Discrete search allocation game with false contacts

This paper deals with a two‐person zero‐sum game called a search allocation game, where a searcher and a target participate, taking account of false contacts. The searcher distributes his search effort in a search space in order to detect the target. On the other hand, the target moves to avoid the searcher. As a payoff of the game, we take the cumulative amount of search effort weighted by the target distribution, which can be derived as an approximation of the detection probability of the target. The searcher's strategy is a plan of distributing search effort and the target's is a movement represented by a path or transition probability across the search space. In the search, there are false contacts caused by environmental noises, signal processing noises, or real objects resembling true targets. If they happen, the searcher must take some time for their investigation, which interrupts the search for a while. There have been few researches dealing with search games with false contacts. In this paper, we formulate the game into a mathematical programming problem to obtain its equilibrium point. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

搜索路径给定时的搜索对策问题及其应用

搜索路径给定时的最优搜索方案问题,也可以理解为是关于搜索者和目标的二人对策问题,主要讨论了当搜索路径给定时的单个搜索者和单个目标的搜索对策问题。首先根据问题的特点,利用动态规划和迭代的方法,确定关于目标逃逸路径混合策略的最优分区,证明该分区是多面体凸集;针对目标不同逃逸路径的分区,求出搜索者的最大期望收益,再将问题转化为二人有限零和对策,计算出搜索者的支付矩阵,确定最优搜索策略。最后结合海军护航行动,对我舰载直升机搜索小型海盗船进行分析和计算,说明搜索路径给定时的最优搜索对策对于双方的资源分配和提高搜索效率具有一定的应用价值。     

A search game taking account of attributes of searching resources

This article deals with a two‐person zero‐sum game called a search allocation game (SAG), in which a searcher and a target participate as players. The searcher distributes his searching resources in a search space to detect the target. The effect of resources lasts a certain period of time and extends to some areas at a distance from the resources' dropped points. On the other hand, the target moves around in the search space to evade the searcher. In the history of search games, there has been little research covering the durability and reachability of searching resources. This article proposes two linear programming formulations to solve the SAG with durable and reachable resources, and at the same time provide an optimal strategy of distributing searching resources for the searcher and an optimal moving strategy for the target. Using examples, we will analyze the influences of two attributes of resources on optimal strategies. © 2007 Wiley Periodicals, Inc. Naval Research Logistics 2008     

More on the search for an infiltrator

We have asymptotically solved a discrete search game on an array of n ordered cells with two players: infiltrator (hider) and searcher, when the probability of survival approaches 1. The infiltrator wishes to reach the last cell in finite time, and the searcher has to defend that cell. When the players occupy the same cell, the searcher captures the infiltrator with probability 1 ? z. The payoff to the hider is the probability that the hider reaches the last cell without getting captured. © 2002 John Wiley & Sons, Inc. Naval Research Logistics, 49: 1–14, 2002; DOI 10.1002/nav.1047     

The search for an intelligent evader: Strategies for searcher and evader in the two-region problem

This paper considers the search for an evader concealed in one of two regions, each of which is characterized by its detection probability. The single-sided problem, in which the searcher is told the probability of the evader being located in a particular region, has been examined previously. We shall be concerned with the double-sided problem in which the evader chooses this probability secretly, although he may not subsequently move: his optimal strategy consists of that probability distribution which maximizes the expected time to detection, while the searcher's optimal strategy is the sequence of searches which limits the evader to this expected time. It transpires for this problem that optimal strategies for both searcher and evader may generally be obtained to a surprisingly good degree of approximation by using the optimal strategies for the closely related (but far more easily solved) problem in which the evader is completely free to move between searches.     

The search for an intelligent evader concealed in one of an arbitrary number of regions

This paper considers the search for an evader concealed in one of an arbitrary number of regions, each of which is characterized by its detection probability. We shall be concerned here with the double-sided problem in which the evader chooses this probability secretly, although he may not subsequently move; his aim is to maximize the expected time to detection, while the searcher attempts to minimize it. The situation where two regions are involved has been studied previously and reported on recently. This paper represents a continuation of this analysis. It is normally true that as the number of regions increases, optimal strategies for both searcher and evader are progressively more difficult to determine precisely. However it will be shown that, generally, satisfactory approximations to each are almost as easily derived as in the two region problem, and that the accuracy of such approximations is essentially independent of the number of regions. This means that so far as the evader is concerned, characteristics of the two-region problem may be used to assess the accuracy of such approximate strategies for problems of more than two regions.     

