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.     

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.     

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.     

On the isbell and marlow fire programming problem

A complete solution is derived to the Isbell and Marlow fire programming problem. The original work of Isbell and Marlow has been extended by determining the regions of the initial state space from which optimal paths lead to each of the terminal states of combat. The solution process has involved determining the domain of controllability for each of the terminal states of combat and the determination of dispersal surfaces. This solution process suggests a solution procedure applicable to a wider class of tactical allocation problems, terminal control attrition differential games. The structure of optimal target engagement policies in “fights to the finish” is discussed.     

基于粒子群算法的H_∞混合灵敏度控制研究

针对步进电机存在负载摄动和失步超步问题,提出了一种基于粒子群优化算法的混合灵敏度设计方法。在H∞混合灵敏度约束下,采用粒子群算法寻找能够反映系统特性的适应度函数最优值,在搜索到合适的加权阵基础上,利用Matlab得到了H∞最优控制器,并利用优化控制器对步进电机进行控制仿真实验。实验结果表明：该系统具有响应快速平稳、抗负载扰动强等特点。     

基于云重心理论的装甲团主攻方向优选

主攻方向选择的合理与否对战斗的成败有重大影响,合理确定主攻方向是战斗决心的核心内容。为解决主攻方向优选问题,引入了云重心理论,根据主攻方向选择的基本要求,通过对相关军事问题的结构化分析,建立了主攻方向的评价指标体系,并采用层次分析法确定各指标的权重。然后通过专家打分法,确定各属性指标的值,再运用云重心理论进行评估,最后通过对比评估结果确定最优主攻方向。通过多种方法的运用,较好的完成了装甲团主攻方向优选的问题,为科学解决主攻方向的优选问题提供了一定的方法参考和理论依据。     

A specially structured nonlinear integer resource allocation problem

We present an algorithm for solving a specially structured nonlinear integer resource allocation problem. This problem was motivated by a capacity planning study done at a large Health Maintenance Organization in Texas. Specifically, we focus on a class of nonlinear resource allocation problems that involve the minimization of a convex function over one general convex constraint, a set of block diagonal convex constraints, and bounds on the integer variables. The continuous variable problem is also considered. The continuous problem is solved by taking advantage of the structure of the Karush‐Kuhn‐Tucker (KKT) conditions. This method for solving the continuous problem is then incorporated in a branch and bound algorithm to solve the integer problem. Various reoptimization results, multiplier bounding results, and heuristics are used to improve the efficiency of the algorithms. We show how the algorithms can be extended to obtain a globally optimal solution to the nonconvex version of the problem. We further show that the methods can be applied to problems in production planning and financial optimization. Extensive computational testing of the algorithms is reported for a variety of applications on continuous problems with up to 1,000,000 variables and integer problems with up to 1000 variables. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 770–792, 2003.     

基于NSGA-Ⅱ的WTA多目标优化(英文)

将多目标遗传算法NSGA-(改进的非支配排序遗传算法)应用于求解武器-目标分配(WTA)问题。首先,针对以往在建立防空型WTA问题的优化模型上的片面性,把WTA问题看做多目标优化问题,建立了综合考虑作战效能和防御效能的WTA双目标优化模型。然后在此基础上,研究和应用了NSGA-来求解WTA问题。最后由仿真算例验证了NSGA-在WTA问题中的应用可行性,表明了NSGA-可以快速地搜索到WTA多目标优化的Pareto最优解集,从而为求解WTA问题提供了一条有效途径。     

LCDP SO算法在协同空战攻击决策中的运用

为了探索提高协同空战攻击决策算法性能的途径,将多子群粒子群优化理论用于求解协同空战攻击决策,利用生命周期粒子群模型（ LCPSO）,提出了一种生命周期离散粒子群（ LCDPSO）协同空战攻击决策算法。基于典型空战想定背景,仿真验证了算法的有效性。通过统计实验的方法,分析比较了LCDPSO协同空战攻击决策算法与多种智能决策算法的准确性、可靠性和快速性,研究结果证明LCDPSO协同空战攻击决策算法优良的综合性能。     

LCDP SO算法在协同空战攻击决策中的运用?

