运筹学论文100篇

论文摘要：文章针对侦察无人机航路规划这一问题，分析了影响航路规划的因素，构建了航路规划的模型。结合侦察无人机航路规划的特点与模型，论证了基于蚁群算法求解的理由与优点，并对蚁群算法的初始信息素强度与启发因子进行了改进。最后以岛屿进攻战役这一特定作战任务为例。利用MATLAB实现了侦察多目标时的航路规划问题。 引言 航路规划是指在目标点与起始点之间，为运动物体寻找满足某种性能指标和某些约束的线路、路径。目前对于航路规划的研究主要用于导弹、鱼雷、飞机等飞行器的飞行线路选择上，对于无人机的侦察航路的系统研究还不多见。在文献[3]中虽然也应用蚁群算法进行了航路规划，但没有充分考虑到威胁点存在和目标点价值对航路的影响，且对蚁群算法没有进行启发因子和信息素初始强度方面的创新。在相关外文文献中，由于美军无人机航程较大，其航路规划的约束条件就相对较少，可供借鉴的内容也很有限。而针对岛屿进攻战役这一特殊作战样式的研究更是尚属空白。本文正是基于这一背景下对该问题进行研究，以实现在充分发挥无人机最大作战效能的同时，又尽可能地降低无人机被毁伤概率。 1、影响航路规划的因素分析 影响侦察无人机航路规划的主要因素有如下四个方面。 目标价值 目标价值是衡量某一时刻对某一目标实施火力突击必要程度的综合指标(用Vm表示)。可采用层次分析法获得各个目标的价值Vm，也可以再进行归一化处理，得到各目标的相对价值系数Ku，以此来衡量目标的重要程度。 对不同的目标实施侦察时，对于价值较高的目标可安排更长的有效侦察时间，而对于价值相对较低的目标，则应适当压缩有效侦察时间。 有效飞行时间(距离) 侦察的主要目的是发现对己方有价值目标并及时描述目标的状态，因此发现目标的概率是航路是否合理的一个重要指标。距离目标越近，飞机上侦察设备能够搜索目标区的时间也就越长，发现目标的概率也就越大。 在执行侦察任务时，为了获得某一目标的有效信息，无人机必需接近目标并使目标处于其机载电子、光学侦察设备的作用距离内。如果为了实时监控某一目标，侦察无人机还必需在此目标的上空盘旋、停留，以使目标长时间地处于机载设备的监控之下。因此对目标的发现概率可以用有效飞行时间来表征。它表示侦察无人机对目标总的侦察、监控时间，为处理方便，若侦察无人机以等速率飞行，则其有效侦察飞行时间也可转变为有效飞行距离表征。 生存能力 侦察无人机要完成侦察任务就必须具备一定的生存能力。而其生存能力主要与侦察无人机的隐形规避性能、敌方雷达、防空武器的性能等相关。即侦察无人机的生存能力既受本身的易感性、易损性、可靠性影响，也受敌方的侦察探测和打击能力影响。 从侦察无人机完成飞行任务过程来看，包括发射、正常飞行和突破拦截三个过程，若用概率Pf、Pl、Ps表示三个过程的完成情况。 航程(油量)限制 航程是指侦察无人机起飞后，中途不经加油所能飞越的最大水平距离，即飞行距离。是表征侦察无人机远航和持久飞行能力的指标。由于其在地面一次所加的油量是有限的，因此它的航路必然受到航程的限制，且由于无线电的作用距离受限，飞机执行任务的位置不能超过其作战半径。 2、航路规划构模 侦察无人机多数情况下执行特定的侦察监视飞行任务，指挥员期望的目标是在有限的飞行时间与航程内发现尽可能多的目标，同时付出的代价最小。 就航路规划的约束条件而言，首先是威胁量不能超过指挥员的许可范围，其二，是侦察无人机总的飞行距离不能超过侦察无人机的航程。一旦两者之一不能成立，表明要求的任务是无法完成的，即 3、蚁群算法及其改进 蚁群算法作为一种新的计算模式引入人工智能领域，被称为蚂蚁系统，该系统基于以下假设： (1)蚂蚁之间通过环境进行通信。每只蚂蚁仅根据其周围的局部环境做出反应，也仅对其周围的局部环境产生影响； (2)蚂蚁对环境的反应由其内部模式决定； (3)在个体水平上，每只蚂蚁仅根据环境做出独立选择。在群体水平上，单只蚂蚁的行为是随机的，但蚁群通过自组织过程形成高度有序的群体行为。 基于蚁群算法进行航路规划的特点 基于蚁群算法的侦察无人机航路规划方法，能够保证在航路制订时得到一条具有较小可被探测概率及可接受航程的飞行航路，这种航路规划方法还具有以下特点：(1)在蚂蚁不断散布生物信息激素的加强作用下，新的信息会很快被加入到环境中，而由于生物信息激素的蒸发更新，旧的信息会不断被丢失，体现出一种动态特性； (2)最优路线是通过众多蚂蚁的合作被搜索得到的，并成为大多数蚂蚁所选择的路线，这一过程具有协同性； (3)由于许多蚂蚁在环境中感受散布的生物信息激素同时自身也散发生物信息激素，这使得不同的蚂蚁会有不同的选择策略，具有分布性。这些特点与未来战场的许多要求是相符的，因而采用蚁群算法对侦察无人机的航路进行规划具有可行性与前瞻性。 蚁群算法的改进 (1)ij(t)的初值 为了更好的考虑威胁，在定义在初始条件下定义轨迹强度不同，根据蚂蚁选择路线最优选择轨迹强度高的路线，而无人机的航路规划中则应该更优的选择距离威胁点较远的航路。那么可以定义轨迹的初始强度与距离成反比。即与威胁点越近的路线，信息素强度越小。对于两目标点间的每条路径，其信息素轨迹初始强度。 4、基于改进蚁群算法的侦察无人机航路规划的实现 航路规划的初始条件 蚁群算法用于航路规划主要运用在对多目标实施搜索侦察的航路规划问题，即航路规划需要得出的是飞行经过各个目标的数量和次序，以使侦察无人机经过尽可能多的目标点。 在进行初始规划的过程中，为更方便蚁群算法的实现，首先确定坐标系，将上述各目标点及威胁点用坐标系来表示，这样可以便于实际的运算。 假设在岛屿进攻战役中以某市为坐标点(100，100)的位置，以3公里为1个坐标系单位长度建立平面直角坐标系(这是在充分考虑了将主要有价值点都包括在一个(120×120)的范围内而合理构建的)。则可以确定上述各点的坐标系位置，得到各点坐标。同时各个目标点的价值系数通过层次分析法可求得到结果(具体过程略)。 蚁群算法模型的实现 蚁周系统的各初始参量的确定 为计算和表示方便，将目标点定义为向量Mi(其中i＝1，2，3，…，12)，威胁点定义为向量Ti(其中i＝1，2，3)。采用蚁群算法实现目标点的类旅行商(TSP，Traveling Salesman Problem)问题，目前已经开发的蚁群算法包括蚁密系统、蚁量系统和蚁周系统，而实际应用多数应用后者。为模拟系统中蚂蚁行为的方便，定义标记。 蚁群算法模型分析 通过比较的方法，定性分析各个情况下的目标函数值和航路规划图。不难发现在考虑了目标点价值和威胁点威胁的情况下，航路尽可能地避开了威胁并优先选择通过目标价值较大的点。这样无人机的被毁伤概率较低，且如果发生被毁伤事件时，已经发现的总体目标价值最大。 针对四种情况进行定量分析，假设指挥员的倾向性为，即略侧重于考虑威胁代价。2000表示对每个目标的有效侦察距离均为2000m，计算目标函数的值，可见考虑完备时虽然航路总长最大但总体的目标函数值也最大，航程最优，即侦察无人机应按照依次通过这些目标点。 5、结束语 通过上述分析，在给定侦察无人机的侦察任务情况下经运算可求得最优的初始航路，它可以有效地提高无人机的侦察效能，降低无人机的被毁伤概率，它对于目前军事斗争准备中如何使用侦察无人机具有一定的指导意义。随着我军侦察无人机性能的提高及型号的不断丰富，在对未来岛屿进攻战役中如何对这些机型进行航路规划尚有待于进一步探讨。