The United States Coast Guard Computer-Assisted Search Planning system (CASP)

This paper provides an overview of the Computer-Assisted Search Planning (CASP) system developed for the United States Coast Guard. The CASP information processing methodology is based upon Monte Carlo simulation to obtain an initial probability distribution for target location and to update this distribution to account for drift due to currents and winds. A multiple scenario approach is employed to generate the initial probability distribution. Bayesian updating is used to reflect negative information obtained from unsuccessful search. The principal output of the CASP system is a sequence of probability “maps” which display the current target location probability distributions throughout the time period of interest. CASP also provides guidance for allocating search effort based upon optimal search theory.     

发动机传感器数据证实的贝叶斯信度网络方法

针对发动机及其部件试验传感器数据证实的多源证据融合问题,描述了建立贝叶斯信度网络的方法,给出了传感器状态和检验关系式不确定性信息表达方法,发展了自动建立贝叶斯信度网络、计算可信度概率及更新网络的算法;给出了贝叶斯信度网络方法在模型发动机上的应用示例。     

舰载反潜直升机吊放声纳区域反潜策略建模

为提高舰载反潜直升机吊放声纳区域反潜搜索作战效能,对舰载反潜直升机吊放声纳区域反潜搜索策略问题进行了建模。根据潜艇目标位置信息的不确定性,研究了潜艇目标位置信息的概率分布函数,采用Markov状态转移概率矩阵描述了潜艇目标位置信息变化的方法。其次,给出了基于贝叶斯理论的潜艇目标信息概率分布函数更新公式。再次,推导了舰载反潜直升机吊放声纳区域反潜最优策略,给出了舰载直升机吊放声纳区域反潜搜索算法。最后给出了典型案例,验证了反潜搜索策略的有效性。研究成果可为舰载反潜直升机吊放声纳区域反潜提供决策依据。     

多核贝叶斯优化的模型决策树算法

构造模型决策树时超参数较多,参数组合复杂,利用网格搜索等调参方法将会消耗大量的时间,影响模型性能的提升。提出了一种多核贝叶斯优化的模型决策树算法,该算法为应对不同分类数据特性,采用三种高斯过程建模寻优,利用贝叶斯优化技术,选出最优的参数组合。实验结果表明,所提算法在参数寻优上要优于传统的模型决策树寻优方法,并且能够在迭代次数不多的情况下找到全局最优参数值,在一定程度上提升了算法的分类性能,节省了大量的调参时间。     

Sequential learning versus no learning in Bayesian regression models

We consider two regression models: linear and logistic. The dependent variable is observed periodically and in each period a Bayesian formulation is used to generate updated forecasts of the dependent variable as new data is observed. One would expect that including new data in the Bayesian updates results in improved forecasts over not including the new data. Our findings indicate that this is not always true. We show there exists a subset of the independent variable space that we call the “region of no learning.” If the independent variable values for a given period in the future are in this region, then the forecast does not change with any new data. Moreover, if the independent variable values are in a neighborhood of the region of no learning, then there may be little benefit to wait for the new data and update the forecast. We propose a statistical approach to characterize this neighborhood which we call the “region of little learning.” Our results provide insights into the trade‐offs that exist in situations when the decision maker has an incentive to make an early decision based on an early forecast versus waiting to make a later decision based on an updated forecast. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 532–548, 2014     

不确定环境下无人机区域目标搜索及载荷参数影响

针对不确定环境下无人机区域搜索问题,建立了实时探测更新的搜索方法,提出了机载光电载荷参数优化配置策略。建立了基于二维离散网格的无人机区域搜索模型,采用概率地图描述目标信息的实时获取与更新;引入不确定度指标、目标网格的重访和网格探测次数控制,建立搜索目标函数;建立了基于粒子群算法的搜索路径滚动优化方法;通过对任务区域平均探测时间步数和误判概率的估计分析,建立了机载光电载荷参数优化配置策略。使用蒙特卡洛方法验证了区域搜索方法的有效性和光电载荷参数配置对搜索效率、误判概率的影响。     

Solving partially observable agent‐intruder games with an application to border security problems

