航线网络鲁棒优化设计及其复杂性问题研究
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摘要
航线网络是航空公司生产运营的基础，对公司的发展具有战略意义，通过优化设计方法构建一个符合公司实际并且鲁棒性强的网络将显得尤为重要。航线网络的优化理论一般是对既定结构的网络作抽象后建立的，对航线网络的规划指导具有一定的局限性。从系统复杂性的角度来分析网络的演化机制及运行特性对网络规划指导也具有重要意义。本文结合经济学理论、运筹学理论、经典算法和智能算法、统计学理论、复杂网络理论等对航线网络鲁棒优化设计及其复杂性问题进行研究。
OD间的客流量、单位流成本及节点的容量都具有很大的不确定性。这些不确定性因素将可能导致现有的网络结构与实际所需求的网络结构之间存在偏差，会对以网络为基础的生产带来很大影响，因此需要设计的航线网络具有较好的鲁棒性。本文以航空公司的客流量、单位流运输成本及容量数据为基础，建立离散型的情景集，在有容量限制的条件下进行枢纽航线网络鲁棒优化设计，并利用Benders分解算法进行求解。考虑到离散型的情景集包含的情景有限，本文定义区间型的情景集，建立了无容量限制的区间型绝对鲁棒优化设计模型和相对鲁棒优化设计模型，将修正最短路算法和模拟退火算法相结合进行求解，并以经典CAB数据和航空公司实际数据对模型进行实例分析。结果表明采用区间型鲁棒优化模型设计的网络有更强的鲁棒性，并且确定情形的优化模型只是该模型的特殊情形。
航线网络优化设计是在既定结构下进行的，因此对航线网络结构进行分析，对于选择特性优良的网络结构具有重要意义。本文在节点或边具有容量限制条件下，建立了具有容量限制的加权网络演化模型，利用平均场理论进行求解，理论解析解及仿真试验结果表明，新建立的网络演化模型能更好地再现实际网络的结构特征，经典BBV模型只是该模型当节点容量趋于无穷大时的特殊情形。网络生成之后，再对网络的运行特性进行分析。利用具有容量限制的演化网络模型，生成了有容量限制和无容量限制的演化网络，对比分析了这两种网络的网络容量、节点和边的中心-处理能力。本文还用预期流模型，生成了中国航线演化网络，并建立网络延误传播模型，从宏观上分析延误在不同参数、不同度值节点处时给网络带来的影响，包括受延误影响的节点总数、传播的距离等。在机场或航空公司的恢复策略下，延误现象一般不会导致网络的严重故障，文中还探讨了网络节点或边出现严重故障时，故障边的边权分配策略。级联失效过程仿真结果表明采用适当的分配策略，可使得网络的级联效应减弱或避免。
Airline network is a foundation for airlines’ operations and is strategic to the development ofairlines. It is important to build an airline network which is matching the realistic of the airlines and isrobust by means of optimization designing after analyzing the situation of airlines in current and aperiod in future. The optimization theory of airline network is generally aiming at the network whichis abstracted and has special structure. It has some limitations when guiding the planning anddesigning of airline network. It is also important to explore the evolution mechanism of network andoperation characteristics on network from the aspect of system complexity analysis. This paper willfocuse on on the robust optimization of airline network design and complexity analysis with the helpof economic theory, operations research theory, classic and intelligence algorithms, statistical theory,theory of complex networks and etc.
With the changes of the market environment, the traffic between the OD, unit transport costs andthe capacity of a node will have much uncertainty. These uncertainty factors will probably lead to adeviation between the existing network structure and the actual needing network structure, and willhave a great impact on the production based on the network, therefore there needs to make thedesigning network have better robustness. By analyzing the data of airline passenger traffic, unit flowtransport cost and nodes’ capacity, this paper defines a discrete scenario set, establishes a robustoptimization design model of Hub and spoke network under the capacity-limited conditions, and solvethe model with the Benders Decomposition algorithm. As the number of scenarios is limited in thediscrete scenario set, in order to analyze the problem in more wide and more complex environment,this paper defines an interval type of scenario set which contains more information, establishes twonetwork design models of uncapacitated interval absolute robust optimization and relative robustoptimization, solves the modes with the methods combining the modified shortest path algorithm andsimulation annealing algorithm, carries out some applications for the models using the classic CABdata and airlines actual data. The results show that the network designed by the models of the intervalrobust optimization has better robustness and the optimization model under the determinedcircumstances is a special case of the interval robust optimization model.
