Simple paths with exact and forbidden lengths

We study new decision and optimization problems of finding a simple path between two given vertices in an arc weighted directed multigraph such that the path length is equal to a given number or it does not fall into the given forbidden intervals (gaps). A fairly complete computational complexity classification is provided and exact and approximation algorithms are suggested.     

基于最短拦截时间的异面拦截机动轨道设计与优化

本文构建了单脉冲机动在燃耗约束下的最短时间拦截轨道设计模型与求解方法,将用数学泛函求边值问题转换为高次代数方程的求解计算,并用牛顿迭代法进行快速寻根,仿真结果表明模型及算法准确、有效,满足精度要求。     

分段线性凸费用网络流的两个算法

本文讨论了分段线性凸费用网络流问题,推广了线性费用网络流中的负回路方法和最小费用路方法,从而得到了求分段线性凸费用网络的最小费用流的两个算法。     

Solution algorithms for the parallel replacement problem under economy of scale

We consider the parallel replacement problem in which machine investment costs exhibit economy of scale which is modeled through associating both fixed and variable costs with machine investment costs. Both finite- and infinite-horizon cases are investigated. Under the three assumptions made in the literature on the problem parameters, we show that the finite-horizon problem with time-varying parameters is equivalent to a shortest path problem and hence can be solved very efficiently, and give a very simple and fast algorithm for the infinite-horizon problem with time-invariant parameters. For the general finite-horizon problem without any assumption on the problem parameters, we formulate it as a zero-one integer program and propose an algorithm for solving it exactly based on Benders' decomposition. Computational results show that this solution algorithm is efficient, i.e., it is capable of solving large scale problems within a reasonable cpu time, and robust, i.e., the number of iterations needed to solve a problem does not increase quickly with the problem size. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 279–295, 1998     

Robust shortest path planning and semicontractive dynamic programming

In this article, we consider shortest path problems in a directed graph where the transitions between nodes are subject to uncertainty. We use a minimax formulation, where the objective is to guarantee that a special destination state is reached with a minimum cost path under the worst possible instance of the uncertainty. Problems of this type arise, among others, in planning and pursuit‐evasion contexts, and in model predictive control. Our analysis makes use of the recently developed theory of abstract semicontractive dynamic programming models. We investigate questions of existence and uniqueness of solution of the optimality equation, existence of optimal paths, and the validity of various algorithms patterned after the classical methods of value and policy iteration, as well as a Dijkstra‐like algorithm for problems with nonnegative arc lengths.© 2016 Wiley Periodicals, Inc. Naval Research Logistics 66:15–37, 2019     

通信受限下分布式多传感器协同跟踪算法

在分布式多传感器目标跟踪系统中,由于局部融合中心(LFC)的物理限制(如:有限的频率信道、处理器容量有限等),只能接收有限个传感器的传送数据。此外,信息传输的方式也将影响传感网的使用寿命,因此,研究了通信受限下的分布式多传感器目标协同跟踪问题。首先对监视区内分布的传感器进行聚类分簇形成若干个子网,接着从通信能耗的角度出发,对传感器采集信息的传递路径进行最优路径规划;进而对子网局部状态进行估计,在子网信息融合中,分别采用最大距离和、最大化信息增量两种准则进行最佳传感器选择,最后通过各子网全局航迹融合实现分布式多传感器协同跟踪。仿真验证了算法的有效性。     

基于k短路径的兵力机动路线优化方法

由于传统Dijkstra算法只能求解最优路径,结合兵力机动路线选择的需要,将求解k短路径的实用算法引入到兵力机动路线优化问题中,给出了算法的数据结构和步骤。在道路权重的确定上,提出将路程、通行能力和安全性三项指标相结合的思想,并给出了综合权重的计算方法。仿真实验表明所提方法具有较强的实用性。     

图论最短路径问题在消防选址中的应用

最短路径问题是图论解决的典型实际问题之一,可用来解决管路铺设、线路安装、厂区布局和设备更新等实际问题。介绍了图论最短路径问题及其算法,并应用图论最短路径问题的分析方法,解决城市消防站的选址问题。     

时变道路网最短路径算法的研究

道路或区域通行限制在日常交通和部队兵力机动过程中普遍存在。通行限制情况下的最短路径问题属于时变道路网最短路径研究的范畴,对时变道路网最短路径算法及算法效率的研究有着广泛而现实的意义。重点讨论了道路网的模型描述、时变道路网拓扑结构的构建技术,最短路径算法的高效实现等内容,并给出了该算法的应用实例。试验结果显示,该算法有效可行。     

Robust shortest path problems with two uncertain multiplicative cost coefficients

We consider a robust shortest path problem when the cost coefficient is the product of two uncertain factors. We first show that the robust problem can be solved in polynomial time by a dual‐variable enumeration with shortest path problems as subproblems. We also propose a path enumeration approach using a K ‐shortest paths finding algorithm that may be efficient in many real cases. An application in hazardous materials transportation is discussed, and the solution methods are illustrated by numerical examples. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013