改进的拉格朗日松弛数据关联算法

在多传感器多目标跟踪领域中,当传感器为被动式的,传统的多维分配算法利用拉格朗日松弛算法求解.拉格朗日乘子更新一般用次梯度方法,但每次迭代都要进行多次极小化运算来求对偶解,导致实时性差.针对这个问题,提出了一种改进的基于拉格朗日松弛的数据关联算法,通过代理修正次梯度方法更新拉格朗日乘子,并在允许时间内获得近似解.仿真实验...     

分布式多站雷达协同定位功率分配改进凸松弛算法

针对分布式多站雷达协同定位下的功率分配问题,提出一种改进凸松弛的启发式算法。给出了分布式多站雷达定位误差的克劳美罗下界(CRLB),建立功率约束下最小化CRLB迹的功率分配模型。设计了一种改进凸松弛算法,通过迭代修正松弛参数和快速功率调整策略解决非凸优化问题消除松弛带来的误差。仿真实验表明,相对于均匀功率分配算法和基于凸松弛的功率分配算法,改进凸松弛启发式功率分配算法下目标的定位性能更优。     

基于遗传算法的航空兵出动架次计算方法

针对航空兵出动架次计算问题,基于资源受限项目调度理论进行问题描述和建模,以给定兵力对目标任务的最大出动架次为效能指标,分析影响因素和约束条件,建立了问题数学模型.根据问题模型特点,采用遗传算法进行求解,针对染色体编码问题,设计了一种扩展任务列表编码方法;针对初始解集求解问题,提出了一种基于优先规则的出动架次分配算法.并构建了航空兵出动架次计算仿真算例对问题模型和求解算法进行验证,实验结果表明,所提模型和算法能够有效求解大规模航空兵出动架次计算问题.     

基于量子粒子群算法的判断矩阵一致性修正

对层次分析法中判断矩阵一致性调整存在的问题进行了分析。把原始判断矩阵认为是理想矩阵受干扰后形成的构造偏差矩阵,在达到基本一致性阈值的前提下使偏差矩阵修改量最小,建立了判断矩阵一致性修正的非线性规划模型。针对遗传模拟退火法收敛结果陷入局部最优的问题,设计了量子粒子群算法求解非线性规划,并和文献的算法进行对比,最后给出算例结果证明该优化算法更简单有效。     

装备维修器材生产路径决策的两阶启发式算法

当前装备供应保障系统中维修器材存在短缺、积压以及配送系统效率低下等问题,亟须对生产、库存和配送作业环节进行集成优化。为客观反映各个决策环节,将该问题公式化为一个混合整数线性规划模型,针对该模型多变量、多约束的特点,提出了一个基于数学规划的两阶启发式算法对其进行求解。结合算例,检验模型的可行性,并选取求解器CPLEX和一个类似的迭代算法与该算法在求解质量和运算时间方面进行对比与分析。结果表明,提出的模型是合理可行的,该算法在求解不同规模实例时表现出优异的性能。     

基于SDP松弛的干扰资源优化分配技术研究

提出一种基于semidefinite programming(简称SDP)松弛的干扰资源优化分配算法。在问题优化过程中首先对模型中非凸的约束条件进行松弛,变为凸约束,将原来的数学模型转化成SDP求解形式,利用内点算法对松弛后的模型求解。该算法利用解析的手段使得干扰资源优化分配问题中的NP难问题在多项式时间内得以解决,并且有较高的可靠性。仿真结果验证了算法的有效性。     

面向多星观测调度的分层迭代算法

提出一种基于分治策略的多星观测分层调度框架,在该框架下,用蚁群优化算法把任务分配至各轨道圈次上,并利用自适应模拟退火算法求解各轨道圈次的调度问题。根据各轨道圈次调度结果的反馈情况,再调整任务分配方案,重复上述过程直到达到算法终止条件。为了提高算法的性能,在设计蚁群算法的启发式信息模型时,应充分考虑卫星调度问题的领域知识;在模拟退火算法中设计两个邻域结构,采用动态选择策略在优化过程中确定最佳邻域搜索结构。仿真实验表明,该方法有效地降低了问题求解的复杂度,尤其在求解大规模多星观测调度问题时表现出优异的性能。     

基于GA-PSO的目标分配问题研究

防空作战中的目标分配问题属于NP完全问题,在综合考虑火力单元作战效能和防御效能的基础上,引入火力单元综合有利度,建立了一种用于大规模多火力单元对抗多轮次目标的静态目标分配模型,给出了基于GA因子的改进PSO算法,并将算法应用于目标分配模型的求解,通过VC 6.0编程和计算机仿真验证了模型的可行性和算法的有效性.     