The optimization design of airline network is carried out under the special structure,so theanalysis of the structure of airline network will be important to select the excellence structure.Under the conditions of node or edge having capacity limit, this paper establishes a network evolution modelwith limited capacity, solves the model with mean field theory. The theoretical solutions andsimulation results indicate that the new model can better reappear some characteristics of actualnetworks and the BBV model is just a special case of the new model when the nodes’ capacity tendesto infinity. After the network is generated, its operation characteristics need to be analyzed. Using thenew evolution model, two types of network are genetated when the nodes’ capacity tendes to finity orinfinity, and then the capacity of the networks and center-deal ability of nodes and edges is caculatedand compared. Flights delay have impacted the air transport heavily, according to the model ofexpected flow, an evolution of Chinese airline network is generated, a delay spreading model iseastablished based on the network. After then, from the aspect of macro-level, considering differentcases, such as the parameters taking different values and the initial delay happening at node withdifferent degree, the delay influences are analyzed, including the whole number of delayed nodes andthe delay spreading distance and etc. Under the recovery strategy of airports or airlines, delayspreading usually does not cause serious influence on network, this paper also analyzes someallocation strategies of the weight of the unfuncitional edges when serious malfunctions happen.Simulation results indicate that the use of appropriate allocation strategies may reduce or avoide thecascading effect.
OD间的客流量、单位流成本及节点的容量都具有很大的不确定性。这些不确定性因素将可能导致现有的网络结构与实际所需求的网络结构之间存在偏差，会对以网络为基础的生产带来很大影响，因此需要设计的航线网络具有较好的鲁棒性。本文以航空公司的客流量、单位流运输成本及容量数据为基础，建立离散型的情景集，在有容量限制的条件下进行枢纽航线网络鲁棒优化设计，并利用Benders分解算法进行求解。考虑到离散型的情景集包含的情景有限，本文定义区间型的情景集，建立了无容量限制的区间型绝对鲁棒优化设计模型和相对鲁棒优化设计模型，将修正最短路算法和模拟退火算法相结合进行求解，并以经典CAB数据和航空公司实际数据对模型进行实例分析。结果表明采用区间型鲁棒优化模型设计的网络有更强的鲁棒性，并且确定情形的优化模型只是该模型的特殊情形。
航线网络优化设计是在既定结构下进行的，因此对航线网络结构进行分析，对于选择特性优良的网络结构具有重要意义。本文在节点或边具有容量限制条件下，建立了具有容量限制的加权网络演化模型，利用平均场理论进行求解，理论解析解及仿真试验结果表明，新建立的网络演化模型能更好地再现实际网络的结构特征，经典BBV模型只是该模型当节点容量趋于无穷大时的特殊情形。网络生成之后，再对网络的运行特性进行分析。利用具有容量限制的演化网络模型，生成了有容量限制和无容量限制的演化网络，对比分析了这两种网络的网络容量、节点和边的中心-处理能力。本文还用预期流模型，生成了中国航线演化网络，并建立网络延误传播模型，从宏观上分析延误在不同参数、不同度值节点处时给网络带来的影响，包括受延误影响的节点总数、传播的距离等。在机场或航空公司的恢复策略下，延误现象一般不会导致网络的严重故障，文中还探讨了网络节点或边出现严重故障时，故障边的边权分配策略。级联失效过程仿真结果表明采用适当的分配策略，可使得网络的级联效应减弱或避免。
Airline network is a foundation for airlines’ operations and is strategic to the development ofairlines. It is important to build an airline network which is matching the realistic of the airlines and isrobust by means of optimization designing after analyzing the situation of airlines in current and aperiod in future. The optimization theory of airline network is generally aiming at the network whichis abstracted and has special structure. It has some limitations when guiding the planning anddesigning of airline network. It is also important to explore the evolution mechanism of network andoperation characteristics on network from the aspect of system complexity analysis. This paper willfocuse on on the robust optimization of airline network design and complexity analysis with the helpof economic theory, operations research theory, classic and intelligence algorithms, statistical theory,theory of complex networks and etc.
With the changes of the market environment, the traffic between the OD, unit transport costs andthe capacity of a node will have much uncertainty. These uncertainty factors will probably lead to adeviation between the existing network structure and the actual needing network structure, and willhave a great impact on the production based on the network, therefore there needs to make thedesigning network have better robustness. By analyzing the data of airline passenger traffic, unit flowtransport cost and nodes’ capacity, this paper defines a discrete scenario set, establishes a robustoptimization design model of Hub and spoke network under the capacity-limited conditions, and solvethe model with the Benders Decomposition algorithm. As the number of scenarios is limited in thediscrete scenario set, in order to analyze the problem in more wide and more complex environment,this paper defines an interval type of scenario set which contains more information, establishes twonetwork design models of uncapacitated interval absolute robust optimization and relative robustoptimization, solves the modes with the methods combining the modified shortest path algorithm andsimulation annealing algorithm, carries out some applications for the models using the classic CABdata and airlines actual data. The results show that the network designed by the models of the intervalrobust optimization has better robustness and the optimization model under the determinedcircumstances is a special case of the interval robust optimization model.