出版专著4部刘桂真，陈庆华，拟阵，国防科技大学出版社，1994谢力同，刘家壮，刘桂真，图与组合拓扑，山东大学出版社，1994刁在筠，刘桂真，宿洁，马建华，运筹学，高等教育出版社，2007 （作为“十一五”国家级规划教材出版第三版）黎伯堂，刘桂真，高等代数解题技巧与方法，山东科技出版社，19991990年以来共发表论文100多篇，代表作如下Xia Zhang and Guizhen Liu, Some graphs of class 1 for f-colorings, Applied Mathematics Letters 21 (2008), 23-29. (SCI)Guizhen Liu，Qinglin Yu, Lanju Zhang, Maximum fractional factors in graphs, Applied Mathematics Letters 20 (2007), 1237-1243. (SCI)Guizhen Liu, Yan Zhu, Jiansheng Cai, On the Randic index of unicyclic graphs with girth g, MATCH Commun. Math. Comput. 58 (2007),127-138. (SCI)Guizhen Liu, Jianfeng Hou, Jiansheng Cai, Some results about f-critical graphs, Networks 50(3) (2007), 197-202. (SCI)Meijie Ma, Guizhen Liu, Junming Xu, Panconnectivity and edge-fault-tolerant pancyclicity of augmented cubes, Parallel Computing 33 (2007), 36-42. (SCI)Jin Yan, Guizhen Liu, On 2-factors with quadrilaterals containing specified vertices in a bipartite graph, Ars Combinatorics 82 (2007),133-144. (SCI)Jianliang Wu, Jianfeng Hou and Guizhen Liu, The linear arboricity of planar graphs with no short cycles, Theoretical Computer Science 381 (2007), 230-233. (SCI)Ping Li, Guizhen Liu, Cycles in Circuit Graphs of Matroids, Graphs and Combinatorics 23 (2007), 425-431. (SCI)Jihui Wang, Guizhen Liu，Some results on fractional edge colorings of graphs, Ars Combinatorics 83 (2007), 249-255. (SCI)Meijie Ma, Guizhen Liu, Xiangfeng Pan, Path embedding in faulty hypercubes, Applied Mathematics and Computation 192 (2007), 233-238. (SCI)Kefeng Diao, Guizhen Liu, D. Rautenbach, P. Chao, A note on the lset number of edges of 3-uniform hypergraphs with upper chromatic number 2, Discrete Mathematics 306 (2006), 670-676. (SCI)Jianfeng Hou, Guizhen Liu, Jiansheng Cai, List edge and list total colorings of planar graphs without 4-cycles, Theoretical Computer Science 369 (2006), 250-255. (SCI)Liu Guizhen, Deng Xiaotie, Xu Changqing, Partitioning series-parallel multigraphs into v*-excluding edge covers, Science in China Series A Mathematics 49(8) (2006), 1082-1093. (SCI)Xia Zhang, Guizhen Liu, Some sufficient conditions for a graph to be of Cf1, Applied Mathematics Letters 19 (2006)，38-44. (SCI)Fan Hongbing, Liu Guizhen, Liu Jiping, Minimal regular 2-graphs and applications, Science in China Series A Mathematics 49(2) (2006),158-172. (SCI)Jiansheng Cai, Guizhen Liu, Stability number and fractional f-factors in graphs, Ars Combinatoria 80 (2006),141-146. (SCI)Jin Yan, Guizhen Liu, On 2–Factors with