多无人机协同规划的数学建模

针对第十三届全国研究生数学建模竞赛A题的多无人机协同规划问题展开研究.首先建立大路径和小路径的最短路径模型完成对十个目标群的扫描任务,其在雷达范围内航行总时间为10.37小时.然后建立实时自适应无人机作战模型针对未知远程雷达在不同情况下制定三级无人机作战策略,仿真结果显示:攻击方无人机滞留防御方雷达有效探测范围内的时间总和为8.81h.     

机器人避障问题

研究机器人在平面区域中绕过静态障碍物到达指定目的地的问题, 分别考虑了路程最短和时间最短两种目标下的最优路径, 给出了计算机自动搜索最优路径的模型和算法。     

基于客户满意度的车辆路径问题及蚁群算法求解北大核心

针对传统车辆路径问题片面强调行驶里程最短的弊端,引入客户满意度目标,提出了基于客户满意度的车辆路径问题数学模型,并通过线性加权将多目标模型转化为单目标.使用蚁群算法求解模型,并在蚂蚁状态转移中引入时间窗宽度因素,以优先考虑那些具有时间紧迫性的客户.对Solomon案例的实验仿真,结果表明了模型的合理性和算法的高效性.     

基于客户满意度的车辆路径问题及蚁群算法求解

针对传统车辆路径问题片面强调行驶里程最短的弊端,引入客户满意度目标,提出了基于客户满意度的车辆路径问题数学模型,并通过线性加权将多目标模型转化为单目标.使用蚁群算法求解模型,并在蚂蚁状态转移中引入时间窗宽度因素,以优先考虑那些具有时间紧迫性的客户.对Solomon案例的实验仿真,结果表明了模型的合理性和算法的高效性.     

m-aryn-cube网络的最优路由

基于可选邻接点的概念,在m-ary n-cube网络中提出一种新的最优寻径算法.这种算法始终在当前结点的可选邻接点中选取最空闲邻接点作为下一个信息传输点.该算法使得从源结点到达目的结点路由是最短路由也是最快速路由,而且在多项式时间内可以完成.     

多波次导弹发射任务策略优化

针对第十四届中国研究生数学建模竞赛E题的多波次导弹发射中的规划问题展开研究.首先,简化各道路节点路径信息后通过Dijkstra算法和模拟退火算法,制定了整体最短暴露时间对应的具体发射点位及机动路线方案,得到最短暴露时间127.7h;再采用穷举法及模拟退火制定合理布设两个转载地域以及确定最优隐蔽节点的策略;最后,在考虑规避敌方打击以及单个发射装置最大暴露时间最短等其他因素下,将多目标优化问题转化为单目标优化问题.     

一种基于Dijkstra算法的机器人避障问题路径规划

移动机器人的避障问题是移动机器人控制领域的研究热点.针对给定的移动机器人避障问题,探讨了最短路径及最短时间路径的路径规划问题.对于最短路径问题,建立了简化的路径网格模型,将其抽象为由节点及边构成的两维图,再使用经典的Dijkstra算法获得可行的最短路径.对于最短时间路径问题,通过分析移动机器人弯道运行的速度曲线,基于几何方法得出了移动时间与过渡圆弧圆心之间严格的数学关系,此后借助MATLAB优化函数获得最佳的移动路径.算法可为类似机器人避障问题的解决提供借鉴.     

航班登机口分配问题的数学建模

登机口作为机场的重要组成部分,其资源利用率直接影响航班服务的效率.针对不同的优先级建立多目标规划模型对航班进行优化分配,采用贪心算法和禁忌搜索算法,结合登机口类型、航班时间的约束,逐次对最大化分配航班问题、最小化中转旅客最短流程时间问题、最小化旅客总体紧张度问题进行建模求解.结果表明该算法不仅提升了求解速度,并且在航班登机口分配问题中展现了较好的综合寻优能力.这对民航机场实现经济效益、提高旅客满意度有一定的参考价值.     

