成数超额混合再保险中最优自留额的确定

Centeno在Sparre Anderson模型中研究了调节系数关于再保险自留额的函数的性质，得到了保险人的调节系数是关于其自留额的单峰函数的结论。本文给出带扩散扰动项的复合Poisson过程的索赔时调节系数与再保险自留额的函数，得出保险公司的最优再保险自留额。     

提高飞行器参数辨识精度的最优方波输入设计

本文应用最优输入设计（ＯＩＤ）的理论和方法,将衡量参数辨识精度的Ｃｒａｍｅｒ－Ｒａｏ下界作为最优准则,从工程实现上考虑,将输入函数类限制在多级方波类,并用动态规划原则进行了最优输入设计。本文针对一种飞航导弹进行了最优方波输入设计,初步解决了飞行器参数辨识中动导数辨识问题。     

基于随机期望值模型的时差定位最优布站算法

为研究在特定的定位和布站区域内,时差定位站点的最优布局问题,以定位区域内任意目标的定位误差期望值最小为布站原则,提出了基于随机期望值模型的时差定位最优布站算法,并利用随机模拟、神经网络与遗传算法相结合的混合智能算法来求解最优布站策略。仿真结果表明,该算法的寻优布站结果接近于系统的最优布站。     

面向多最优解组合优化问题的决策求解算法

针对具有固定物品总和、多最优解特征的组合优化问题,以固定总和实数子集问题和购买鸡翅问题为例,给出了这类多最优解组合优化问题的形式化表示。在分析枚举等经典算法基础上,提出了基于整数状态表示和实数状态表示的0-1决策递归搜索多最优解动态规划算法。针对该算法在最优解数量较大时,时间复杂度趋向O(mⁿ)的问题,提出了基于相同决策路径合并和基于0-x决策的两种改进算法。实验中两种改进算法的计算时间基本符合与O(nb+nm)的正比关系,表明对于这类多最优解组合优化问题具有良好的求解性能。     

最优停止理论中离散化方法的应用

离散化方法是研究连续参数最优停止理论和马尔可夫过程最优停止理论的有效方法。本文对这一方法进行了阐述，并用此方法解决了两个实际问题。     

两级维修系统备件库存量的最优化模型研究

本文讨论了确定两级维修系统最优备件库存量的问题 ,建立了几个确定最优备件库存量的优化模型 ,得到了几个有价值的结论 ,最后基于这些结论给出了一个实例。     

基于图论的舰船综合电力系统主网最优拓扑结构分析

首先,基于图论的基本概念和原理,将输配电主网的拓扑结构优化问题建模为一个多约束条件下的多目标优化问题;然后,利用约束法的主要思想,提出了一种最优拓扑结构的两级(元件级与区域配电板级)分析方法;最后,通过四机两区域配电板算例的分析,验证了该方法的正确性与有效性。算例分析结果表明:在正确性方面,该方法得出的两个最优拓扑结构分别满足系统体积最小与供电连续的优化目标,是算例对应拓扑结构优化问题的Pareto-最优解;在有效性方面,该方法直接得出了算例的最优拓扑结构,与基本的枚举法相比具备了显著的有效性。     

系统可靠度的模糊分配

本文把模糊规划理论应用于系统可靠度的最优分配问题,给出两类常见的可靠度分配模型,并以实例说明解决此类问题的思想方法。     

多目标的分布式协同进化MDO算法

通过引入非优超排序和排挤的多目标处理机制 ,将分布式协同进化MDO算法的能力扩展到多目标的多学科设计优化问题。多目标的分布式协同进化MDO算法在保持各学科充分自治和各学科并行设计优化协同的基础上 ,通过一次运行即可获得具有良好分布的多个Pareto最优解 ,逼近整个Pareto最优前沿。应用于导弹气动 /发动机 /控制三学科两目标设计优化问题 ,与约束法计算结果的对比表明算法能够有效逼近该问题的Pareto最优前沿 ,为设计决策提供了丰富的信息     