The optimization design of airline network is carried out under the special structure,so theanalysis of the structure of airline network will be important to select the excellence structure.Under the conditions of node or edge having capacity limit, this paper establishes a network evolution modelwith limited capacity, solves the model with mean field theory. The theoretical solutions andsimulation results indicate that the new model can better reappear some characteristics of actualnetworks and the BBV model is just a special case of the new model when the nodes’ capacity tendesto infinity. After the network is generated, its operation characteristics need to be analyzed. Using thenew evolution model, two types of network are genetated when the nodes’ capacity tendes to finity orinfinity, and then the capacity of the networks and center-deal ability of nodes and edges is caculatedand compared. Flights delay have impacted the air transport heavily, according to the model ofexpected flow, an evolution of Chinese airline network is generated, a delay spreading model iseastablished based on the network. After then, from the aspect of macro-level, considering differentcases, such as the parameters taking different values and the initial delay happening at node withdifferent degree, the delay influences are analyzed, including the whole number of delayed nodes andthe delay spreading distance and etc. Under the recovery strategy of airports or airlines, delayspreading usually does not cause serious influence on network, this paper also analyzes someallocation strategies of the weight of the unfuncitional edges when serious malfunctions happen.Simulation results indicate that the use of appropriate allocation strategies may reduce or avoide thecascading effect.
引文
[1]朱金福.航空运输规划.西安，西北工业大学出版社，2009.
[2]耿淑香.航空公司运营管理方略．北京：中国民航出版社,2000.
[3]柏明国，朱金福.全连通航线网络和枢纽航线网络的比较研究.系统工程理论与实践,2006,(9):113-117.
[4] Pels E, Nijkamp P, Rietveld P. A note on the optimality of airline networks. EconomicsLetters,2000,69(3):429-434.
[5] Brueckner J K. Network structure and airline scheduling. The Journal of IndustrialEconomics,2004,(2):291-312.
[6] Zhang Y. Network structure and capacity requirement: The case of China. TransportationResearch Part E: Logistics and Transportation Review,2010,46(2):189-197.
[7] Hakimi S L. Optimum locations of switching centers and the absolute centers andmedians of a graph,1964,450-459.
[8] Campbell J F. Integer programming formulations of discrete hub location problems.European Journal of Operational Research,1994,72:387-405.
[9] O'Kelly M E. A quadratic integer program for the location of interacting hub facilities.European Journal of Operational Research,1987,32(3): p.393-404.
[10] Davidovi T, Ramljak D, elmi M and et al. Bee colony optimization for the p-centerproblem. Computers&Operations Research,2011,38(10):1367-1376.
[11] O’Kelly M,Skorin-Kapov D, Skorin-Kapov J. Lower bounds for the hub locationproblem1. Manggement Science,1995,41(4)713-721.
[12] Skorin-Kapov D, Skorin-Kapov J, O'Kelly M. Tight linear programming relaxations ofuncapacitated p-hub median problems. European Journal of Operational Research,1996,94(3):582-593.
[13] Ernst A T, Krishnamoorthy M. Efficient algorithms for the uncapacitated single allocationp-hub median problem, Location Science,1996,4(3): p.139-154.
[14] Ebery J. Solving large single allocation p-hub problems with two or three hubs. EuropeanJournal of Operational Research,2001,128(2):447-458.
[15] O'Kelly M E, BRYAN D, SKORIN-KAPOV D and et al. Hub network design withsingle and multiple allocation: A computational study. Location Science,1996,4(3):125-138.
[16] Sohn J, Park S. Efficient solution procedure and reduced size formulations for p-hublocation problems. European Journal of Operational Research,1998,118-126.
[17] Skorin-Kapov D, Skorin-Kapov J.On tabu search for the location of interacting hubfacilities,1994.73:502-509.
[18] Campbell J F. Hub location and the p-hub median problem. Operations Research,1996,44(6):923-935.
[19] Ernst A T, Krishnamoorthy M. An exact solution approach based on shortest-paths forp-hub median problems. Informs Journal on Computing,1998,10(2):149-162.
[20] Pirkul H, Schilling D A.An efficient procedure for designing single allocation hub andspoke systems. Management Science,1998,44(12):235-242.
[21] Smith K, Krishnamoorthy M, Palaniswami M. Neural versus traditional approaches to thelocation of interacting hub facilities. Location Science,1996.4(3):155-171.
[22] Sohn J, Park S. A linear program for the two-hub location problem. European Journal ofOperational Research,1997,100(3):617-622.
[23] Ili A, Aleksandar, Uro evi D,Brimberg J and et al.A general variable neighborhoodsearch for solving the uncapacitated single allocation p-hub median problem. EuropeanJournal of Operational Research,2010,206(2):289-300.
[24] Contreras I, Diaz J a, Fernandez E.Branch and Price for Large-Scale Capacitated HubLocation Problems with Single Assignment. INFORMS Journal on Computing,2011,23(1):41-55.
[25] Campbell J F. Location and allocation for distribution systems with transshipments andtransportation economies of scale. Annals of Operations Research,1992,40:77-99.
[26] Ernst A T, Krishnamoorthy M.Exact and heuristic algorithms for the uncapacitatedmultiple allocation p-hub median problem. European Journal of Operational Research,1998,104:100-112.
[27] Sasaki M, Suzuki A, Drezner Z.On the selection of hub airports for an airlinehub-and-spoke system. Computers&Operations Research,1999,26:1411-1422.
[28] Ernst A T, Krishnamoorthy M. Solution algorithms for the capacitated single allocationhub location problem. Annals of Operations Research,1999,86:141-159.