铁路应急设施非概率可靠性选址优化研究

为解决小样本、贫信息下铁路应急资源储备点的可靠性选址问题,创新性地将选址-路径问题与区间非概率可靠性方法结合起来,考虑灾情发生后应急设施点在可接受的时间范围内响应受灾点的需求能力及其稳定程度,采用区间值度量路段阻抗,基于区间非概率可靠性理论及区间运算规则,提出路径的非概率可靠性度量及可靠最短路径选择方法;建立基于区间时间阻抗下可靠最短路径的无容量设施选址模型,提出约束条件限制的Monte Carlo改进算法,确定了铁路资源储备点选址的最优方案。实例表明,本文的优化方案能更好地保证救援的时间可靠性,改进的求解算法具有更小的时间复杂度,有效地缩短了运算时间,改善了解的质量。本文的方法与模型体系对于实现铁路应急设施可靠性选址,为决策者提供决策支持,提高铁路应急响应能力具有重要的指导意义。     

城市消防站点布局的改进启发式算法

面对数量较多需要及时处理的突发事故,为了满足最短应急时间限制,最低应急资源数和最少的出救点等目标,在城市规划决策中,考虑在一个确定应急限制期下的安全消防站选址问题,给出一个反映决策者对时间和费用偏好的折衷选址方案十分必要.从实际应用出发,运用改进启发式算法方法研究时间与资源限制条件下的多出救点组合模型求解问题.给出了应急限制期和安全消防设施点建立的费用模型,从理论上证明了模型求解方法的正确性.在给定限制期条件下,通过分析得出应急服务设施点选择方法.通过算例说明该计算方法的具体应用,为交通安全消防站点选择提供参考,该方法还适用于诸如医院急救站等类似公共设施的规划建设.     

关于建立物流网络可用性测度指标体系的研究

论文以保障应急行动的物流网络为研究对象,给出了物流网络可用性定义,提出了研究物流网络可用性指标体系的程序和原则,并系统划分了可用性指标研究的四层次结构,建立了物流网络可用性指标体系.该指标体系的建立对于研究应急物流网络的可用性具有重要的理论和现实意义.     

相异路径选择问题的模型与仿真结果研究

相异路径选线问题考虑的是,给定一运输网络的源宿接点,找出源宿节点之间在空间上有差异的路径,多个相异路径对于军事后勤供应,有害物品运输等在异常情况（如原来的最佳线路因气候等原因不可用）下的决策,具有重要意义。本着重对四种生成空间相异路径的算法进行了分析和评价,并构建了基于边的通道最短路的相异路径的算法,在此基础上,主要对IRM,GSP和EGSP给出了仿真实验计算结果,通过对结果的分析,找到了影响结果的几个关键因素。     

Ranking paths in stochastic time-dependent networks

In this paper we address optimal routing problems in networks where travel times are both stochastic and time-dependent. In these networks, the best route choice is not necessarily a path, but rather a time-adaptive strategy that assigns successors to nodes as a function of time. Nevertheless, in some particular cases an origin–destination path must be chosen a priori, since time-adaptive choices are not allowed. Unfortunately, finding the a priori shortest path is an NP-hard problem.     

Modeling a supply chain using a network of queues

In this paper, a supply chain is represented as a two-input, three-stage queuing network. An input order to the supply chain is represented by two stochastic variables, one for the occurrence time and the other for the quantity of items to be delivered in each order. The objective of this paper is to compute the minimum response time for the delivery of items to the final destination along the three stages of the network. The average number of items that can be delivered with this minimum response time constitute the optimum capacity of the queuing network. After getting serviced by the last node (a queue and its server) in each stage of the queuing network, a decision is made to route the items to the appropriate node in the next stage which can produce the least response time.     

Time analysis for planning a path in a time-window network

A systematic method is proposed to generate time information on the paths and nodes on a time-window network for planning and selecting a path under a constraint on the latest entering time at the destination node. Specifically, three algorithms are proposed to generate six basic time characteristics of the nodes, including the earliest and latest times of arriving at, entering, and departing from each node on the network. Using the basic time characteristics, we identify inaccessible nodes that cannot be included in a feasible path and evaluate the accessible nodes’ flexibilities in the waiting time and staying time. We also propose a method for measuring adverse effects of including an arc. Finally, based on the time characteristics and the proposed analyses, we develop an algorithm that can find the most flexible path in a time-window network.     

