Maximizing the ratio of two convex functions over a convex set

The purpose of this article is to present an algorithm for globally maximizing the ratio of two convex functions f and g over a convex set X. To our knowledge, this is the first algorithm to be proposed for globally solving this problem. The algorithm uses a branch and bound search to guarantee that a global optimal solution is found. While it does not require the functions f and g to be differentiable, it does require that subgradients of g can be calculated efficiently. The main computational effort of the algorithm involves solving a sequence of subproblems that can be solved by convex programming methods. When X is polyhedral, these subproblems can be solved by linear programming procedures. Because of these properties, the algorithm offers a potentially attractive means for globally maximizing ratios of convex functions over convex sets. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Modeling the operation of multireservoir systems using decomposition and stochastic dynamic programming

Stochastic dynamic programming models are attractive for multireservoir control problems because they allow non‐linear features to be incorporated and changes in hydrological conditions to be modeled as Markov processes. However, with the exception of the simplest cases, these models are computationally intractable because of the high dimension of the state and action spaces involved. This paper proposes a new method of determining an operating policy for a multireservoir control problem that uses stochastic dynamic programming, but is practical for systems with many reservoirs. Decomposition is first used to reduce the problem to a number of independent subproblems. Each subproblem is formulated as a low‐dimensional stochastic dynamic program and solved to determine the operating policy for one of the reservoirs in the system. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

A mathematical programming approach for improving the robustness of least sum of absolute deviations regression

This paper discusses a novel application of mathematical programming techniques to a regression problem. While least squares regression techniques have been used for a long time, it is known that their robustness properties are not desirable. Specifically, the estimators are known to be too sensitive to data contamination. In this paper we examine regressions based on Least‐sum of Absolute Deviations (LAD) and show that the robustness of the estimator can be improved significantly through a judicious choice of weights. The problem of finding optimum weights is formulated as a nonlinear mixed integer program, which is too difficult to solve exactly in general. We demonstrate that our problem is equivalent to a mathematical program with a single functional constraint resembling the knapsack problem and then solve it for a special case. We then generalize this solution to general regression designs. Furthermore, we provide an efficient algorithm to solve the general nonlinear, mixed integer programming problem when the number of predictors is small. We show the efficacy of the weighted LAD estimator using numerical examples. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

任务规划系统研究综述

任务规划系统作为举世瞩目的高科技技术,已经引起了广泛的关注和应用.目前世界上一些主要国家都在研制任务规划系统,且进展很快.为了更好地推进我国学者对于任务规划系统的研究,对任务规划系统的研究进行了全面综述.主要内容包括任务规划系统的发展、应用、主要实现方法及未来发展方向.在应用中,综述了任务规划系统在战场态势评估、无人飞行器、机器人领域的应用.在主要实现方法中,主要描述了数学规划、D*优化算法、Agent方法和遗传算法四种方法.最后给出了任务规划系统未来发展方向:现代技术的融合、发展战略级任务规划系统及未来社会任务规划系统预研.     

D运输问题在物资调度中的应用

D运输问题是含离散目标约束的目标规划问题.首先将此多目标问题转化为单一目标问题,使之简化为传统的运输问题,然后使用一种相对简单的方法求解.最后结合一个实例,讨论了D运输问题在物资调度中的应用.     

基于DEA系统下的武器装备采办理论及运用

数据包络分析DEA(data envelopment analysis)系统主要是针对武器装备性能的论证和武器装备采办提供相应的分析工具。介绍了该系统组成及DEA模型算法的基本思路,分析了武器装备采购费用的相对有效性,并简要阐述了该系统在军事领域的应用前景。     

新型舰炮武器情报指挥系统模拟试验方法

在简要介绍模拟试验系统及搜索雷达模拟器功能和工作原理的基础上,针对某型近程反导舰炮武器情报指挥系统,提出了包括模拟试验流程、仿真数学模型及评估方法的一套模拟试验方法,弥补了单一外场试验考核不充分的不足,达到了全面科学评价被试系统的目的。该模拟方法是外场试验的补充和完善,开拓了靶场试验的新思路。     

Column generation for stochastic green telecommunication network planning with switchable base stations

We present the green telecommunication network planning problem with switchable base stations, where the location and configuration of the base stations are optimized, while taking into account uncertainty and variability of demand. The problem is formulated as a two‐stage stochastic program under demand uncertainty with integers in both stages. Since solving the presented problem is computationally challenging, we develop the corresponding Dantzig‐Wolfe reformulation and propose a solution approach based on column generation. Comprehensive computational results are provided for instances of varying characteristics. The results show that the joint location and dynamic switching of base stations leads to significant savings in terms of energy cost. Up to 30% reduction in power consumption cost is achieved while still serving all users. In certain cases, allowing dynamic configurations leads to more installed base stations and higher user coverage, while having lower total energy consumption. The Dantzig‐Wolfe reformulation provides solutions with a tight LP‐gap eliminating the need for a full branch‐and‐price scheme. Furthermore, the proposed column generation solution approach is computationally efficient and outperforms CPLEX on the majority of the tested instances. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 351–366, 2016     

飞行器航路规划算法分析

针对现代军用飞行器任务规划系统航路规划的特点,分析了飞行器航路规划的基本要求,阐述了目前国内外应用和研究的几种航路规划算法:A*搜索算法、遗传算法、粒子群算法、数学规划算法、电势理论法等,并对飞行器航路规划算法的发展趋势进行了展望.     

整数线性规划问题的一个新算法

本文给出求解整数线性规划问题的一个算法。基本思想是通过求出其伴随线性规划问题的最优单纯形表,把整数线性规划化成正整数系数的不定方程,然后从不定方程的非负整数解集中选取一组满足整数线性规划的约束条件的解,作为整数线性规划的最优解。