Prescribed Properties in a Bipartite Graph, Acta Mathematica Sinica 22(4) (2006), 1115-1120. (SCI)Liu Guizhen, Deng Xiaotie, A polynomial algorithm for finding (g,f)-coloring orthogonal to stars in bipartite graphs, Science in China Series A Mathematics (2005) 48(3), 322-332. (SCI)Liu Guizhen, Zhang Lanju, Properties of fractional k-factors of graphs, Acta Mathematica Sinica 25 B (2) (2005), 301-304. (SCI)Song Huimin, Liu Guizhen, On f-edge cover-coloring of simple graphs, Acta Mathematica Sinica 25 B (1) (2005), 145-151. (SCI)Liu Guizhen, Liu Yan, On (g,f)-uniform graphs, Acta Math. Appl. Sinica, English Ser. 21(4) (2005), Guizhen, W. Zang, f-factors in bipartite (m,f)-graphs, Discrete Applied Math. 136(1) (2004). (SCI)Yan Liu, Guizhen Liu, Number of maximum matchings of bipartite graphs with positive surplus, Discrete Math. 274 (2004), 311-318. (SCI)Ma Yinghong, Liu Guizhen, Some results on fractional k-extendable graphs, Chinese Journal of Engineering Mathematics 21(4)(2004), 567-573. (EI)Yan Jin, Liu Guizhen, Vertex-disjoint quadrilaterals in bipartite graphs, J. Systems Science and complexing17(4) (2004), qiuju, Liu Guizhen, (g,f)-factors with special properties in bipartite (mg,mf)-graphs, Appl. Math. J. Chinese Univ. Ser B 19(2) (2004) Kefeng, Liu Guizhen, Upper bounds on minimum number of C-edgesod 4-uniform C-hypergraphs, Mathematica Applicata 17 (4) (2004), Guizhen, Feng Haodi, Yu Jiguo, 2-factors with some properties in 2d-regular graphs, Proceedings of the international conference on Mathematical programming, Shanghai University press (2004),251-258. (ISTP)Yan Jin, Liu Guizhen, A new result on independent large cycles in bipartite graphs, Proceedings of the international conference on Mathematical programming, Shanghai University press (2004), 400-404. (ISTP)Song Huimin, Liu Guizhen, Aplications of an equitable edge-coloring theorems, Proceedings of the international conference on Mathematical programming, Shanghai University press (2004), 350-355. (ISTP)Feng Li, Liu Guizhen, Edge disjoint graphs in (mg+k-1,mf-k+1)-graphs, Proceedings of the international conference on Mathematical programming, Shanghai University presof the international conference on Mathematical programming, Shanghai University press (2004), 163-169. (ISTP)Guizhen Liu, Binhai Zhu, Some problems on factorizations with constrains in bipartite graphs, Discrete Applied Math. 128 (2003), 421-434. (SCI)Yu Jiguo, Liu Guizhen, (g,f)-factors in bipartite (mg,mf)-graphs, Mathematica Applicata 16(1) (2003), Liu et al., A PTAS for minimizing total completion time of bounded batch scheduling, LNCS 2337(2002), 304-314. (SCI, ISTP)H. Feng and Guizhen Liu, Orthogonal factorizations of graphs, J. Graph Theory 40(4) (2002), 267-278. (SCI)Yan Liu, Guizhen Liu, The fractional matching numbers of graphs, Networks 40(3) (2002), 228-231. (SCI)Liu Guizhen, Long Heping, Randomly orthogonal (g,f)-factorizations in graphs, Acta. Appl, Math. Sinica, English Ser. (2002). 