[29] Ebery J, Krishnamoorthy M, Ernst A and et al. The capacitated multiple allocation hublocation problem: Formulations and algorithms. European Journal of Operational Res-earch,2000,120(3):614-631.
[30] Boland N, Krishnamoorthy M, Ernst A T and et al. Preprocessing and cutting for multipleallocation hub location problems. European Journal of Operational Research,2004,155(3):638-653.
[31] Marín A. Formulating and solving splittable capacitated multiple allocation hub locationproblems. Computers&Operations Research,2005,32(12):3093-3109.
[32] Mar n A, Cánovas L, Landete M. New formulations for the uncapacitated multipleallocation hub location problem. European Journal of Operational Research,2006,172(1):274-292.
[33] Labb M, Yaman H, Gourdin E. A branch and cut algorithm for hub location problems.Math. Program., Ser. A,2005,102:371-405.
[34] Costa M G,Captivo M E, Clímaco J. Capacitated single allocation hub locationproblem—A bi-criteria approach. Computers&Operations Research,2008,35(11):3671-3695.
[35] Contreras I, Cordeau J F, Laporte G.Benders decomposition for large-scale uncapacitatedhub location. Operations Research,2011,59(6):1477-1490.
[36] Hamacher H W, Labbe M, Nickel S and et al. Adapting polyhedral properties fromfacility to hub location problems. Discrete Applied Mathematics,2004,145:104-116.
[37] Ernst A T, Hamacher H, Jiang H and et al.Uncapacitated single and multiple allocationp-hub center problems. Computers&Operations Research,2009,36(7):2230-2241.
[38] Campbell A M, Lowe T J, Zhang L. The p-hub center allocation problem. EuropeanJournal of Operational Research,2007,176(2):819-835.
[39] Meyer T, Ernst A T, Krishnamoorthy M. A2-phase algorithm for solving the singleallocation p-hub center problem. Computers and Operations Research,2009,36(12):3143-3151.
[40] Kara B Y, Tansel B C.The single-assignment hub covering problem: Models andlinearizations. Journal of the Operational Research Society,2003,59-64.
[41] Aykin T. Networking policies for hub-and-spoke systems with application to the airtransportation system,1995,29(3):201-221.
[42] O’Kelly M E, Bryan D L.Hub location with flow economies of scale. TransportationResearch Part B: Methodological,1998,32(8):605-616.
[43] Campbell J F, Ernst A T, Krishnamoorthy M. Hub arc location problems: part I:introduction and results. Management Science,2005,51(10):1540-1555.
[44] Campbell J F. Designing Hub Networks with Connected and Isolated Hubs. Proceedingsof the43rd Hawaii International Conference on System Sciences,2010:1-10.
[45] Kim H. Reliable p-hub location problems and protection models for hub networkdesign[博士学位论文]2008.
[46] Kim H, O'Kelly M E. Reliable p-Hub Location Problems in TelecommunicationNetworks. Geographical Analysis,2009,41(3):283-306.
[47] Sim T, Lowe T J, Thomas B W. The stochastic-hub center problem with service-levelconstraints. Computers& Operations Research,2009,36(12):3166-3177.
[48] Contreras I, Cordeau J F, Laporte G.Stochastic uncapacitated hub location. EuropeanJournal of Operational Research,2011,212(3):518-528.
[49] Yang T H. Stochastic air freight hub location and flight routes planning. AppliedMathematical Modelling,2009,33(12):4424-4430.
[50] Lium A G, Crainic T G, Wallace S W.A Study of Demand Stochasticity in ServiceNetwork Design. Transportation Science,2009,43(2):144-157.
[51] Alumur S A, Nickel S, Saldanha-da-Gama F.Hub location under uncertainty.Transportation Research Part B: Methodological,2012,46(4):529-543.
[52] Kouvelis P, Y G. Robust discrete optimization and its applications. KluwerA cadem icPublishers,Boston,1997.
[53] Guti6rrez G J, Kouvelis P,Kurawarwala A A. A robustness approach to uncapacitatednetwork design problems. European Journal of Operational Research,1996,94:362-376.
[54]姜涛,朱金福.非严格的中枢辐射航线网络设计的鲁棒优化方法.信息与控制，2007，36(5):539-545.
[55]姜涛,朱金福，覃义.基于最短路的中枢辐射航线网络鲁棒优化方法.系统工程，2007，25(1):53-59.
[56]姜涛,朱金福，覃义.中枢辐射航线网络的鲁棒优化方法研究.小型微型计算机系统,2008,29(7):1366-1371.
[57]柏明国,姜涛，朱金福.基于禁忌算法的中枢辐射航线网络鲁棒优化方法.数学的实践和认识,2008,38(13):60-69.
[58] Averbakh I. On the complexity of a class of combinatorial optimization problems withuncertainty. Mathematical Programming,2001,90(2):263-272.
[59] Averbakh I, Lebedev V.Interval data minmax regret network optimization problems.Discrete Applied Mathematics,2004,138(3):289-301.
