On the treatment of force-level constraints in times-equential combat problems

The treatment of force-level constraints in time-sequential combat optimization problems is illustrated by further studying the fire-programming problem of Isbell and Marlow. By using the theory of state variable inequality constraints from modern optimal control theory, sharper results are obtained on necessary conditions of optimality for an optimal fire-distribution policy (in several cases justifying conjectures made in previous analysis). This leads to simplification of the determination of the domains of controllability for extremals leading to the various terminal states of combat. (Additionally, some new results for the determination of boundary conditions for the adjoint variables in optimal control problems with state variable inequality constraints have arisen from this work.) Some further extensions of previous analysis of the fire-programming problem are also given. These clarify some key points in the solution synthesis. Some important military principles for target selection and the valuation of combat resources are deduced from the solution. As a result of this work, more general time-sequential combat optimization problems can be handled, and a more systematic solution procedure is developed.     

Sequencing many jobs on a multi-purpose facility

Suppose a given set of jobs has to be processed on a multi-purpose facility which has various settings or states. There is a choice of states in which to process a job and the cost of processing depends on the state. In addition, there is also a sequence-dependent changeover cost between states. The problem is then to schedule the jobs, and pick an optimum setting for each job, so as to minimize the overall operating costs. A dynamic programming model is developed for obtaining an optimal solution to the problem. The model is then extended using the method of successive approximations with a view to handling large-dimensioned problems. This extension yields good (but not necessarily optimal) solutions at a significant computational saving over the direct dynamic programming approach.     

Target selection in Lanchester combat: Linear-law attrition process

We develop the solution to a simple problem of target selection in Lanchester combat against two enemy force types each of which undergoes a “linear-law” attrition process. In addition to the Pontryagin maximum principle, the theory of singular extremals is required to solve this problem. Our major contribution is to show how to synthesize the optimal target selection policies from the basic optimality conditions. This solution synthesis methodology is applicable to more general dynamic (tactical) allocation problems. For constant attrition-rate coefficients we show that whether or not changes can occur in target priorities depends solely on how survivors are valued and is independent of the type of attrition process.     

An examination of the effects of the criterion functional on optimal fire-support policies

This paper examines the dependence of the structure of optimal time-sequential fire-support policies on the quantification of military objectives by considering four specific problems, each corresponding to a different quantification of objectives (i.e. criterion functional). We consider the optimal time-sequential allocation of supporting fires during the “approach to contact” of friendly infantry against enemy defensive positions. The combat dynamics are modelled by deterministic Lanchester-type equations of warfare, and the optimal fire-support policy for each one-sided combat optimization problem is developed via optimal control theory. The problems are all nonconvex, and local optima are a particular difficulty in one of them. For the same combat dynamics, the splitting of supporting fires between two enemy forces in any optimal policy (i.e. the optimality of singular subarcs) is shown to depend only on whether the terminal payoff reflects the objective of attaining an “overall” military advantage or a “local” one. Additionally, switching times for changes in the ranking of target priorities are shown to be different (sometimes significantly) when the decision criterion is the difference and the ratio of the military worths (computed according to linear utilities) of total infantry survivors and also the difference and the ratio of the military worths (computed according to linear utilities) of total infantry survivors and also the difference and the ratio of the military worths of the combatants' total infantry losses. Thus, the optimal fire-support policy for this attack scenario is shown to be significantly influenced by the quantification of military objectives.     

Optimal force mix in heterogeneous combat

This article presents models for determining the optimum number of Red weapons required to win a heterogeneous combat in which m(m> 1) types of Red weapons face a single type of Blue weapon under a newly defined termination policy. Red aims at either minimizing the total cost or maximizing the aggregated remaining force strength. Kuhn-Tucker and simulated annealing techniques are used for obtaining the optimal solution. The methodology is illustrated by analysing heterogeneous combat to determine (i) the feasibility of introducing new types of weapons and (ii) the number of weapons required to win if a specific type of weapon, say infantry, dominates. © 1995 John Wiley & Sons, Inc.     