18(3), Lianying, Liu Guizhen, Edge covered coloring and fractional edge covered coloring, J. of Systems . Science. and complexing (2002).15(2), Jianliang and Liu guizhen, The linear arboricity of composition graphs, J. Sys. Sci. and Com. (2002). 15(4), Liu and Q. Yu, Generalization of matching extensions in graphs, Discrete Math. 213 (2001), 231,311-320. (SCI)Liu Guizhen, Zhang Lanju, Fractional (g,f)-factors of graphs, Acta. Math. Scientia 21B(4) (2001), 541-545. (SCI)Liu Guizhen, Dong Henian, Orthogonal (g,f)-factorizations of bipartite graphs, Acta Math. Scientia 21B(3) (2001), 316-322. (SCI)G. Li, Guizhen Liu, A generalization of orthogonal Factorizations in graphs, Acta Mathematica Sinica, English Series 17(4) (2001), 669-678. (SCI)Yan Xiaoxia, Liu Guizhen, Edge disjoint (g,f)-factors orthogonal to r disjoint subgraphs in (mg+k,mf-k)-graphs, Mathematica Applicata, 2001,14(4) . C. B. Lam, Guizhen Liu et al., Orthogonal (g,f)-factorizations in networks, Networks 35(4) (2000), 285-287. (SCI)Liu Guizhen, On (g, f)-uniform graphs, Advance in Mathematics 29(3), (2000)， Guizhen and Zhang Lanju, Maximum fractional (0, f)-factors of graphs, Mathematica Applicata,(2000),13(1), Liu, Q. Yu, k-factors and extendability with prescribed components, congr. Numer. (1999)，139，77-88 (ISTP)., , An extension of one theoremn of critical edge-chromatic graphs, Mathematica Applicata,1999,12(3), Liu, Q. Yu, Toughness and perfect matchings in graphs, Ars combinatoria, (1998), 41(3), 267-272. (SCI)G. Li and Guizhen Liu, (g,f)-factorizations orthogonal to a subgraph in graphs, Science in China SerA, (1998), 41(3), 267-272. (SCI)L. Xie, Guizhen Liu, B. Xu, On endo-homology of complexs of graphs, Discrete Math., (1998), 188, 285-291. (SCI)Guizhen Liu, Q. Yu, On n-edge-deletable and n-critical graphs, Bulletin of the ICA, (1998), 24, Guizhen and Wang Jianfang, (a,b,k)-critical graphs, Advanced in Mathematics,(1998),27(6), and , (a,b,k)-critical graphs, Chinese Science Bulletin, (1997), 42(17), 1492-1493. (SCI)Li Guojun and Liu Guizhen,(g,f)-factorizations Orthogonal to a subgraph in graphs, Science in China A 40(1997).Li Guojun and Liu Guizhen, Factorization orthogonal to a subgraph in graphs, Advanced in Mathematics,(1997),26(5), Guizhen, A 2-factorization orthogonal to a star in a graph, and (1996). Liu and G. Yan, Orthogonal [k-1,k+1]-factorizations in graphs, J. Statistical and inference 51(1996)195-200.(SCI)Liu Guizhen, (g,f)-factorizations orthogonal to a star in graphs, Science in China A38:7(1995)805-812.(SCI)Xie Litong and Liu Guizhen,Combinatorics Graph Theory Algorithms and Applications,World Scientific Publishing Co.