为了探索提高协同空战攻击决策算法性能的途径,将多子群粒子群优化理论用于求解协同空战攻击决策,利用生命周期粒子群模型（ LCPSO）,提出了一种生命周期离散粒子群（ LCDPSO）协同空战攻击决策算法。基于典型空战想定背景,仿真验证了算法的有效性。通过统计实验的方法,分析比较了LCDPSO协同空战攻击决策算法与多种智能决策算法的准确性、可靠性和快速性,研究结果证明LCDPSO协同空战攻击决策算法优良的综合性能。     

混合遗传算法及其在运载火箭最优上升轨道设计中的应用

运载火箭最优上升轨道设计问题是一类终端时刻未定、终端约束苛刻的最优控制问题,经典算法求解这类问题时收敛性差、局部收敛等问题表现得比较突出。针对上述问题,将具有良好全局收敛性的遗传算法应用到运载火箭最优上升段设计问题求解中,为了提高遗传算法的收敛速度和克服早熟问题,结合遗传算法和单纯型算法的优点,设计了两种混合遗传算法。计算结果表明,所设计的混合遗传算法是求解复杂问题的有效全局优化方法,可以成功地解决一类终端时刻可变飞行器最优控制问题。     

An algorithm for solving general fractional interval programming problems

A Linear Fractional Interval Programming problem (FIP) is the problem of extremizing a linear fractional function subject to two-sided linear inequality constraints. In this paper we develop an algorithm for solving (FIP) problems. We first apply the Charnes and Cooper transformation on (FIP) and then, by exploiting the special structure of the pair of (LP) problems derived, the algorithm produces an optimal solution to (FIP) in a finite number of iterations.     

针对自适应滤波的组网雷达欺骗干扰优化策略

针对组网雷达系统在跟踪目标发生机动时采用自适应滤波来估计目标状态的特点,在点迹融合数据处理结构的组网雷达基础上提出了一种欺骗干扰优化策略.根据状态和量测方程描述了组网雷达跟踪目标的模型,同时建立了跟踪机动目标的自适应滤波模型.在此基础上,建立了欺骗干扰模型,并在目标机动检测约束下,推导了虚假目标欺骗干扰对于组网雷达融合...     

Interval estimation of a global optimum for large combinatorial problems

Consider an “intractable” optimization problem for which no efficient solution technique exists. Given a systematic procedure for generating independent heuristic solutions, we seek to obtain interval estimates for the globally optimal solution using statistical inference. In previous work, accurate point estimates have been derived. Determining interval estimates, however, is a considerably more difficult task. In this paper, we develop straightforward procedures which compute confidence intervals efficiently in order to evaluate heuristic solutions and assess deviations from optimality. The strategy presented is applicable to a host of combinatorial optimization problems. The assumptions of our model, along with computational experience, are discussed.     

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.     

基于理想点距离算法的灭火作战方案优选

分析了传统的灭火作战方案优选方法存在的弊端,提出了基于模糊集理论的计算理想点距离的优选法,明确了语言变量与模糊集理论的相关定义,规定了模糊评价语言与三角模糊数的换算方法,阐述了理想点距离的计算方法,建立了灭火作战方案优选模型,验证了该方法在灭火作战方案优选方面的科学性、有效性以及合理性.     

防空导弹反TBM作战指挥中目标分配关键问题研究

依据防空反导作战理论和目标分配的要求,对防空导弹反TBM作战指挥中目标分配的关键问题进行了研究。分别对威胁排序方法、拦截可行性条件、目标分配原则和目标分配算法进行了分析,提出了一种反TBM作战指挥中目标分配问题的算法,最后讨论了目标分配的评价问题。通过实际应用表明此方法是切实可行的。     

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.     

A note on a constrained replacement model for ships subject to degradations in utility

In a recent paper, Peter J. Kalman considers a stochastic constrained optimal replacement model using the case of ship replacement as an example. However, the development of the constrained model proposed is not pursued and the optimal interval between replacements is determined in the absence of constraints. Among other things, it is the purpose of the present paper to extend the previous results to develop explicit types of constraints for the case of ship replacement and to determine how the optimal replacement interval may change as a result of these constraints. The constraints are concerned with the state of readiness of each ship in a group of ships. Readiness is assumed to be measured on an ordinal valued utility scale. It is proposed that ordinal valued data on ship combat readiness ratings collected by the Navy may be a useful source of empirical information for a model of the type discussed.     

Optimal power control in a wireless network using a model with stochastic link coefficients

This paper addresses optimal power allocation in a wireless communication network under uncertainty. The paper introduces a framework for optimal transmit power allocation in a wireless network where both the useful and interference coefficients are random. The new approach to power control is based on a stochastic programming formulation with probabilistic SIR constraints. This allows to state the power allocation problem as a convex optimization problem assuming normally or log‐normally distributed communication link coefficients. Numerical examples illustrate the performance of the optimal stochastic power allocation. A distributed algorithm for the decentralized solution of the stochastic power allocation problem is discussed. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005