基于粒子群优化的观测站部署算法

针对红外观测站部署问题,在研究观测站位置对定位精度影响的基础上,提出了基于粒子群优化的观测站部署算法。首先对ECEF坐标系下的CRLB矩阵进行推导;然后将观测站优化部署问题抽象为非线性规划模型,并将红外传感器联合定位的CRLB作为目标函数;最后采用粒子群优化算法求解该模型,避免了传统的非线性规划算法需要求解目标函数梯度的难题。结果表明,本文的部署算法具有一定的理论依据和工程意义;可以为实际红外观测站的静态部署和动态部署提供参考。     

分块自适应加权改进大规模概率模糊聚类

为解决传统基于贝叶斯理论的概率模糊聚类(Bayesian Fuzzy Clustering,BFC)算法在处理大规模数据集聚类时的时间开销和存储代价瓶颈,提出基于数据分块的单程自适应加权BFC算法,算法在大规模数据集分块的基础上,设计了基于数据加权的改进BFC算法,用于数据分块内数据聚类,以挑选出对聚类贡献最具代表的标识数据及其自适应权值,在块间迭代聚类过程中,将标识数据及其权值合并到下一数据块中并参与聚类,从而将上一数据块的聚类信息有效地传递到下一数据块中,最后分析算法的收敛性和时间复杂度.实验结果表明,算法在继承传统BFC算法良好聚类性能基础上,减少计算复杂度,有效提高聚类效率,适用于大规模数据集聚类.     

军队人力资源培训问题的整数线性规划模型

文章研究了军队人力资源培训问题,并基于时间和费用两个指标,建立了一个满足培训时间约束且费用最省的0-1整数线性规划模型,给出了基于Lagrange松驰分解的模型求解算法。在算法中,采用一种简单可行的Lagrange乘子更新方法代替传统的次梯度法。另外,文章证明了算法获得最优解的两个充分条件,计算实例初步表明给出的算法是行之有效的。     

An algorithm (GIPC2) for solving integer programming problems with separable nonlinear objective functions

This paper presents an algorithm for solving the integer programming problem possessing a separable nonlinear objective function subject to linear constraints. The method is based on a generalization of the Balas implicit enumeration scheme. Computational experience is given for a set of seventeen linear and seventeen nonlinear test problems. The results indicate that the algorithm can solve the nonlinear integer programming problem in roughly the equivalent time required to solve the linear integer programming problem of similar size with existing algorithms. Although the algorithm is specifically designed to solve the nonlinear problem, the results indicate that the algorithm compares favorably with the Branch and Bound algorithm in the solution of linear integer programming problems.     

A generalized euclidean procedure for integer linear programs

This paper investigates a new procedure for solving the general-variable pure integer linear programming problem. A simple transformation converts the problem to one of constructing nonnegative integer solutions to a system of linear diophantine equations. Rubin's sequential algorithm, an extension of the classic Euclidean algorithm, is used to find an integer solution to this system of equations. Two new theorems are proved on the properties of integer solutions to linear systems. This permits a modified Fourier-Motzkin elimination method to be used to construct a nonnegative integer solution. An experimental computer code was developed for the algorithm to solve some test problems selected from the literature. The computational results, though limited, are encouraging when compared with the Gomory all-integer algorithm.     