In this paper, we introduce partially observable agent‐intruder games (POAIGs). These games model dynamic search games on graphs between security forces (an agent) and an intruder given possible (border) entry points and high value assets that require protection. The agent faces situations with dynamically changing, partially observable information about the state of the intruder and vice versa. The agent may place sensors at selected locations, while the intruder may recruit partners to observe the agent's movement. We formulate the problem as a two‐person zero‐sum game, and develop efficient algorithms to compute each player's optimal strategy. The solution to the game will help the agent choose sensor locations and design patrol routes that can handle imperfect information. First, we prove the existence of ?‐optimal strategies for POAIGs with an infinite time horizon. Second, we introduce a Bayesian approximation algorithm to identify these ?‐optimal strategies using belief functions that incorporate the imperfect information that becomes available during the game. For the solutions of large POAIGs with a finite time horizon, we use a solution method common to extensive form games, namely, the sequence form representation. To illustrate the POAIGs, we present several examples and numerical results.     

无源雷达截获概率建模与窗口变量影响仿真

在截获概率概念和截获条件的基础上,综合时域、空域、频域等窗口函数构建截获概率模型,分别建立截获过程的4个窗口函数子模型,研究截获概率与窗口函数变量的影响关系。以SPS-48雷达为辐射源,仿真分析各窗口函数变量对截获概率的影响程度,讨论分区策略下无源雷达参数优化对截获概率的影响并总结截获概率提高方法,为无源雷达设计、研制、试验以及使用提供技术支撑。     

On patrolling a channel

A simple formula is found to be just as accurate as a complicated one for estimating the probability of detection achievable by an ingenious searcher patrolling a channel or barrier. The difference between “detection” and “closure” is emphasized in an extension.     

空域频域不确定条件下电磁探测卫星规划方法研究

电磁探测卫星对区域目标的覆盖搜索在反恐及海上搜救等领域发挥着重要作用.针对电磁探测卫星区域搜索任务中存在的空域频域不确定性,构建了电磁探测卫星区域搜索问题(EDSASP)中不确定因素的量化描述模型及决策要素模型,提出了基于贝叶斯决策的电磁卫星任务规划方法,并以信息探测收益和前端截获收益为优化目标,建立了空域频域不确定条...     

Augmented nested sampling for stochastic programs with recourse and endogenous uncertainty

We propose a novel simulation‐based approach for solving two‐stage stochastic programs with recourse and endogenous (decision dependent) uncertainty. The proposed augmented nested sampling approach recasts the stochastic optimization problem as a simulation problem by treating the decision variables as random. The optimal decision is obtained via the mode of the augmented probability model. We illustrate our methodology on a newsvendor problem with stock‐dependent uncertain demand both in single and multi‐item (news‐stand) cases. We provide performance comparisons with Markov chain Monte Carlo and traditional Monte Carlo simulation‐based optimization schemes. Finally, we conclude with directions for future research.     

模糊决策融合的红外弱小目标序列检测

针对红外序列图像中运动弱小点目标的检测问题,重点研究序列关联检测算法.在多帧关联检测的基础上,引入决策融合概念,建立了基于模糊决策融合的序列关联检测方法.基于贝叶斯最小风险准则建立分布式决策模糊融合方法,有效融合单帧检测的结果,提高序列检测算法的性能.实测数据的实验结果验证了基于贝叶斯最小风险准则的分布式决策模糊融合方法的可行性和有效性.     

武器系统概率指标的贝叶斯决策评定方法

剖析了武器系统试验工程领域中常用二项分布经典假设检验方法存在的问题,从贝叶斯决策思想和理论出发提出了概率指标评定的新方法,通过实例对比证明了贝叶斯决策评定方法有效解决了二项分布经典假设检验方法中存在的问题。     

Effects of cueing in cooperative search

We consider the effects of cueing in a cooperative search mission that involves several autonomous agents. Two scenarios are discussed: one in which the search is conducted by a number of identical search‐and‐engage vehicles and one where these vehicles are assisted by a search‐only (reconnaissance) asset. The cooperation between the autonomous agents is facilitated via cueing, i.e., the information transmitted to the agents by a searcher that has just detected a target. The effect of cueing on the target detection probability is derived from first principles using a Markov chain analysis. In particular, it is demonstrated that the benefit of cueing on the system's effectiveness is bounded. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006