多无人机对组网雷达的协同干扰问题研究

在现代战场中,航迹欺骗干扰技术是针对组网雷达提出的协同干扰技术,旨在利用多架无人机在同一时刻对组网雷达中的部分雷达实施相互关联的虚假目标欺骗干扰.充分考虑了实际情况下无人机飞行模态、飞行速度、飞行高度的约束限制,对雷达的位置分布以及虚假航迹线进行可视化,并将三维空间模型投影到二维平面后进行建模分析.主要针对一个虚拟的无人机航迹欺骗干扰问题,建立时空模型,通过构建可达交互矩阵和雷达扫描算法,结合0-1整数规划,得到无人机协同飞行的最优策略.     

通行受限下需求可拆分的应急物资卡车-多无人机协同配送路径优化

研究通行受限情景下需求可拆分的应急物资卡车-多无人机协同配送路径优化问题,综合考虑灾区路网状况、卡车可途中发射/接受无人机、无人机单次起飞可配送多个需求点、需求可拆分等因素,以应急物资配送任务完成时间最短为目标,构建卡车-多无人机协同配送路径优化模型.根据问题与模型特征设计一种改进蚁群算法求解.实验结果表明:文章方法能合理分配卡车与无人机的配送任务,科学规划通行受限情景下需求可拆分的应急物资卡车-多无人机协同配送路径;卡车途中发射/接收无人机方式能有效缩短无人机飞行距离,减少卡车与无人机的协同时间,缩短通行受限情景下的应急物资配送时间,具有可行性、合理性与有效性.     

考虑协同效应的突发事件救援人员分组方法

针对突发事件的应急救援人员分组问题,提出了一种考虑人员间协同效应的应急救援人员分组方法。首先,对突发事件应急救援人员分组问题进行了描述。然后,基于系统协同理论的思想,提出了救援小组的协同度模型,定量化的度量救援人员间的协同效应。进一步地,综合考虑救援人员的基础效能与协同效应,基于协同度模型给出了救援人员完成不同任务的实际效能的表达式。在此基础上,以最大化各救援小组的实际效能为目标,构建了突发事件应急救援人员分组的优化模型,并给出了将这一多目标0-1二次规划模型转换为单目标0-1线性规划模型的方法,进而可求解并确定救援人员的最优分组方案。最后,通过一个实例分析说明了本文所提出方法的可行性和有效性。     

多无人机协同规划的数学建模

针对第十三届全国研究生数学建模竞赛A题的多无人机协同规划问题展开研究.首先建立大路径和小路径的最短路径模型完成对十个目标群的扫描任务,其在雷达范围内航行总时间为10.37小时.然后建立实时自适应无人机作战模型针对未知远程雷达在不同情况下制定三级无人机作战策略,仿真结果显示:攻击方无人机滞留防御方雷达有效探测范围内的时间总和为8.81h.     

公务员最优录用分配方案的数学模型

本文通过建立0-1规划模型,设计了一种公务员招聘中的最优录用分配方案,并运用L INGO软件求得了一个实际问题的最优解.     

基于轨迹偏差改进算法的无人机飞行冲突评估

以有人驾驶飞机改装的大型无人机开展计划飞行任务作为研究背景,根据飞行姿态、运行要素和空域运行结构等特征,完成了中低空空域内轨迹偏差算法模型的改进.运用改进模型分析计算,获得了基于导航定位精度下,飞行预设位置点与实际位置点的差异和分布趋势,结合ICAO(international civil aviation organization)设计的飞行标准,首次建立了在满足民航运行安全标准下,多机种大型飞机联合运行空域内的飞行冲突量化结果.计算结果表明:改进模型综合考虑了大型无人机在转弯及直线阶段的轨迹偏差,通过偏差数据建立模板评价飞行冲突态势,获得了联合运行空域内飞行器间安全值,推导空域密度,为机场及进离场阶段执行联合计划飞行任务,提供了科学规划的依据.     