[60] Kasperski A, Zieliński P.An approximation algorithm for interval data minmax regretcombinatorial optimization problems. Information Processing Letters,2006,97(5):177-180.
[61] Pereira J, Averbakh I. Exact and heuristic algorithms for the interval data robustassignment problem. Computers&Operations Research,2011,38(8):1153-1163.
[62]周涛.复杂网络研究概述.物理，2005，34(1):31-36.
[63] Baggio R, Scott N, Cooper C.Network science: a review focused on tourism. Annals ofTourism Research,2010:1-24.
[64] Erdos P, RBNYI A. On the evolution of random graphs. Transactions of the AmericanMathematical Society,1960,286(1):343-347.
[65] Erdos P, Renyi A. On random graphs,Publications Mathematicae,6,290.,1959.
[66] Watts D J, Strogatz S H.Collective dynamics of 'small-world' networks. Nature,1998,393:440-442.
[67] Barabasi A, Albert R.Emergence of Scaling in Random Networks. Science,1999,286:509-512.
[68]王文旭.复杂网络的演化动力学及网络上的动力学过程研究[博士学位论文]2007.
[69] Newman M. Assortative Mixing in Networks. Physical Review Letters,2002,89(20):1-4.
[70] Goh K.-I, Oh E, Kahng B and et al. Betweenness centrality correlation in social networks.Physical Review E,2003,67(1):1-4.
[71] Ravasz E, Barabási A.-L.Hierarchical organization in complex networks. Physical ReviewE,2003,67(2):1-7.
[72] Barabasi A, Albert R, Jeong H. Mean-field theory for scale-free random networks.1999,272:173-187.
[73] Barrat A, Barthélemy M, Vespignani A. Modeling the evolution of weighted networks.Physical Review E,2004,70(6):1-12.
[74] Barrat A, Barthélemy M, Vespignani A. Weighted Evolving Networks: CouplingTopology and Weight Dynamics. Physical Review Letters,2004,92(22):2-5.
[75] Ebel H,Mielsch L.-I, Bornholdt S.Scale-free topology of e-mail networks. PhysicalReview E,2002,66(3):1-4.
[76] Zhou T, Wang B H.Topological properties of integer networks. Physica A: StatisticalMechanics,2006:12-14.
[77] Amaral L A N, Scala A, Barthelemy M and et al.Classes of small-world networks.Proceedings of the National Academy of Sciences of the United States of America,2000,97(21):11149-11152.
[78] Wang M, Wu B Q, Wu X and et al.The Topological and Statistical Analysis of PublicTransport Network Based on Fuzzy Clustering.2:1183-1191.
[79]刘宏鲲,张效莉,曹崀等.中国城市航线网络航线连接机制分析.中国科学G辑:物理学、力学、天文学,2009,39(7):935-942.
[80]王姣娥,莫辉辉,金凤君.中国航线网络空间结构的复杂性.2009,64(8):899-910.
[81] CHI Li-Ping, WANG Ru, SU Hang and et al. Structural properties of US flight network.Chinese physics,2003,20(8):1393-1396.
[82] Li W, Cai X.Statistical analysis of airport network of China. Physical Review E,2004,69(4):1-6.
[83] Guimer R, Amaral L A N. Modeling the world-wide airport network. The EuropeanPhysical Journal B:Condensed Matter,2004,38(2):381-385.
[84]高峰，党亚茹.世界航空客运网络的节点度分布特征.科学学与科学技术管理,2009,7:75-80.
[85]党亚茹,李雯静.基于网络视角的航空客流结构分析.交通运输系统工程与信息,2010,10:167-174.
[86] Bagler G. Analysis of the airport network of India as a complex weighted network.Physica A,2008,387:2972-2980.
[87] Han D D. Network Topology of the Austrian Airline Flights. Arxiv preprintphysics/0703193,2007(1):1-7.
[88] Newman M E J, Watts D J.Scaling and percolation in the small-world network model.Physical review E,1999,60(6):7332-7342.
[89]章忠志,荣莉莉. BA网络的一个等价演化模型.系统工程，2005，23（2）：1-5.
[90]陈禹，宗骁，郝杰等. BA模型的三种扩展.系统工程学报，2005，20（2）：120-127.
[91] Li X, Chen G. A local-world evolving network model. Physica A: Statistical Mechanicsand its Applications,2003,328:274-286.
[92] Cao Y J, Wang G Z, Jiang Q Y and et al. A neighbourhood evolving network model,2006,349:462-466.
[93] Jost J, Joy M.Evolving networks with distance preferences. Physical Review E,2002,66(3):1-7.
[94] Chen Q, Shi D.The modeling of scale-free networks. Physica A: Statistical Mechanics andits Applications,2004,335:240-248.
[95]李增扬,韩秀萍,陆君安等.内部演化的BA无标度网络模型.复杂系统与复杂性科学,2005,2(2):1-6.
[96]蒋品群,罗晓曙,汪秉宏等.一个新的演化网络模型中节点的吸引力研究.广西师范大学学报,2009,27(4):15-18.
[97]李季,汪秉宏,蒋品群等.节点数加速增长的复杂网络生长模型.物理学报，2006，55（8）：4051-4057.