Many Sources Asymptotics for Networks with Small Buffers

In this paper, we obtain the overflow asymptotics in a network with small buffers when the resources are accessed by a large number of stationary independent sources. Under the assumption that the network is loop-free with respect to source–destination routes, we identify the precise large deviations rate functions for the buffer overflow at each node in terms of the external input characteristics. It is assumed that each type of source requires a Quality of Service (QoS) defined by bounds on the fraction of offered work lost. We then obtain the admissible region for sources which access the network based on these QoS requirements. When all the sources require the same QoS, we show that the admissible region asymptotically corresponds to that which is obtained by assuming that flows pass through each node unchanged.     

The maximin HAZMAT routing problem

The hazardous material routing problem from an origin to a destination in an urban area is addressed. We maximise the distance between the route and its closest vulnerable centre, weighted by the centre’s population. A vulnerable centre is a school, hospital, senior citizens’ residence or the like, concentrating a high population or one that is particularly vulnerable or difficult to evacuate in a short time. The potential consequences on the most exposed centre are thus minimized. Though previously studied in a continuous space, the problem is formulated here over a transport (road) network. We present an exact model for the problem, in which we manage to significantly reduce the required variables, as well as an optimal polynomial time heuristic. The integer programming formulation and the heuristic are tested in a real-world case study set in the transport network in the city of Santiago, Chile.     

On the enrouting protocol problem under uncertainty

In this paper we present a two-stage stochastic mixed 0–1 dynamic multicommodity model and algorithm for determining the enrouting protocol in the telecommunications network under uncertainty. Given the network connectivity, node processing and buffer and arc flow capacity, the aim is to determine the outgoing arc for the information flow reaching a given node for each destination terminal node (i.e., obtaining the route to be followed by the information flow from each origin terminal node to each destination terminal node). The origin–destination (O–D) flow matrix is given by the number of information packets to be sent from the origin terminal nodes to the destination terminal nodes along a given time horizon, i.e., a call scale. The uncertainty in the O–D flow matrix is treated via a scenario tree approach. The main goal is to minimize a composite function of the expected lost information, a penalization of the deviation from the FIFO strategy on the information flow entering the network, and the expected number of nodes visited by the information packets. A mixture of an enrouting arc generation scheme and a genetic algorithm for obtaining the enrouting protocols over the scenarios is presented. The tool presented in this paper could be used for simulating the enrouting protocols to analyze the saturation of the network, but it has a time constraint for real time operation. Faster algorithms are needed to define the routing tables during the operation stage. Computational experience is reported.     

Dynamic journeying under uncertainty

We introduce a journey planning problem in multi-modal transportation networks under uncertainty. The goal is to find a journey, possibly involving transfers between different transport services, from a given origin to a given destination within a specified time horizon. Due to uncertainty in travel times, the arrival times of transport services at public transport stops are modeled as random variables. If a transfer between two services is rendered unsuccessful, the commuter has to reconsider the remaining path to the destination. The problem is modeled as a Markov decision process in which states are defined as paths in the transport network. The main contribution is a backward induction method that generates an optimal policy for traversing the public transport network in terms of maximizing the probability of reaching the destination in time. By assuming history independence and independence of successful transfers between services we obtain approximate methods for the same problem. Analysis and numerical experiments suggest that while solving the path dependent model requires the enumeration of all paths from the origin to the destination, the proposed approximations may be useful for practical purposes due to their computational simplicity. In addition to on-time arrival probability, we show how travel and overdue costs can be taken into account, making the model applicable to freight transportation problems.     

Network deployment of radiation detectors with?physics-based detection probability calculations

We describe a model for deploying radiation detectors on a transportation network consisting of two adversaries: a nuclear-material smuggler and an interdictor. The interdictor first installs the detectors. These installations are transparent to the smuggler, and are made under an uncertain threat scenario, which specifies the smuggler??s origin and destination, the nature of the material being smuggled, the manner in which it is shielded, and the mechanism by which the smuggler selects a route. The interdictor??s goal is to minimize the probability the smuggler evades detection. The performance of the detection equipment depends on the material being sensed, geometric attenuation, shielding, cargo and container type, background, time allotted for sensing and a number of other factors. Using a stochastic radiation transport code (MCNPX), we estimate detection probabilities for a specific set of such parameters, and inform the interdiction model with these estimates.