Using Lagrangean relaxation to minimize the weighted number of late jobs on a single machine

This paper tackles the general single machine scheduling problem, where jobs have different release and due dates and the objective is to minimize the weighted number of late jobs. The notion of master sequence is first introduced, i.e., a sequence that contains at least an optimal sequence of jobs on time. This master sequence is used to derive an original mixed‐integer linear programming formulation. By relaxing some constraints, a Lagrangean relaxation algorithm is designed which gives both lower and upper bounds. The special case where jobs have equal weights is analyzed. Computational results are presented and, although the duality gap becomes larger with the number of jobs, it is possible to solve problems of more than 100 jobs. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 50: 2003     

A combination of Lagrangian relaxation and column generation for order batching in steelmaking and continuous‐casting production

This article considers the order batching problem in steelmaking and continuous‐casting production. The problem is to jointly specify the slabs needed to satisfy each customer order and group all the slabs of different customer orders into production batches. A novel mixed integer programming model is formulated for the problem. Through relaxing the order assignment constraints, a Lagrangian relaxation model is then obtained. By exploiting the relationship between Lagrangian relaxation and column generation, we develop a combined algorithm that contains nested double loops. At the inner loop, the subgradient method is applied for approximating the Lagrangian dual problem and pricing out columns of the master problem corresponding to the linear dual form of the Lagrangian dual problem. At the outer loop, column generation is employed to solve the master problem exactly and adjust Lagrangian multipliers. Computational experiments are carried out using real data collected from a large steel company, as well as on large‐scaled problem instances randomly generated. The results demonstrate that the combined algorithm can obtain tighter lower bound and higher quality solution within an acceptable computation time as compared to the conventional Lagrangian relaxation algorithm. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Nonadjacent extreme point methods for solving linear programs

In this article we present some advanced basis or block-pivoting, relaxation, and feasible direction methods for solving linear programming problems. Preliminary computational results appear to indicate that the former two types of simplex-based procedures may hold promise for solving linear programming problems, unlike the third type of scheme which is shown to be computationally unattractive.     

A branch and bound algorithm for allocation problems in which constraint coefficients depend upon decision variables

A branch and bound algorithm is developed for a class of allocation problems in which some constraint coefficients depend on the values of certain of the decision variables. Were it not for these dependencies, the problems could be solved by linear programming. The algorithm is developed in terms of a strategic deployment problem in which it is desired to find a least-cost transportation fleet, subject to constraints on men/materiel requirements in the event of certain hypothesized contingencies. Among the transportation vehicles available for selection are aircraft which exhibit the characteristic that the amount of goods deliverable by an aircraft on a particular route in a given time period (called aircraft productivity and measured in kilotons/aircraft/month) depends on the ratio of type 1 to type 2 aircraft used on that particular route. A model is formulated in which these relationships are first approximated by piecewise linear functions. A branch and bound algorithm for solving the resultant nonlinear problem is then presented; the algorithm solves a sequence of linear programming problems. The algorithm is illustrated by a sample problem and comments concerning its practicality are made.     

变量有界线性目标规划的对偶算法

本文讨论了变量有界的线性目标规划问题,给出了求解这类问题的一个对偶算法,此方法与变量有界线性规划问题的对偶算法相类似。文中证明了算法的有效性,并举例说明了计算过程。     

海量电磁数据中雷达信号的高效分选方法

针对海量电磁数据中雷达信号难以进行快速准确分选的问题,提出一种新的聚类分选方法,即改进k-means算法的Map Reduce并行化实现方法。通过引入初始聚类中心个数k1、最大聚类中心个数kmax和距离门限rt3个参数,克服了k-means算法需要事先确定k值和易受孤立点影响的局限;基于Hadoop平台实现了对改进k-means算法的Map Reduce并行化,克服了k-means算法串行实现时间复杂度高的局限。最后,实验表明改进k-means算法取得了更高的分选准确率,Map Reduce并行化后具有良好的加速比和扩展性,能够很好地对海量电磁数据中雷达信号进行高效分选。     

基于局部平稳高斯模型的小波变换域盲图像水印检测

盲数字水印是数字作品版权保护系统的关键技术之一。由于在检测时没有原始图像作为参考 ,所以水印检测器的设计成为盲水印算法的核心。基于图像小波变换系数的局部平稳高斯模型 ,提出了一种新的盲水印检测器。实验结果表明该检测器与被广泛应用的线性相关检测器相比具有更好的鲁棒性