[98] Zhang X, Zhao Q. Degree distribution of a new model for evolving.2010，74(3):469-474.
[99] Xu X.-J, Hu X.-M, Zhang L.-J.Network evolution by nonlinear preferential rewiring ofedges. Physica A: Statistical Mechanics and its Applications,2011,390(12):2429-2434.
[100] Wang W X, Wang B H, Hu B and et al. General Dynamics of Topology and Traffic onWeighted Technological Networks. Physical Review Letters,2005,94(18):1-4.
[101]汪秉宏,王文旭,周涛.交通流驱动的含权网络.物理，2006,35(4):304-310.
[102]钱江海,韩定定.基于预期流优化的空间网络引力模型.物理学报，2009,58(5):3028-3033.
[103] Qian J.-H, Han D.-D.A spatial weighted network model based on optimal expected traffic.Physica A: Statistical Mechanics and its Applications,2009,88(19):4248-4258.
[104] Zhao H, Gao Z Y. Weighted Networks Model Based on Traffic Dynamics with LocalPerturbation. Communications in Theoretical Physics,2007,48(5):953-956.
[105] Wang W.-X, Hu B, Zhou T and et al.Mutual selection model for weighted networks. Phy-sical Review E,2005,72(4):1-8.
[106] Pan Z, Li X, Wang X.Generalized local-world models for weighted networks. PhysicalReview E,2006,73(5):1-9.
[107] Sun X, Feng E, Li J.From unweighted to weighted networks with local information.Physica A: Statistical Mechanics and its Applications,2007,385(1):370-378.
[108] Antal T, Krapivsky P. Weight-driven growing networks. Physical Review E,2005.71(2):1-6.
[109] Yang X, Jiang F, Chen S. Modeling Evolution of Weighted Clique Networks. Commu-nications in Theoretical Physics,2011,56(5):952-956.
[110] Cholvi V, Laderas V, López L and et al. Self-adapting network topologies in congestedscenarios. Physical Review E,2005,71(3):1-4.
[111] Guimerà R, Díaz-Guilera A, Vega-Redondo F and et al. Optimal Network Topologies forLocal Search with Congestion. Physical Review Letters,2002,89(24):1-4.
[112] Wang W.-X, Wang B H, Yin C Y and et al. Traffic dynamics based on local routingprotocol on a scale-free network. Physical Review E,2006,73(2):1-7.
[113] Wang W.-X, Yin C Y, Yan G and et al. Integrating local static and dynamic informationfor routing traffic. Physical Review E,2006,74(1):1-5.
[114] Hu M B, Jiang R, Wu Y H and et al. Routing on a weighted scale-free network. PhysicaA: Statistical,2008,387:4967-4972.
[115] Yan G, Zhou T, Hu B and et al. Efficient routing on complex networks. Physical Review E,2006,73(4):1-5.
[116] Ling X, Hu M B, Jiang R and et al. Pheromone routing protocol on a scale-free network.Physical Review E,2009,80(6):3-7.
[117] Newman M E J. Spread of epidemic disease on networks. Physical Review E,2002,66(1):1-11.
[118] Hufnagel L, Brockmann D, Geisel T.Forecast and control of epidemics in a globalizedworld. Proceedings of the National Academy of Sciences of the United States of America,2004,101(42):15124-15129.
[119] Pastor-Satorras R, Vespignani A. Epidemic Spreading in Scale-Free Networks. PhysicalReview Letters,2001,86(14):3200-3203.
[120] Ni S, Weng W, Shen S and et al. Epidemic outbreaks in growing scale-free networks withlocal structure. Physica A: Statistical Mechanics and its Applications,2008,387(21):5295-5302.
[121] Ni S, Weng W, Fan W. Threshold of sis epidemics. Acta physica polonica B,2008,39(3):739-749.
[122] Barthélemy M, Barrat A, Pastor-Satorras R and et al. Velocity and Hierarchical Spread ofEpidemic Outbreaks in Scale-Free Networks. Physical Review Letters,2004,92(17):18-21.
[123] Yan G, Zhou T, Wang J and et al. epidemic spreading in weighted scale free networks.Chinese Physics Letters,22(2):510-513.
[124] Motter A, Lai Y.-C.Cascade-based attacks on complex networks. Physical Review E,2002,66(6):2-5.
[125] Motter A E. Cascade Control and Defense in Complex Networks. Physical Review Letters,2004,93(9):1-4.
[126] Wang J.-W, Rong L.-L.Cascade-based attack vulnerability on the US power grid. SafetyScience,2009,47(10):1332-1336.
[127]谢丰,程苏琦,陈冬青等.基于级联失效的复杂网络抗毁性.清华大学学报，2011，51(10):1252-1257.
[128] Bao Z. J, Y. J. Cao,L. J. Ding and et al.Comparison of cascading failures in small-worldand scale-free networks subject to vertex and edge attacks. Physica A: StatisticalMechanics and its Applications,2009,388(20):4491-4498.