多无人机协同任务规划问题

研究无人机任务规划问题,从无人机侦查和轰炸两方面入手.首先,运用迭代算法求解出从基地到雷达区域边际上任一目标出入口的最短路径.在此基础上,以无人机在雷达范围内滞留时间最短,以及被探测次数最少为目标,建立多目标最优化模型.通过改进交叉算子的遗传算法找出最优侦查路径.对于轰炸任务,以无人机在雷达范围内滞留时间最短,以及轰炸总时间最短为目标,建立多目标最优化模型.采用改变惯性权重的自适应粒子群算法找出最佳轰炸路线.由于计算时间较长,本文对68个目标进行聚类分析,提出针对轰炸任务的快速算法,相较原轰炸方案,其计算效率提高80%以上.     

多无人机协同任务策略优化

从研究多无人机协同任务的系统资源分配、任务分配、航线规划、轨迹优化等问题入手,建立了多基地多无人机协同侦察模型.针对问题,首先利用"栅格化聚拢"的思想对目标点进行过滤优化,进而对目标群和无人机基地进行了任务分配,而后结合蚁群算法、贪心算法、最短路径算法等思想,通过Matlab平台,计算出能够让无人机停留在雷达探测区域总时间最少的最优策略.     

无人机在次生灾害巡查中的优化运用

运用优化工具与优化方法对无人机在抢险救灾过程的次生灾害巡查阶段进行了系统性的研究.首先确立巡查的区域范围,采用往返式"Z"型航行路线,结合无人机的续航时间确定无人机的全部行走路线.根据每架无人机在有效时间内可航行的总路径,结合优化计算将整个巡查区域划分为多个小区域.基于改良的贪婪算法求解出各个小区域的最佳无人机探测方案,以期获得整体最优飞行路线.由于每个小区域在一定时间间隔内需要重复巡查,对每个小区域进行细致的路径规划和无人机数量安排,确保满足巡查要求.     

基于瑞利分布的大型风电场风机维护方案优化

针对大型风电场风能利用率低下的问题,从优化风机维护方案的角度出发,在假设风速服从瑞利分布的前提下,建立了两阶段多目标0-1规划模型,确定了所有风机每年2次的维护方案,方案以风电场风能利用率最大为目标,兼顾了维修人员的值班任务和维护任务的均衡,具有操作简单、可行性强的优势.     

邮路规划与邮车调度最优化理论研究

对小规模MTSP问题,建立了可精确求解方案的0-1规划模型,并在满足邮政运输需求的前提下给出了最佳方案.问题一首先以县支局、县局为顶点构建无向赋权图,通过Floyd算法求解各局间的最短距离;然后以Fijk为决策变量,以邮车工作时间、车辆运载能力为主要约束,建立以总空载损失费用最小为目标的0-1非线性规划模型,运用规划软件Lingo求解.问题二考虑到市邮路成本,我们采用分层规划策略,首先以市支局、县局为顶点构建无向赋权图,求解出最短路矩阵,建立以邮路运行成本最小为目标的0-1非线性规划模型IIA求解;然后,建立各县区的最短路矩阵,同样建立规划模型IIB求解各县运输方案.问题三由于县局地理位置不变,对区邮路无影响,故以全市各县支局为中心采用逐步最优方法对所有县区支局重新划分;然后采用模型IIB求解.第四问中考虑县局迁移,我们建立近似的启发式算法完成县局选址,并运用规划模型II求解的到新方案.最后,我们对两种区域划分调整方法还进行了定量的分析.     

The variable radius covering problem

In this paper we propose a covering problem where the covering radius of a facility is controlled by the decision-maker; the cost of achieving a certain covering distance is assumed to be a monotonically increasing function of the distance (i.e., it costs more to establish a facility with a greater covering radius). The problem is to cover all demand points at a minimum cost by finding optimal number, locations and coverage radii for the facilities. Both, the planar and discrete versions of the model are considered. Heuristic approaches are suggested for solving large problems in the plane. These methods were tested on a set of planar problems. Mathematical programming formulations are proposed for the discrete problem, and a solution approach is suggested and tested.     

一种新的逼近精确罚函数的罚函数及性质

针对可微非线性规划问题提出了一个新的逼近精确罚函数的罚函数形式,给出了近似逼近算法与渐进算法,并证明了近似算法所得序列若有聚点,则必为原问题最优解. 在较弱的假设条件下,证明了算法所得的极小点列有界,且其聚点均为原问题的最优解,并得到在Mangasarian-Fromovitz约束条件下,经过有限次迭代所得的极小点为可行点.     

