On efficient algorithms for finding efficient salvo policies

We consider the salvo policy problem, in which there are k moments, called salvos, at which we can fire multiple missiles simultaneously at an incoming object. Each salvo is characterized by a probability p_i: the hit probability of a single missile. After each salvo, we can assess whether the incoming object is still active. If it is, we fire the missiles assigned to the next salvo. In the salvo policy problem, the goal is to assign at most n missiles to salvos in order to minimize the expected number of missiles used. We consider three problem versions. In Gould's version, we have to assign all n missiles to salvos. In the Big Bomb version, a cost of B is incurred when all salvo's are unsuccessful. Finally, we consider the Quota version in which the kill probability should exceed some quota Q. We discuss the computational complexity and the approximability of these problem versions. In particular, we show that Gould's version and the Big Bomb version admit pseudopolynomial time exact algorithms and fully polynomial time approximation schemes. We also present an iterative approximation algorithm for the Quota version, and show that a related problem is NP-complete.     

基于数据压缩的LSP参数高效量化算法

文中为解决超长帧编码系统中联合帧数过多导致LSP参数量化性能下降这个问题,将多项式拟合引入超长帧编码系统中,利用多项式拟合压缩LSP参数矩阵,以降低量化时实际联合的帧数。再用分裂矩阵量化器进行量化。仿真结果表明,在120 bps的参数量化速率下,此算法的量化性能优于矩阵量化算法(MQ),平均谱失真比MQ算法降低了0.0719 dB,平均分段信噪比提高了0.1971 dB。     

Approximation results for min‐max path cover problems in vehicle routing

This article studies a min‐max path cover problem, which is to determine a set of paths for k capacitated vehicles to service all the customers in a given weighted graph so that the largest path cost is minimized. The problem has wide applications in vehicle routing, especially when the minimization of the latest service completion time is a critical performance measure. We have analyzed four typical variants of this problem, where the vehicles have either unlimited or limited capacities, and they start from either a given depot or any depot of a given depot set. We have developed approximation algorithms for these four variants, which achieve approximation ratios of max{3 ‐ 2/k,2}, 5, max{5 ‐ 2/k,4}, and 7, respectively. We have also analyzed the approximation hardness of these variants by showing that, unless P = NP , it is impossible for them to achieve approximation ratios less than 4/3, 3/2, 3/2, and 2, respectively. We have further extended the techniques and results developed for this problem to other min‐max vehicle routing problems.© 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

反舰导弹纯方位发射捕捉概率计算方法

反舰导弹的纯方位发射对目标信息要求不高,在目标信息的探测越来越艰难的今天,是反舰导弹较为重要的一种发射方式,也将会成为未来海战场上常用的作战方式.介绍了反舰导弹捕捉概率的计算方法和传统纯方位发射的捕捉概率的计算方法,并从分析反舰导弹捕捉概率的计算模型和影响因素出发,指出传统的反舰导弹纯方位发射的捕捉概率计算模型存在不足,并给出了修正后的计算模型.     

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.     

An attacker‐defender model for analyzing the vulnerability of initial attack in wildfire suppression

Wildfire managers use initial attack (IA) to control wildfires before they grow large and become difficult to suppress. Although the majority of wildfire incidents are contained by IA, the small percentage of fires that escape IA causes most of the damage. Therefore, planning a successful IA is very important. In this article, we study the vulnerability of IA in wildfire suppression using an attacker‐defender Stackelberg model. The attacker's objective is to coordinate the simultaneous ignition of fires at various points in a landscape to maximize the number of fires that cannot be contained by IA. The defender's objective is to optimally dispatch suppression resources from multiple fire stations located across the landscape to minimize the number of wildfires not contained by IA. We use a decomposition algorithm to solve the model and apply the model on a test case landscape. We also investigate the impact of delay in the response, the fire growth rate, the amount of suppression resources, and the locations of fire stations on the success of IA.     

柔软物体力触觉形变模型验证系统

为了验证柔性物体力-形变模型的合理性,构建了基于CC2531芯片的无线数据收发平台、力传感器测量平台和FALCON手控器位移测量平台的力-形变模型验证系统。以新鲜猪肝脏为实验对象,研究了弹性形变实验和穿刺实验的作用力与位移之间的关系;以力-形变测量数据为基础,进行了参数验证校调。仿真实验结果表明:模型中力-形变特性与实际测量值保持一致。该系统能广泛应用于柔性物体力-形变模型验证,对于促进力触觉虚拟医学仿真系统的发展具有重要意义。     

船舶静态电场跟踪的渐进更新扩展卡尔曼滤波器

为了实现利用船舶静态电场对船舶进行跟踪的目的,针对传统卡尔曼滤波算法中存在的问题,设计一种新的非线性滤波器。建立船舶的状态空间模型,分析传统卡尔曼滤波算法在船舶跟踪中存在的问题;依据渐进贝叶斯思想,利用连续白噪声与离散白噪声序列噪声协方差之间的关系,设计一种新的渐进更新扩展卡尔曼滤波器。仿真结果表明,该滤波器能有效地抑制由于初始误差较大而造成的滤波性能下降和滤波发散,能够有效地跟踪船舶,具有较高的实用价值。     

Optimal switchover times between two activities utilizing the same resource

The “gold‐mining” decision problem is concerned with the efficient utilization of a delicate mining equipment working in a number of different mines. Richard Bellman was the first to consider this type of a problem. The solution found by Bellman for the finite‐horizon, continuous‐time version of the problem with two mines is not overly realistic since he assumed that fractional parts of the same mining equipment could be used in different mines and this fraction could change instantaneously. In this paper, we provide some extensions to this model in order to produce more operational and realistic solutions. Our first model is concerned with developing an operational policy where the equipment may be switched from one mine to the other at most once during a finite horizon. In the next extension we incorporate a cost component in the objective function and assume that the horizon length is not fixed but it is the second decision variable. Structural properties of the optimal solutions are obtained using nonlinear programming. Each model and its solution is illustrated with a numerical example. The models developed here may have potential applications in other areas including production of items requiring the same machine or choosing a sequence of activities requiring the same resource. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 186–203, 2002; DOI 10.1002/nav.10008     

论消防工作与政府投入的数学原理

近年来,政府对消防投入水平较低。通过建立数学模型,从消防部门与政府的相互关系进行理论论证,抛砖引玉,提出消防工作的建议。