[129]李勇,吴俊,谭跃进.容量均匀分布的物流保障网络级联失效抗毁性.系统工程学报，2010，25(6):853-860.
[130] Wang W.-X, Chen G.Universal robustness characteristic of weighted networks againstcascading failure. Physical Review E,2008,77(2):1-5.
[131] Mirzasoleiman B, Babaei M, Jalili M and et al.Cascaded failures in weighted networks.Physical Review E,2011,84(4):1-8.
[132]吴金闪,狄增如.从统计物理学看复杂网络研究.物理学进展，2004，24（1）：18-46.
[133]侯振霆，孔祥星，史定华等.BA模型的数学基础.数学物理进展，2010，30A(5):1313-1321.
[134]史定华.网络-探索复杂性的新途径.系统工程学报,2005,20(2):115-120.
[135]史定华.复杂网络的随机刻画和演化规律.力学进展,2008,38(6):679-691.
[136]何大韧,刘宗华，汪秉宏.杂网络研究的一些统计物理学方法及其背景.力学进展，2008，38(6):692-701.
[137]吕琳媛,陆君安,张子柯等.复杂网络观察.复杂系统与复杂性科学,2010,7(2-3):173-186.
[138]章忠志,周水庚,方锦清.复杂网络确定性模型研究的最新进展.复杂系统与复杂性科学,2008,5(4):29-46.
[139] Evans T S. Complex Networks. arxiv.org/cond-mat/0405123v1,2004:1-31.
[140] Dorogovtsev S N, Mendes J F F.Evolution of networks. arXiv:cond-mat/0106144,2001:67-67.
[141] Rodríguez-Martín I, Salazar-González J J.Solving a capacitated hub location problem.European Journal of Operational Research,2008,184(2):468-479.
[142]中国民用航空总局科技规划司.从统计看民航,北京：中国民航出版社,1996-2011.
[143]陈欣.机场空侧容量评估与优化方法研究[博士学位论文]2007.
[144]胡明华，刘松，苏兰根.基于统计分析的单跑道容量估计模型研究.数据采集与处理,2000,15(1):74-77.
[145] Alumur S, Kara B Y.Network hub location problems: The state of the art. EuropeanJournal of Operational Research,2008,190(1):1-21.
[146] Aykin T.The hub location and routing problem. European Journal of Operational Research,1995,83:200-219.
[147] Chen J.-F.A hybrid heuristic for the uncapacitated single allocation hub location problem.Omega,2007,35(2):211-220.
[148]柏明国,朱金福,姚韵.枢纽航线网络的构建方法及应用.系统工程，2006，24(5):29-34.
[149] Sim T, Lowe T J, Thomas B W.The stochastic-hub center problem with service-levelconstraints. Computers&Operations Research,2009,36(12):3166-3177.
[150] Kouvelis P, Y G.Robust Discrete Optimization and its Applications. Boston： KluwerAcademic Publishers，1997．
[151]吴小欢,朱金福，吴薇薇.航线网络区间相对鲁棒优化设计.系统工程学报，2012，27(1):69-78.
[152] Faloutsos M, Faloutsos P, Faloutsos C.On power-law relationships of the internettopology. ACM SIGCOMM Computer Communication Review,1999,251-262.
[153] Zhang J, Cao X, Du W and et al. Evolution of Chinese airport network. Physica A:Statistical Mechanics and its Applications,2010,389(18):3922-3931.
[154] Xu X, Hu J, Liu F and et al.Scaling and correlations in three bus-transport networks ofChina. Physica A: Statistical Mechanics and its Applications,2007,374(1):441-448.
[155] Liu H.-K, Zhang X.-L, Zhou T.Structure and external factors of chinese city airlinenetwork. Physics Procedia,2010,3(5):1781-1789.
[156] Xue T, Chen J, He Y and et al. Complex network properties of Chinese power grid. Intern-ational Journal of Modern Physics B,2010,18(17):2599-2603.
[157] Moreno Y, G′omez J B, Pacheco A F.Instability of scale-free networks under node-bre-aking avalanches. Europhysics Letters,2002,58(4):630-636.
[158] Callaway D S, Newman M E J, Strogatz S H and et al. Network robustness and fragility:Percolation on random graphs. arXiv:cond-mat/0007300,2000:1-4.
[159] Korniss G.Synchronization in weighted uncorrelated complex networks in a noisyenvironment: Optimization and connections with transport efficiency. Physical Review E,2007,75(5):38-41.
[160] Li C, Chen G.A comprehensive weighted evolving network model. Physica A: StatisticalMechanics and its Applications,2004,343:288-294.
[161] Cao Y J, Wang G Z, Jiang Q Y and et al. A neighborhood evolving network model.Physics Letters A,2006,349:462-466.
[162] Zheng J.-F, Gao Z.-Y.A weighted network evolution with traffic flow. Physica A:Statistical Mechanics and its Applications,2008,387(24):6177-6182.
[163] Yin B.-B, Zhu L.-Z, Cai K.-Y.The BA model with finite-precision preferential attachment.Physica A: Statistical Mechanics and its Applications,2009,388(14):2806-2814.