潜艇纯方位解算目标运动要素中机动原则的确定

利用定性分析和计算机模拟探讨了潜艇最优机动准则的确定,并提出了潜艇的机动原则。     

Optimal nonmyopic gambling strategy for the generalized Kelly criterion

We consider the optimal wagers to be made by a gambler who starts with a given initial wealth. The gambler faces a sequence of two-outcome games, i.e., “win” vs. “lose,” and wishes to maximize the expected value of his terminal utility. It has been shown by Kelly, Bellman, and others that if the terminal utility is of the form log x, where x is the terminal wealth, then the optimal policy is myopic, i.e., the optimal wager is always to bet a constant fraction of the wealth provided that the probability of winning exceeds the probability of losing. In this paper we provide a critique of the simple logarithmic assumption for the utility of terminal wealth and solve the problem with a more general utility function. We show that in the general case, the optimal policy is not myopic, and we provide analytic expressions for optimal wager decisions in terms of the problem parameters. We also provide conditions under which the optimal policy reduces to the simple myopic case. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 639–654, 1997     

相依风险下的超额赔款再保险

本文通过求二次效用函数的货币期望效用的最大值来确定自留额，认为索赔次数服从二元泊松分布，超额赔款再保险的保费按期望值原理进行计算。     

A dynamic nonlinear constrained optimal replacement model

A stochastically constrained optimal replacement model for capital equipment is constructed. Each piece of capital equipment, or machine, is characterized by its age and “utility” or “readiness” class. The readiness of a machine at any age is a stochastic function of its initial utility class and its age. The total discounted replacement cost of several replacement streams, each commencing with an initial machine, is minimized with respect to the replacement age and initial utility class of each machine, subject to a readiness constraint stating the lower bound on the expected number of machines in each utility class at any time. A general solution procedure is outlined and a specific case is solved in detail.     

Optimal betting strategies for favorable games

We examine the problem of a gambler interested in maximizing the expected value of a convex utility function of his fortune after n plays of a game. We allow any probability distribution to rule the outcome of each play, and this distribution may change from play to play according to a Markov process. We present results regarding the existence of an optimal policy and its structural dependence on the gambler's fortune. The well-known results of Bellman and Kalaba for exponential and logarithmic utility functions and coin-tossing games are generalized. We also examine the situation of general stale spaces and show that the same structural results hold.     

一种用于机电产品测试性设计的传感器优选MINLP模型

在单故障假设条件下,考虑了传感器的失效概率和设备的故障率,提出一种以故障检测率和故障隔离率为约束条件的降低传感器费用和失效概率的混合整数非线性规划(MINLP)模型,从而为机电产品测试性设计中传感器选择问题提供了一种可行和有效的解决方法,并进行了案例验证,说明了该方法的有效性。     

Joint pricing and ordering policy for exponentially decaying inventory with known demand

This paper is concerned with the problem of simultaneously setting price and production levels for an exponentially decaying product. Such products suffer a loss in utility which is proportional to the total quantity of stock on hand. A continuous review, deterministic demand model is considered. The optimal ordering decision quantity is derived and its sensitivity to changes in perishability and product price is considered. The joint ordering pricing decision is also computed and consideration of parametric changes of these decisions indicates a non-monotonic response for optimal price to changes in product decay. Issues of market entry and extensions to a model with shortages are also analyzed.     

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.     

A note on the limitations of goal programming as observed in resource allocation for marine environmental protection

After first formulating the problem of the Marine Environmental Protection program of the Coast Guard as a multiple-objective linear program, we investigate the applicability and limitations of goal programming. We point out how the preemptive goal-programming approach is incompatible with utility preferences. Then we observe the tendency of optimal solutions for standard linear goal programs to occur at extreme points. We also note problems of more general approaches, such as dealing with additively separable approximations to preferences.     

联合作战的远程火力战法动态分析方法*

用定量动态分析方法开发远程火力战法是联合作战规划中必须解决的重要问题。借助仿真和博弈分析的混合方法,在对博弈效用函数计算的基础上,构建基于识别真目标、假目标以及火力命中目标概率的二人非零和(TPNZS)非合作博弈模型来开发远程火力战法动态分析方法,对两个典型的联合作战远程火力打击战法性能的初步动态分析表明:战场势态的动态变化直接影响定量规划最优战法的结果。     

军事攻防中的多属性资源分配对策模型

针对资源受限情形下的两阶段攻防资源分配问题,提出一种基于多属性决策的资源分配对策模型。防守者首先将有限的防护资源分配到不同的目标上,继而进攻者选择一种威胁组合方式对目标实施打击。基于博弈论相关知识,模型的求解结果可以使防守者最小化自身损失,使进攻者最大化进攻收益。同时,针对模型的特点,给出了一些推论和证明。通过一个示例验证了模型的合理性以及相关推论的准确性,能够为攻、防双方规划决策提供辅助支持。