边有容量约束的网络最小费用最大流算法是完全可行和有效的。     

求解最小费用最大流的新方法

文中给出了一种求解网络最小费用最大流的新方法,寻找由始点到终点的每条有向链,找到有向链可通过的最大容量,根据最大容量计算出此条有向链的最小费用最大流,根据最大容量和最小费用最大流可以计算出单位费用.选取单位费用最小的有向链进行最大容量的增广.文中通过对最小费用路算法进行改进,使得该算法容易理解,却又避免了最小费用路算法每次都要经过剩余网络进行增广,从而大大提高了求解最小费用最大流执行的效率.该算法通过实例给出了具体算法步骤并且表明了算法的实用性     

最小费用最大流问题的一种新算法

现有的最小费用最大流算法都有自身的缺陷,增广链的选取不当会给计算带来不便,同时费用也达不到理想的效果。鉴于对最小费用最大流算法的增广链选取和最小费用的探索,文章通过对费用差的定义给出了一种求最小费用最大流的新算法。新算法的原则是优先选择费用差最小的有向路径进行增广,当费用差相同时就选择修正后的路径。通过对最小费用最大流算法的改进,新算法易理解且便于计算。通过实例说明了新算法的有效性和执行效率。     

最小费用最大流算法(C++)实现

最小费用最大流是一类网络优化问题,它与最大流的区别在于,它不仅要考虑流量问题,还要考虑费用因素,其优化的目标是流量最大且费用最小。本文综合求最大流原理和求最短路原理,在直接输入初始状态下就求出任何一个网络图的最小费用值,最大流值以及其他一些相关数据。该算法程序可以为我们减少大量计算,提高工作效率,因而它在信息学竞赛,国际信息学竞赛,大学生数学建模比赛等方面都能得到应用。     

求解最小费用最大流问题的信念传播算法

最小费用最大流问题是一种组合优化问题,在经济、工业等领域具有重要研究意义和应用价值.针对部分最小费用最大流问题求解算法效率较低的情况,依据最小费用最大流问题的线性规划方程,将问题模型映射为对应因子图模型,改进描述函数,给出迭代方程,设计了求解最小费用最大流问题的信念传播算法.利用迭代方程优先对最大可行流特征值进行收敛计算,得到最大流,设置最大流阈值,在此基础上进行最小费用计算,从而求得问题最优解.最后选取若干带权有向图模型进行数值实验,验证了算法的可行性及有效性,且算法在求解效率上优于部分算法.     

最小费用最大流算法（C＋＋）实现

最小费用最大流是一类网络优化问题，它与最大流的区别在于，它不仅要考虑流量问题，还要考虑费用因素，其优化的目标是流量最大且费用最小。本文综合求最大流原理和求最短路原理，在直接输入初始状态下就求出任何一个网络图的最小费用值。最大流值以及其他一些相关数据。该算法程序可以为我们减少大量计算，提高工作效率，因而它在信息学竞赛，国际信息学竞赛，大学生数学建模比赛等方面都能得到应用。     

一种基于改进堆优化Dijkstra算法的最小费用最大流算法

通过最短路径算法在残存网络中搜索汇点的最小费用路径是流网络中求解最小费用最大流的主要方式,而Dijkstra算法是最高效的最短路径算法之一。本文通过证明残存网络中不存在负循环,采用改进的堆优化Dijkstra算法在残存网络中搜索最小费用路径以提升算法的效率。实验结果表明,与经典的基于最短路径快速算法的最小费用最大流算法和基于Bellman-Ford算法的最小费用最大流算法对比,本文提出的改进算法具有更高的时间效率。     

网络优化的最大利润问题及其增广路算法

仿照最小费用最大流问题的物理意义,将网络上的费用参数转化成为一种利润参数,提出一个最大利润流问题,并建立了该问题的数学规划模型;给出一个求解该问题的最大利润增广路算法,该算法能快速有效地求得该问题的最优解及目标函数值。用示例对算法的求解过程进行了演示,结果表明该算法比一般的线性规划方法更加的方便,且直观得多。     

最小费用最大流新解尝试

最小费用最大流是有向图中常见的问题,一般的解法是从已给出的初始流量构造增广链,逐步得到最大流。最小元素法是运输问题初始方案的构造方法之一,仿照这种方法构造出来的最小费用最大流问题的＂最小元素法＂,并且对于比较简单的有向图求解最小费用最大流问题,容易得到最优解。     

Finding minimum and equitable risk routes for hazmat shipments

This paper deals with the generation of minimal risk paths for the road transportation of hazardous materials between an origin–destination pair of a given regional area. The main considered issue is the selection of paths that minimize the total risk of hazmat shipments while spreading the risk induced on the population in an equitable way. The problem is mathematically formulated, and two heuristic algorithms are proposed for its solution. Substantially, these procedures are modified versions of Yen's algorithm for the k-shortest path problem, which take into due consideration the risk propagation resulting from close paths and spread the risk equitably among zones of the geographical region in which the transportation network is embedded. Furthermore, a lower bound based on a Lagrangean relaxation of the given mathematical formulation is also provided. Finally, a series of computational tests, referring to a regional area is reported.     