(1995). Liu and Q. Yu, Star-factors of vertex-deletion graphs, (1995) Litong and Liu Guizhen,On Whitney's and Tutte's conjecture,Acta Math. Sinica 38:3(1995), Orthogonal (g,f)-factorizations in (1995)153-158.(SCI)Liu Guizhen, Some conditions for f-covered graphs, Acta 14(1994) Guizhen, (g,f)-factors and factorizations in graphs, Acta Math. Sinica 37:2(1994) Guizhen, On solutions of Alspach problems, Chinese Science Bulletin 39:7(1994)541-544.(SCI)Liu Guizhen, the Paths between two vertices in tree graphs, J. Sys. Sci and Math. Scis. 5:2(1992). Liu, B. Alspach and K. Heinrich, Some results on orthogonal factorizations in graphs, Advance of Mathematics 21:2(1992). Chen and G. Liu, Toughness of graphs and [a,b]-factors with prescribed properties, JCMCC 12(1992) Guizhen, Toughness and k-covered graphs, J. Appl. Sciences 15:3(1992), and ,Orthogonal factorizations of graphs, Contemporary Design Theory:A collection of surveys, John Wiley and sons Inc(1992). Heinrich, P. Hell and G. Liu, A simple existence criterion for (g,f)-factors, Discrete Math, 85(1990)313-317.(SCI)Liu Guizhen, Proof of a conjecture on matroid base graphs, Science in China A 33: 11(1990)1329-1337.(SCI)1990年以前共发表论文36篇，代表作如下 and , Paths and cycles in Matroid base graphs, graph and Combinatorics 5:3(1989)207-211.(SCI)G. Liu, On [a,b]-covered graphs, JCMCC 5(1989) Guizhen, Regular k-covered graphs, Acta Math, Scientia9:2(1989)39-43.(SCI)G. Liu, A lower bound on connectivities of matroid base graphs, Discrete Math,69:1(1988). Liu, On connectivities of tree graphs, Theory,(1988)12(3),453-459.(SCI)Zheng H. and Liu Guizhen, some properties on Paths in matroid base graphs, J. Sys. Sci. and Math. Sci. 1:2(1988). Heinrich and G. Liu, A lower bound 0n the number of spanning trees with k end vertices, J. Graph Theory 12:1(1988). Liu, On connectivities of base graph of some matroids, J. Sys. Sci. and Math Scis 1:1(1988). Liu, On f-covered graphs, Congr. Number. 61-(1988), Guizhen, On (g,f)-covered graphs, Acta (1988)181-184.(SCI)Liu Guizhen, The connectivities of adjacent tree graphs, Acta Math, (1987) Guizhen, A theorem on the 1-factors of r-hypertrees, Advance of Mathematics, 15:4(1986) Guizhen, On the lower bound of Chartrand's problem in simple graphs, J. Appl. Sciences4:4(1986) Guizhen, Welsh's conjecture is true for simple binary matroids, Kexue Tong bao 30:9(1985) Guizhen, An algorithm for lexicographically generating ordered rooted trees, J. sys. Sci. and (1985) Guizhen, A theorem on the 1-factors of (m,n)-trees, Acta 5:3(1985) Guizhen, Matroid complexes-geometrical representations on Matroids, Acta Math, Scientia5:1(1985) Guizhen, A lower bound in solutions of chartrands problem, Acta Math. Appl. Sinica 1:1(1984)93-96.