Optimal strategies for problems of simultaneous attack against an area defense with impact-point prediction

An area to be defended consists of separated point targets. These targets are subject to an attack in which the offensive weapons are assumed to arrive simultaneously. The defense has area defenders, each of which is capable of intercepting any attacker'. Furthermore, the defense has impact-point prediction, i.e., it has knowledge of each attacker's intended target prior to allocation of the area interceptors. For a given attack, the defense wishes to allocate its interceptors against attackers so as to maximize the expected total survival value of the targets. In its first move, the offense seeks an attack allocation which will minimize expected total surviving value against best defense. We develop an algorithm to determine optimal attack and defense strategies and the optimal value of this sequential min-max problem. Branch-and-bound techniques are used to obtain integer solutions, and illustrative computational results are provided.     

Optimal strategies for problems of simultaneous attack against an area defense without impact-point prediction

An area to be defended consists of separated point targets. These targets are subject to an attack in which the offensive weapons are assumed to arrive simultaneously. The defense has area defenders, each of which is capable of intercepting any attacker. The defense has no impact-point prediction; that is, it has no knowledge of any attacker's destination prior to allocation of area interceptors. For a given attack, the defense wishes to allocate its interceptors to maximize the total expected survival value of the targets. For a given attack size, the offense seeks a strategy to minimize total expected surviving value against best defense. We determine an optimal defensive strategy directly and develop an algorithm to determine an optimal attack and the optimal value of the min-max problem. A dynamic programming technique is used to obtain integer solutions, and illustrative computational results are provided.     

Robust preallocated preferential defense

The problem is to protect a set of T identical targets that may come under attack by A identical weapons. The targets are to be defended by D identical interceptors, which must be preallocated to defend selected targets. The attacker is aware of the number of interceptors, but is ignorant of their allocation. The size of the attack is chosen by the attacker from within a specified range. The robust strategies developed in this article do not require the defender to assume an attack size. Rather, the defender chooses a strategy which is good over a wide range of attack sizes, though not necessarily best for any particular attack size. The attacker, knowing that the defender is adopting a robust strategy, chooses the optimal attack strategy for the number of weapons he chooses to expend. The expected number of survivors is a function of the robust defense strategy and optimal attack strategy against this robust defense.     

Robustness of preallocated preferential defense with assumed attack size and perfect attacking and defending weapons

The problem is to protect a set of t targets by n perfect interceptors against an attack by m perfect weapons. If the defender solves for an optimal preallocated preferential defense and associated game value assuming m₁ attackers, and the attacker knows the assumption of the defender and utilizes m₂ attackers, he may be able to achieve significantly more damage than had the defender assumed that there would be m₂ attackers. The article treats the robustness of preallocated preferential defense to assumptions about the size of the attack and presents results of an alternative approach.     

以发射质量最小为优化目标的反TBM拦截器优化研究

以反ＴＢＭ拦截器发射质量最小为优化目标,系统地研究了反ＴＢＭ拦截器总体优化技术,建立了反ＴＢＭ拦截器数学模型和优化算法,并得出重要结论。     

Systems defense games: Colonel blotto,command and control

The classical “Colonel Blotto” games of force allocation are generalized to include situations in which there are complementarities among the targets being defended. The complementarities are represented by means of a system “characteristic function,” and a valuation technique from the theory of cooperative games is seen to indicate the optimal allocations of defense and attack forces. Cost trade-offs between systems defense and alternative measures, such as the hardening of targets, are discussed, and a simple example is analyzed in order to indicate the potential of this approach.     

Optimality of the greedy shooting strategy in the presence of incomplete damage information

Consider a situation where a single shooter engages, sequentially, a cluster of targets that may vary in terms of vulnerability and value or worth. Following the shooting of a round of fire at a certain target, the latter may either be killed or remain alive. We assume neither partial nor cumulative damage. If the target is killed, there is a possibility that the shooter is not aware of that fact and may keep on engaging that target. If the shooter recognizes a killed target as such, then this target is considered to be evidently killed. If the objective is to maximize the weighted expected number of killed targets, where the weight reflects the value of a target, then it is shown that a certain type of a shooting strategy, called a Greedy Strategy, is optimal under the general assumption that the more a target is engaged, but still not evidently killed, the less is the probability that the next round will be effective. If all weights are equal, then the greedy shooting strategy calls to engage, at each round, the least previously engaged target that is not evidently killed. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 613–622, 1997     