Asymptotic nonlinear stability of traveling waves to conservation laws arising from chemotaxis

In this paper, we establish the existence and the nonlinear stability of traveling wave solutions to a system of conservation laws which is transformed, by a change of variable, from the well-known Keller-Segel model describing cell (bacteria) movement toward the concentration gradient of the chemical that is consumed by the cells. We prove the existence of traveling fronts by the phase plane analysis and show the asymptotic nonlinear stability of traveling wave solutions without the smallness assumption on the wave strengths by the method of energy estimates.     

Saddle-Point Optimality: A Look Beyond Convexity

The fact that two disjoint convex sets can be separated by a plane has a tremendous impact on optimization theory and its applications. We begin the paper by illustrating this fact in convex and partly convex programming. Then we look beyond convexity and study general nonlinear programs with twice continuously differentiable functions. Using a parametric extension of the Liu-Floudas transformation, we show that every such program can be identified as a relatively simple structurally stable convex model. This means that one can study general nonlinear programs with twice continuously differentiable functions using only linear programming, convex programming, and the inter-relationship between the two. In particular, it follows that globally optimal solutions of such general programs are the limit points of optimal solutions of convex programs.     

基于贝叶斯信息更新的失事飞机发现概率模型

了目标搜索区域的确定方法以及失事飞机在目标搜索区域的初始概率分布,得到发现概率的计算公式。以发现概率为目标,构造了一个求解最优搜寻策略的Max Max化规划模型,模型可以动基于贝叶斯方法,提出了一个失事飞机的发现概率模型,利用飞机失联前后的信息数据,给出态地对坠机点的概率分布进行更新,使下一步搜寻任务得到及时的修正和调整。考虑到洋流对坠机点的影响,本文还提出了一个关于基点先验概率分布的重构策略。此外,对任务搜索区域最优路径的选取问题做了进一步探讨,给出了一个任务搜索区域上搜寻路径的选取方法     

New results for molecular formation under pairwise potential minimization

We establish new lower bounds on the distance between two points of a minimum energy configuration of N points in ℝ³ interacting according to a pairwise potential function. For the Lennard-Jones case, this bound is 0.67985 (and 0.7633 in the planar case). A similar argument yields an estimate for the minimal distance in Morse clusters, which improves previously known lower bounds. Moreover, we prove that the optimal configuration cannot be two-dimensional, and establish an upper bound for the distance to the nearest neighbour of every particle, which depends on the position of this particle. On the boundary of the optimal configuration polytope, this is unity while in the interior, this bound depends on the potential function. In the Lennard-Jones case, we get the value . Also, denoting by V _N the global minimum in an N point minimum energy configuration, we prove in Lennard-Jones clusters for all N≥2, while asymptotically holds (as opposed to in the planar case, confirming non-planarity for large N).     

Saddle point and exact penalty representation for generalized proximal Lagrangians

In this paper, we introduce a generalized proximal Lagrangian function for the constrained nonlinear programming problem and discuss existence of its saddle points. In particular, the local saddle point is obtained by using the second-order sufficient conditions, and the global saddle point is given without requiring compactness of constraint set and uniqueness of the optimal solution. Finally, we establish equivalent relationship between global saddle points and exact penalty representations.     

Locating least-distant lines in the plane

In this paper we deal with locating a line in a plane. Given a set of existing facilities, represented by points in the plane, our objective is to find a straight line l minimizing the sum of weighted distances to the existing facilities, or minimizing the maximum weighted distance to the existing facilities, respectively. We show that for all distance measures derived from norms, one of the lines minimizing the sum objective contains at least two of the existing facilities. For the center objective we always get an optimal line which is at maximum distance from at least three of the existing facilities. If all weights are equal, there is an optimal line which is parallel to one facet of the convex hull of the existing facilities.     

Convergence analysis of a nonlinear Lagrangian algorithm for nonlinear programming with inequality constraints

In this paper, we establish a nonlinear Lagrangian algorithm for nonlinear programming problems with inequality constraints. Under some assumptions, it is proved that the sequence of points, generated by solving an unconstrained programming, convergents locally to a Kuhn-Tucker point of the primal nonlinear programming problem.