Differential-game examination of optimal time-sequential fire-support strategies

Optimal time-sequential fire-support strategies are studied through a two-person zero-sum deterministic differential game with closed-loop (or feedback) strategies. Lanchester-type equations of warfare are used in this work. In addition to the max-min principle, the theory of singular extremals is required to solve this prescribed-duration combat problem. The combat is between two heterogeneous forces, each composed of infantry and a supporting weapon system (artillery). In contrast to previous work reported in the literature, the attrition structure of the problem at hand leads to force-level-dependent optimal fire-support strategies with the attacker's optimal fire-support strategy requiring him to sometimes split his artillery fire between enemy infantry and artillery (counterbattery fire). A solution phenomnon not previously encountered in Lanchester-type differential games is that the adjoint variables may be discontinuous across a manifold of discontinuity for both players' strategies. This makes the synthesis of optimal strategies particularly difficult. Numerical examples are given.     

基于仿真实验的弹道导弹阵地优选

合理部署弹道导弹位置对于提高作战效能具有至关重要的作用。基于解析计算的优化方法难以反映环境因素、武器装备的技术和动力特性等不确定性因素对部署位置的影响,求得的结果存在置信度低的问题。故将解析法与仿真实验相结合,以体系对抗条件下弹道导弹作战效能评估的数学模型为基础,建立了由各种作战实体和行动的模型聚合而成的弹道导弹攻防对抗仿真模型,然后通过仿真实验找出最优部署位置,最后给出了应用示例。实验表明该方法具有速度快、效率高、结果清晰直观的特点,可为指挥员提供科学、快速的决策支持。     

Target selection in lanchester combat: Heterogeneous forces and time-dependent attrition-rate coefficients

We develop solutions to two fire distribution problems for a homogeneous force in Lanchester combat against heterogeneous enemy forces. The combat continues over a period of time with a choice of tactics available to the homogeneous force and subject to change with time. In these idealized combat situations the lethality of each force's fire (as expressed by the Lanchester attrition-rate coefficient) depends upon time. Optimal fire distribution rules are developed through the combination of Lanchester-type equations for combat attrition and deterministic optimal control theory (Pontryagin maximum principle). Additionally, the theory of state variable inequality constraints is used to treat the nonnegativity of force levels. The synthesis of optimal fire distribution policies was facilitated by exploiting special mathematical structures in these problems.     

基于双向启发式属性约简的战术决策建模研究

从预警机指挥引导的多机协同空战原则分析出发,针对超视距协同空战决策过程中的不确定性和不完备性问题,提出了一种不完备信息系统中的基于双向启发式属性约简的战术粗决策建模方法。首先考虑粗糙集决策过程中条件属性发生缺失或不确定的情况,根据扩展不完备信息概念建立了不完备决策信息系统的最优完备选择;其次基于分辨矩阵的属性约简算法,以属性频度的大小作为启发信息进行决策信息系统约简的双向选择,得出决策信息系统的最佳约简集合;然后依据使决策最有可能发生的原则,给出决策信息系统的最优选择,以该最优选择为代表提取出决策规则;最后根据软、硬杀伤结合使用的CGF实体超视距协同空战作战想定,建立了CGF实体综合战术决策模型,并通过作战决策实例对该方法的正确性和有效性进行了验证。结果表明：该方法能在作战态势信息不完备的情况下正确给出CGF实体综合战术行为。     

炮兵作战决策方案优选的方法

炮兵作战方案的选择,是炮兵作战指挥决策的关键环节,其合理与否,直接关系到炮兵作战效能的发挥和作战的成败.根据炮兵作战的实际,阐述了炮兵作战方案优选的依据,给出了运用层次分析法确定影响作战方案选择的各因素权重的方法步骤,在对优选依据的建模要素进行分析的基础上,构建了每个要素的效用函数计算模型,并给出了评估方案的计算方法,提供了模型应用的一般步骤.     

Lanchester-type models of warfare and optimal control

The optimization of the dynamics of combat (optimal distribution of fire over enemy target types) is studied through a sequence of idealized models by use of the mathematical theory of optimal control. The models are for combat over a period of time described by Lanchester-type equations with a choice of tactics available to one side and subject to change with time. The structure of optimal fire distribution policies is discussed with reference to the influence of combatant objectives, termination conditions of the conflict, type of attrition process, and variable attrition-rate coefficients. Implications for intelligence, command and control systems, and human decision making are pointed out. The use of such optimal control models for guiding extensions to differential games is discussed.     