基于目标威胁规则的雷达情报按需分发

针对预警监视网络中信息过载的问题,为了提高情报分发的效率,提出了基于目标威胁规则的情报按需分发方法。依据目标特征以及保卫对象,利用模糊综合决策和层次分析法估计目标威胁值,在此基础上,通过设定阈值过滤,并与用户作战需求模型动态匹配,最终将所得到的目标情报信息分发给特定情报用户。仿真表明,该方法能够有效地实现情报的按需分发。     

巡航导弹强弱点分析及防御方法

巡航导弹具有突防能力强、命中精度高、灵活性强、技术上易于实现和造价低等优点而备受各个国家重视,已经发展成为现代战争的重要武器,是上世纪90年代以后的主要空中作战目标之一.对巡航导弹的强点与弱点进行了分析,并研究了防御巡航导弹的可行方法.     

To catch an intruder: Part A—uncluttered scenario

We analyze an interdiction scenario where an interceptor attempts to catch an intruder as the intruder moves through the area of interest. A motivating example is the detection and interdiction of drug smuggling vessels in the Eastern Pacific and Caribbean. We study two models in this article. The first considers a nonstrategic target that moves through the area without taking evasive action to avoid the interdictor. We determine the optimal location the interceptor should position itself to best respond when a target arrives. The second model analyzes the strategic interaction between the interceptor and intruder using a Blotto approach. The intruder chooses a route to travel on and the interceptor chooses a route to patrol. We model the interaction as a two‐player game with a bilinear payoff function. We compute the optimal strategy for both players and examine several extensions. © 2017 Wiley Periodicals, Inc. Naval Research Logistics, 64: 29–40, 2017     

Combined proportional navigation law for interception of high-speed targets

A new proportional navigation (PN) guidance law, called combined proportional navigation (CPN), is proposed. The guidance law is designed to intercept high-speed targets, which is a common case for ballistic targets. The range of target-to-interceptor speed ratio during target interception is derived when guidance laws are applied in high-speed targets interception, and the effectiveness of negative navigation ratio in the PN-based guidance law is proven analytically in some lemmas. Based on the lemmas, the lateral acceleration command of CPN is defined, and the solution to the appearance of singularity in time-varying navigation ratio is given. The simulation results show that CPN can determine head-on engagement (as PN) or tail-chase engagement (as RPN) through initial path angle compared with PN and retro proportional navigation (RPN), and can adjust the value of navigation ratio for head-on engagement or tail-chase engagement. Therefore, the capture region of CPN is larger than that of other guidance laws using PN-based methods.     

全球信息栅格及其对美军导弹防御系统的作用

导弹防御系统是美军重点发展的战略武器系统。C4ISR作为导弹防御系统体系中重要的通信指挥自动化系统,由于其自身存在着信息网闭塞与狭窄的缺点,制约着导弹防御系统的功能发挥。美军目前正在全力建设全球信息栅格,通过整合各种信息资源,构成一个可以共享"陆、海、空、天"多维信息的互连互通互操作网络,提升导弹防御系统的一体化信息交互,建成一个多层次、全方位、覆盖全球的导弹拦截系统。     

截击机机群作战起飞规划效能模型

研究了截击机机群起飞架数的规划方法.通过对多攻击机机群进攻方式及截击攻击机机群目标分配形式的分析,以单一机群对单一机群在均匀目标分配形式下的作战效果为基础,根据来袭目标及我方最佳截击区域情况,合理地规划多机场作战飞机的起飞架数.建立了多机场飞机异地起降对多攻击机机群进行最优目标分配的形式及其量化关系模型,最后通过实例仿真和分析,证实了该模型的有效性和实用性.     

灰靶理论的空中目标威胁评估与排序

对空中目标的威胁程度进行科学的评估与排序是防空指挥的重要环节,是防空指挥员进行火力分配的主要依据,也是防空指挥自动化系统的重要功能之一.灰靶理论是处理模式序列的灰关联分析理论,其核心概念是靶心度,可以依据靶心度进行模式分级.分析了影响空中目标威胁程度的主要因素,并基于灰靶理论建立了空中目标威胁评估与排序的数学模型,提出了应用灰靶理论进行威胁评估与排序的方法,为防空指挥员进行科学决策提供了理论依据.     

When is a base stock policy optimal in recovering disrupted cyclic schedules?

