正则化方法在拉普拉斯数值反演中的应用

本文用正则化方法给出了拉普拉斯变换的数值反演方法,并考虑了问题的不适定性,此方法在实际中有较强的应用价值.     

Clustered coverage orienteering problem of unmanned surface vehicles for water sampling

This study investigates a clustered coverage orienteering problem (CCOP), which is a generalization of the classical orienteering problem. The problem is widely motivated by the emerging unmanned techniques (eg, unmanned surface vehicles and drones) applied to environmental monitoring. Specifically, the unmanned surface vehicles (USVs) are used to monitor reservoir water quality by collecting samples. In the CCOP, the water sampling sites (ie, the nodes) are grouped into clusters, and a minimum number of nodes must be visited in each cluster. With each node representing a certain coverage area of the water, the objective of the CCOP is to monitor as much as possible the total coverage area in one tour of the USV, considering that overlapping areas provide no additional information. An integer programming model is first formulated through a linearization procedure that captures the overlapping feature. A two-stage exact algorithm is proposed to obtain an optimal solution to the problem. The efficiency and effectiveness of the two-stage exact algorithm are demonstrated through experiments on randomly generated instances. The algorithm can effectively solve instances with up to 60 sampling sites.     

Optimal source placement for point coverage in active multistatic sonar networks

The allocation of underwater sensors for tracking, localization, and surveillance purposes is a fundamental problem in anti-submarine warfare. Inexpensive passive receivers have been heavily utilized in recent years; however, modern submarines are increasingly quiet and difficult to detect with receivers alone. Recently, the idea of deploying noncollocated sources and receivers has emerged as a promising alternative to purely passive sensor fields and to traditional sonar fields composed of collocated sources and receivers. Such a multistatic sonar network carries a number of advantages, but it also brings increased system complexity resulting from its unusual coverage patterns. In this work, we study the problem of optimally positioning active multistatic sonar sources for a point coverage application where all receivers and points of interest are fixed and stationary. Using a definite range sensor model, we formulate exact methods and approximation algorithms for this problem and compare these algorithms via computational experiments. We also examine the performance of these algorithms on a discrete approximation of a continuous area coverage problem and find that they offer a significant improvement over two types of random sensor deployment.     

数学名题与HPM研究

数学名题对于数学教育和HPM研究都具有重要的价值。法国数学教育家、数学史家史威兹提出,在数学问题配置与求解中可选择历史上不同时期、不同文化的一些数学名题。在此基础上,我们提出了HPM视角下的问题解决教学这一新课题。HPM视角下的问题解决教学侧重于对历史上所用各种数学思想方法进行比较分析,使学生了解不同文化背景中的数学思考方式,其目的在于培养学生数学洞察力,启发数学思想方法,提升数学思维能力,并可在社会历史文化与数学思维的双重醺陶下,获得数学认知活动的文化意义,在数学教育中实践多元文化关怀的理想。     

需求可拆分的应急物资调度问题的蚁群算法

应急物资调度问题是个典型的需求可拆分的车辆路径问题,区别于传统的车辆路径问题,将每个需求节点只能由一辆车访问的约束去除,允许需求节点由多辆车进行访问。针对应急物资调度问题的特点,建立相应的多目标车辆路径数学规划模型(SDVRP),并根据模型特点设计改进蚁群优化算法。最后,进行相应的算例分析,验证了该模型和算法的有效性。     

兵力展开问题研究

如何将基地的兵力以最短时间展开到多个阵地中,是运输问题中的一种。为解决此问题对著名的兵力展开问题进行了研究。建立了兵力展开问题的数学模型,此模型是一个混合整数规划模型。提出了一种求解方法,该方法可解决类似的混合整数规划问题。最后给出了一个实例。     

相依目标群系统火力分配问题分析与解法

本文中讨论由若干个相依目标群组成的平面点目标系统的火力分配问题。对于武器型号相同的情形,得到了“边际毁伤递减原理”和“循序最优方案即全局最优方案”等结论,并在此基础上提出了问题的解算方法。对于武器型号不同的情形,提出了“循序最优枚举法”,并得出有关结论。     

虚拟PDM环境下基于特征增长的协同设计

协同设计目前已经成为解决复杂产品设计问题的关键技术之一.在分析了现有协同设计问题的基础上,提出通过构建虚拟PDM(VPDM,Virtual PDM),应用交换特征增长数据的方法,来解决企业间异构PDM、CAD应用系统的协同设计问题.给出了虚拟PDM的定义,并介绍了基于虚拟PDM进行协同设计的基本原理.建立了基于虚拟PD...     

瓶颈指派问题的一种多项式时间算法

本文对瓶颈指派问题给出了一种新的算法,该算法不需要利用最大流算法,而类似于解经典指派问题的匈牙利算法。该算法是一个多项式时间算法,其复杂性为Ｏ（ｎ３）     

一种无约束最优化方法——恰当共轭方向法

本文提出了一种求解无约束最优化问题的方法,称之为“恰当共轭方向法”。与通常的共轭方向法(如共轭梯度法)相比,这种方法可以节省大量的一维搜索工作量,并且还能提高收敛速率。