一种求解最少时间最小费用路问题的算法

针对同时带有弧费用和弧时间的运输网络中最少时间最小费用路的问题,本文提出了一种算法。该算法能高效地求出此类网络中从源节点到目的节点的双目标最短路（最少时间最小费用路）。实例计算表明,该算法是有效的。     

Applying genetic algorithm to a new bi-objective stochastic model for transportation,location, and allocation of hazardous materials

In 2013, approximately 15,600 HAZMAT accidents with 158 injuries and fatalities have been reported in the USA (“Transportation Statistics Bureau”). Managing hazardous material (HAZMAT) transportation and locating the disposal sites for these materials properly can significantly reduce the risk of accidents and its environmental and social aspects. In this research, a new stochastic model for transportation, location, and allocation of hazardous materials is proposed. The cost of transportation is considered to be of a stochastic nature. The objective function minimizes the total cost and risk of locating facilities and transportation of HAZMATs. The decisions which have to be made are: (1) where to open the facilities and disposal sites; (2) to which facilities every customer should be assigned; (3) to which disposal site each facility should be assigned; and (4) which routes a facility should choose to reach the customers and disposal sites. A novel genetic algorithm (GA) is applied to the model. The results show the efficiency of the proposed GA in terms of finding high quality solutions in a short time.     

最少时间最小费用路问题的修改Dijkstra算法

针对同时带有顶点权和弧权的运输网络的最少时间最小费用路问题,首先将该网络转化为一般的只带弧权的运输网络,然后设计了求解该类问题的修改的“带前点标号的Dijkstra算法”,最后给出在物资公路运输中的一个实例。     

Robust Facility Location Problem for Hazardous Waste Transportation

We consider a robust facility location problem for hazardous materials (hazmat) transportation considering routing decisions of hazmat carriers. Given a network and a known set of nodes from which hazmat originate, we compute the locations of hazmat processing sites (e.g. incinerators) which will minimize total cost, in terms of fixed facility cost, transportation cost, and exposure risk. We assume that hazmat will be taken to the closest existing processing site. We present an exact full enumeration method, which is useful for small or medium-size problems. For larger problems, the use of a genetic algorithm is explored. Through numerical experiments, we discuss the impact of uncertainty and robust optimization in the hazmat combined location-routing problem.     

Application of a quantitative risk assessment method to emergency response planning

Transportation-related hazardous materials releases pose obvious hazards to the general public and response personnel. Statistical risk assessment techniques are valuable in quantifying these hazards and evaluating methods to reduce the risk. In this paper, we describe a quantitative risk assessment approach for hazardous materials transportation that has a strong emphasis on consequence modeling and employs considerable statistical data from past incidents. We illustrate application of this method to evaluating distances to which the public should be protected immediately following an accidental release of toxic materials that pose an inhalation hazard. While this paper focuses on emergency response aspects of the problem, the framework we describe has applications to societal risk estimation and routing optimization for a wide variety of hazardous materials.     

Fuzzy multi-objective chance-constrained programming model for hazardous materials transportation

Hazardous materials transportation is an important and hot issue of public safety. Based on the shortest path model, this paper presents a fuzzy multi-objective programming model that minimizes the transportation risk to life, travel time and fuel consumption. First, we present the risk model, travel time model and fuel consumption model. Furthermore, we formulate a chance-constrained programming model within the framework of credibility theory, in which the lengths of arcs in the transportation network are assumed to be fuzzy variables. A hybrid intelligent algorithm integrating fuzzy simulation and genetic algorithm is designed for finding a satisfactory solution. Finally, some numerical examples are given to demonstrate the efficiency of the proposed model and algorithm.     

多目标多时间窗车辆路径问题的鸽群-水滴算法

针对智能水滴算法求解带时间窗车辆路径规划收敛速度慢、计算精度差的问题,根据带时间窗车辆路径问题的应用要求,利用整数线性规划方法,以配送车辆的最小运输总成本、最短运输距离和最少安排数量为目标,综合考虑了车辆出发点、服务点、装载量、行驶距离、服务时间窗等诸多约束条件,构建了多目标多时间窗车辆路径模型;为了精准快速求解多目标多时间窗车辆路径模型,提出一种鸽群-智能水滴互补改进优化算法,将河道水滴离散二进制变换后,采用地图罗盘算子和地标算子分别改进水滴的流动速度和方向,并利用自适应变邻域扰动策略干扰水滴携带的泥土量,提高水滴算法的开发和探索能力;利用理想点法和罚函数与多目标优化混合方法分别处理多目标函数与约束条件,并以两种经典的带时间窗车辆路径问题为实例,通过与遗传算法、智能水滴算法和鸽群-水滴算法的计算结果进行比较,结果表明：在相同的算法参数和经济指标下,鸽群-水滴算法相比于智能水滴算法求解模型中的运输路径缩短20 km左右、运输成本节约403元左右,且该算法的求解时间和迭代次数也明显优于其他两种人工智能算法。     

多配送中心危险货物配送路径鲁棒优化

针对危险货物配送路径对不确定因素敏感度较高的问题,提出了鲁棒性可调的多配送中心危险货物配送路径鲁棒优化方法。首先,以最小化运输风险和最小化运输成本为目标,根据Bertsimas鲁棒离散优化理论,建立鲁棒优化模型;然后,在改进型强度Pareto进化算法（SPEA2）的基础上设计一种三段式编码的多目标遗传算法进行求解,在遗传操作中对不同染色体段分别采用不同的交叉和变异操作,有效避免了种群进化过程中不可行解的产生;最后,以庆阳市西峰区部分路网为例进行实证研究,并将配送方案落实到运输过程的路段中,形成具体的运输路径。研究结果表明：在多配送中心下,运用该鲁棒优化模型及算法,能快速得到具有较好鲁棒性的危险货物配送路径。