The extended economic lot scheduling problem (EELSP) is concerned with scheduling the production of a set of items in a single facility to minimize the long-run average holding, backlogging, and setup costs. Given an efficient cyclic production schedule for the EELSP, called the target schedule, we consider the problem of how to schedule production after a single schedule disruption. We propose a base stock policy, characterized by a base stock vector, that prescribes producing an item until its inventory level reaches the peak inventory of the target schedule corresponding to the item's position in the production sequence. We show that the base stock policy is always successful in recovering the target schedule. Moreover, the base stock policy recovers the target schedule at minimal excess over average cost whenever the backorder costs are proportional to the processing times. This condition holds, for example, when the value of the items is proportional to their processing times, and a common inventory carrying cost and a common service level is used for all the items. Alternatively, the proportionality condition holds if the inventory manager is willing to select the service levels from a certain set that is large enough to guarantee any minimal level of service, and then uses the imputed values for the backorder costs. When the proportionality condition holds we provide a closed-form expression for the total relevant excess over average cost of recovering the target schedule. We assess the performance of the base stock policy when the proportionality condition does not hold through a numerical study, and suggest some heuristic uses of the base stock policy. © 1994 John Wiley & Sons, Inc.     

真比例导引律的降维分析方法

提出了三维真比例导引律的降维分析方法。首先研究视线的运动规律,提出了视线的两种旋转角速度及其计算方法,建立了视线运动方程与新的弹目相对运动方程。其次通过对弹目相对运动的分析,发现在三维空间中存在视线瞬时旋转平面,可以在该平面内构造二维制导律,以应用于三维拦截问题的制导控制。然后将空间真比例导引律不加任何近似与线性化直接引入视线瞬时旋转平面,使其维度从三维降为二维,并对其制导特性进行了分析。最后通过仿真对比分析,验证了真比例导引律降维分析方法的有效性。     

空中反恐中保卫目标重要度指标体系研究

空中恐怖袭击具有突然性和随意性的特点,其目的是通过制造恐怖事件引起巨大影响,带来社会恐慌。通过分析空中恐怖袭击对袭击目标选择的特点,剖析其规律性,从而建立空中反恐保卫目标重要度指标体系和保卫目标重要度评价模型,对保卫目标进行科学有效地划定与排序,便于在空中反恐作战中对保卫目标及早进行确定、实施空中警戒范围划定和战斗部署。     

Optimal pricing and inventory control policy in periodic‐review systems with fixed ordering cost and lost sales

This paper studies a periodic‐review pricing and inventory control problem for a retailer, which faces stochastic price‐sensitive demand, under quite general modeling assumptions. Any unsatisfied demand is lost, and any leftover inventory at the end of the finite selling horizon has a salvage value. The cost component for the retailer includes holding, shortage, and both variable and fixed ordering costs. The retailer's objective is to maximize its discounted expected profit over the selling horizon by dynamically deciding on the optimal pricing and replenishment policy for each period. We show that, under a mild assumption on the additive demand function, at the beginning of each period an (s,S) policy is optimal for replenishment, and the value of the optimal price depends on the inventory level after the replenishment decision has been done. Our numerical study also suggests that for a sufficiently long selling horizon, the optimal policy is almost stationary. Furthermore, the fixed ordering cost (K) plays a significant role in our modeling framework. Specifically, any increase in K results in lower s and higher S. On the other hand, the profit impact of dynamically changing the retail price, contrasted with a single fixed price throughout the selling horizon, also increases with K. We demonstrate that using the optimal policy values from a model with backordering of unmet demands as approximations in our model might result in significant profit penalty. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

基于遗传算法的防空兵群最优火力分配模型研究

结合战场目标价值分析,根据防空兵火力分配情况,运用遗传算法建立了最佳火力分配模型,使防空武器最大限度的发挥火力单位效能,达到最大毁伤效果。采用了实数编码方案,对选择,交叉,变异等操作进行了改进。最后通过计算,验证了方案的可行性和优越性.     

Suboptimal decision rule for attacking targets of opportunity

A player having only a definite number of weapons is hunting targets. His total hunting time is also limited. Targets of opportunity with various values arrive at random, and as soon as a target arrives the player observes the target value and decides whether or not to shoot it down. The issue is what the decision rule is which guarantees him a maximum expected gain during the hunting time. Poisson arrival of the targets, uniform distribution of the target value, and the shoot-look-shoot scheme qre assumed. A decision rule is derived which is not optimal but has a very simple form and gives almost as good value as the optimal decision rule does.