Technical note: Finite-time regret analysis of Kiefer-Wolfowitz stochastic approximation algorithm and nonparametric multi-product dynamic pricing with unknown demand

We consider the problem of nonparametric multi-product dynamic pricing with unknown demand and show that the problem may be formulated as an online model-free stochastic program, which can be solved by the classical Kiefer-Wolfowitz stochastic approximation (KWSA) algorithm. We prove that the expected cumulative regret of the KWSA algorithm is bounded above by where κ₁, κ₂ are positive constants and T is the number of periods for any T = 1, 2, … . Therefore, the regret of the KWSA algorithm grows in the order of , which achieves the lower bounds known for parametric dynamic pricing problems and shows that the nonparametric problems are not necessarily more difficult to solve than the parametric ones. Numerical experiments further demonstrate the effectiveness and efficiency of our proposed KW pricing policy by comparing with some pricing policies in the literature.     

A multi‐stage stochastic programming approach for network capacity expansion with multiple sources of capacity

In networks, there are often more than one sources of capacity. The capacities can be permanently or temporarily owned by the decision maker. Depending on the nature of sources, we identify the permanent capacity, spot market capacity, and contract capacity. We use a scenario tree to model the uncertainty, and build a multi‐stage stochastic integer program that can incorporate multiple sources and multiple types of capacities in a general network. We propose two solution methodologies for the problem. Firstly, we design an asymptotically convergent approximation algorithm. Secondly, we design a cutting plane algorithm based on Benders decomposition to find tight bounds for the problem. The numerical experiments show superb performance of the proposed algorithms compared with commercial software. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 600–614, 2017     

一种面向Agent的概念化建模方法*

面向Agent的建模方法为基于Agent系统的概念化描述提供了一种新的技术.针对多Agent系统分析与建模问题,扩展并规范了面向Agent概念化建模过程,定义了Agent模型及其扩展模型,并给出了形式化描述.同时,给出面向Agent的分析和设计过程,为其具体建模提供了一种高层指导.最后,与其它现有面向Agent的方法在应用方面进行了类比分析,为该方法的广泛和深入地应用研究打下基础.     

随机共振理论在雷达信号截获中的应用

雷达侦察主要通过无源侦察接收设备对空域中敌方雷达辐射源信号进行检测,若要实现对敌辐射源信号的截获,基本条件就是敌雷达信号能量能够达到雷达信号侦收设备的截获灵敏度。然而现代战场中,电磁环境复杂多变,敌雷达信号往往被干扰信号、噪声等掩盖,导致侦收设备漏警概率提高。针对以上问题,提出基于随机共振原理的雷达信号截获判断的方法,增大了截获信号的输出信噪比,解决了由于噪声过大掩盖的雷达信号的侦收问题。将该方法应用于雷达告警接收机的前端截获部分,大大降低了截获系统的漏警概率,保证了整个截获系统的稳定性。仿真实验验证了该方法的有效性。     

FIPA规范的防空导弹体系Agent建模方法

针对防空导弹体系建模的复杂性,探讨研究防空导弹体系的Agent建模方法.提出了基于G/A矩阵的Agent建模方法步骤,通过分析角色之间的关系描述了Agent组织结构,给出了角色类和Agent类的统一定义,并建立了Agent结构框架和类实现模型,最后构建了基于FIPA规范的MAS综合集成框架.该方法的提出,为防空导弹体系的进一步建模提供了方法依据.     

An integer decomposition algorithm for solving a two‐stage facility location problem with second‐stage activation costs

We study a stochastic scenario‐based facility location problem arising in situations when facilities must first be located, then activated in a particular scenario before they can be used to satisfy scenario demands. Unlike typical facility location problems, fixed charges arise in the initial location of the facilities, and then in the activation of located facilities. The first‐stage variables in our problem are the traditional binary facility‐location variables, whereas the second‐stage variables involve a mix of binary facility‐activation variables and continuous flow variables. Benders decomposition is not applicable for these problems due to the presence of the second‐stage integer activation variables. Instead, we derive cutting planes tailored to the problem under investigation from recourse solution data. These cutting planes are derived by solving a series of specialized shortest path problems based on a modified residual graph from the recourse solution, and are tighter than the general cuts established by Laporte and Louveaux for two‐stage binary programming problems. We demonstrate the computational efficacy of our approach on a variety of randomly generated test problems. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

基于扩展Petri网的防空C~4ISRK系统建模分析

针对地空导弹武器系统防空中的火力分配问题,建立了战术级防空C4ISRK系统的Petri网模型。对其进行扩展,即联合谓词Petri网和赋色Petri网,建立旅级火力分配的改进模型,给出了具体的前置谓词公式。为有效分析战术决策的正确性提供了依据和思路。     

试析世博安保中的军事“软实力”运用

世博会的圆满召开，不仅需要强大的军事“硬实力”作后盾，也需要军事“软实力”作支撑。本文从军事“软实力”的基本概念入手，将其分解为感化认同力、形象吸引力、心理威慑力等三个子要素；从各要素出发，以完成世博安保任务为着眼点，提出加强军事“软实力”的具体思路。     

A partial characterization of the optimal ordering/rationing policy for a periodic review system with two demand classes and backordering

We consider a finite horizon periodic review, single product inventory system with a fixed setup cost and two stochastic demand classes that differ in their backordering costs. In each period, one must decide whether and how much to order, and how much demand of the lower class should be satisfied. We show that the optimal ordering policy can be characterized as a state dependent (s,S) policy, and the rationing structure is partially obtained based on the subconvexity of the cost function. We then propose a simple heuristic rationing policy, which is easy to implement and close to optimal for intensive numerical examples. We further study the case when the first demand class is deterministic and must be satisfied immediately. We show the optimality of the state dependent (s,S) ordering policy, and obtain additional rationing structural properties. Based on these properties, the optimal ordering and rationing policy for any state can be generated by finding the optimal policy of only a finite set of states, and for each state in this set, the optimal policy is obtained simply by choosing a policy from at most two alternatives. An efficient algorithm is then proposed. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

动态飞行仿真中人体六自由度模型研究

应用多体系动力学方法,结合飞行力学,给出了动态飞行仿真中飞行员的六自由度数学模型,并将其应用在动态飞行仿真建模中,分析结果表明这种数学模型是可行的。