多机协同目标与火力资源分配

在协同空战中,快速正确的空战决策是己方战机少受敌方伤害并取得战争胜利的前提。目标与火力资源分配是决策过程的重要部分。多机空战与单机空战相比有明显的不同,不同之处是面临多个敌方目标,根据我方资源最优分配作战对象和火力,基于遗传算法实现了两种算法的有人无人目标与火力资源分配。仿真结果表明,带有毁伤概率门限的算法既节省火力资源又快速有效。     

炮兵指挥决策中优选作战方案的神经网络模型

优选作战方案是炮兵指挥决策的重要内容.如何从炮兵众多的作战方案中确定其价值,并根据作战任务需要选出最佳方案,是炮兵指挥员及其参谋人员的-项重要任务.根据神经网络中联想记忆的-般模型和迭代解法对炮兵作战方案进行分析和排序,并可运用计算机进行处理,为炮兵指挥员的决策行为提供依据.     

多机协同多目标攻击的目标分配和攻击排序

研究了多机协同空战中多目标攻击的目标分配和攻击排序的过程和方法.首先通过对影响空战态势的因素进行分析,提出一种新的综合距离优势、角度优势和能量优势构造综合优势函数的工程方法,并利用综合优势函数计算出目标分配矩阵,然后介绍了在目标分配矩阵上进行多机协同目标分配和攻击排序的过程和算法,最后用仿真验证了该算法的有效性.     

多阶段传感器-武器联合任务管理方法

针对动态环境下的传感器-武器联合任务管理问题展开研究。根据在动态作战过程中出现的有效新目标、有效空闲传感器和武器数量设定阶段门限,以决定进入下一阶段的时机,从而构建多阶段的作战过程。从打击方案质量及系统响应时间的角度出发,分析构建分布式作战体系对系统作战效能的影响,使系统在每个任务管理阶段可以决定响应流程。通过仿真实验验证了所构建的分布式作战体系与设定的阶段门限可以明显提升系统的作战效能。     

雷达诱饵对空空导弹对抗干扰效果分析

在复杂电子对抗条件下,采用伴飞诱饵对雷达制导空空导弹进行干扰可以有效地提高载机的突防和生存概率。为一次得到在干扰下空空导弹脱靶量与时间的关系,分析诱饵对空空导弹干扰的对抗过程,创新性的采用伴随方法建立了诱饵作用下空空导弹末制导伴随模型,并通过放真程序进行仿真得到对抗过程中各种条件下的空空导弹末制导脱靶量,结果表明,载机在合适的时间投放诱饵并机动能够引起较大脱靶量并降低空空导弹对载机的威胁程度,证明了伴随方法的有效性并为伴飞诱饵的应用提供理论依据。     

多鱼雷攻击多目标的可攻性判据及占位参数优化

本文建立了一套系统解决单艇用多鱼雷攻击多目标的可攻击判据和求解对应优化占位参数的方法。本文的研究中采用了独特的分析坐标系,这样在解决和建立可攻击判据的问题上,不仅避免了繁杂的数值计算,还给出了完备的解析解形式及系统化的概念。所得结论对发展现代潜艇鱼雷攻击战术和实现作战决策科学化具有一定的学术价值和实用意义。     

Note: Dynamic lot sizing for a finite rate input process

The basic single-product dynamic lot-sizing problem involves determining the optimal batch production schedule to meet a deterministic, discrete-in-time, varying demand pattern subject to linear setup and stockholding costs. The most widely known procedure for deriving the optimal solution is the Wagner-Whitin algorithm, although many other approaches have subsequently been developed for tackling the same problem. The objective of this note is to show how these procedures can readily be adapted when the input is a finite rate production process. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 221–228, 1997     

接近观测最后逼近段最优制导方法

接近观测是一种新兴的天基观测手段,精确地导引飞行器到达目标附近合适的观测点是关键技术之一。针对接近观测最后逼近段制导问题,提出了一种最优末制导方法。在惯性系中建立了相对运动方程,把目标和观测点的相对位置作为终端约束,引入了综合考虑飞行时间与燃料消耗要求的性能指标,从而把接近目标的过程转化为最优控制问题,求解出最优推力方向、发动机工作时间和飞行时间。在此基础上,设计了最优制导方案。仿真分析表明最优末制导方法的精度较高,能够满足抵近观察任务的要求,同时对深空探测、交会对接等任务具有借鉴意义。     

基于模糊双矩阵对策的作战效能评估模型

讨论了策略集清晰、支付值模糊的模糊双矩阵对策的一种求解方法，并以某型导弹混编群对抗ARM（反辐射导弹）及载机为案例进行研究，建立了基于模糊双矩阵对策的作战效能评估模型，研究结果对于双方资源分配，提高作战效能具有一定的军事应用价值。