[164] Han D D, Qian J H, Ma Y G.Emergence of double scaling law in complex systems.Europhysics Letters,2011,94(2):1-6.
[165] Ferretti L, Cortelezzi M.Preferential attachment in growing spatial networks. PhysicalReview E,2011,84(1):1-8.
[166] Tong J, Zhang Z, Dai R.Weighted scale-free networks induced by group preferentialmechanism. Physica A: Statistical Mechanics and its Applications,2011,390(10):1826-1833.
[167] Guo W.-P, Li X, Wang X.-F.Epidemics and immunization on Euclidean distance preferredsmall-world networks. Physica A: Statistical Mechanics and its Applications,2007,380:684-690.
[168] Yoo J, Lee J.S, Kahng B.Disease spreading on fitness-rewired complex networks. PhysicaA: Statistical Mechanics and its Applications,2011,390(23):4571-4576.
[169] Lacasa L, Cea M, Zanin M.Jamming transition in air transportation networks. Physica A:Statistical Mechanics and its Applications,2009,388(18):3948-3954.
[170] Guimerà R, Arenas A, D′az-Guilera A and et al. Dynamical properties of modelcommunication networks. Physical Review E,2002,66(2):1-8.
[171] Pu C L, Zhou S Y, Wang K and et al.Efficient and robust routing on scale-free networks.Physica A: Statistical Mechanics and its Applications,2012,391(3):866-871.
[172] Yin C Y, Wang B H, Wang W X and et al. Efficient routing on scale-free networks basedon local information. Physics Letters A,2006,351:220-224.
[173] Tang M, Zhou T. Efficient routing strategies in scale-free networks with limitedbandwidth. Physical Review E,2011,84(2):1-5.
[174] Echenique P, Gómez-Garde es J, Moreno Y.Improved routing strategies for Internettraffic delivery. Physical Review E,2004,70(5):1-4.
[175] Guan Z.-H, Chen L, Qian T.-H.Routing in scale-free networks based on expandingbetweenness centrality. Physica A: Statistical Mechanics and its Applications,2011,390(6):1131-1138.
[176]陈华良,刘忠信,陈增强等.复杂网络的一种加权路由策略研究.物理学报，2009，58(9):6068-6073.
[177] Arenas A, Díaz-Guilera A,Guimerà R.Communication in Networks with HierarchicalBranching. Physical Review Letters,2001,86(14):3196-3199.
[178] Pastor-Satorras R, Vespignani A.Epidemic dynamics and endemic states in complexnetworks. Physical Review E,2001,63(6):1-8.
[179] Bibb Latan′e J H L. Personality Social Psych.1995，21：795.
[180] Wu J J, Sun H J, Gao Z Y.Cascading failures on weighted urban traffic equilibriumnetworks. Physica A: Statistical Mechanics and its Applications,2007,386(1):407-413.
[181] Wang J, Rong L, Zhang L and et al. Attack vulnerability of scale-free networks due tocascading failures. Physica A: Statistical Mechanics and its Applications,2008,387(26):6671-6678.
[182] Wu Z.-X, Peng G, Wang W.-X and et al. Cascading failure spreading on weightedheterogeneous networks. Journal of Statistical Mechanics: Theory and Experiment,2008.2008(5):1-15.
[183] Wang J.-W, Rong L.-L. Effect Attack on Scale-Free Networks due to Cascading Failures.Chinese Physics Letters,2008,25(10):3826-3829.
[184]窦炳琳，张世永.复杂网络上级联失效的负载容量模型.系统仿真学报，2011.23(7):1459-1464.
[185]徐立新，杨建梅，姚灿中等.基于加权网络模型的电网连锁故障分析.控制理论与应用,2011,28(11):1607-1612.
[186] Sun H J, Zhao H, Wu J J.A robust matching model of capacity to defense cascadingfailure on complex networks. Physica A: Statistical Mechanics and its Applications,2008,387:6431-6435.
[187] Ash J, Newth D.Optimizing complex networks for resilience against cascading failure.Physica A: Statistical Mechanics and its Applications,2007,380:673-683.
[188] Zhao H, Gao Z Y.Cascade defense via navigation in scale free networks. The EuropeanPhysical Journal B,2007,57(1):95-101.
[189] Wang B, Kim B J.A high-robustness and low-cost model for cascading failures.Europhysics Letters,2007,78:1-6.
[2]耿淑香.航空公司运营管理方略．北京：中国民航出版社,2000.
[3]柏明国，朱金福.全连通航线网络和枢纽航线网络的比较研究.系统工程理论与实践,2006,(9):113-117.
[4] Pels E, Nijkamp P, Rietveld P. A note on the optimality of airline networks. EconomicsLetters,2000,69(3):429-434.
[5] Brueckner J K. Network structure and airline scheduling. The Journal of IndustrialEconomics,2004,(2):291-312.
[6] Zhang Y. Network structure and capacity requirement: The case of China. TransportationResearch Part E: Logistics and Transportation Review,2010,46(2):189-197.
[7] Hakimi S L. Optimum locations of switching centers and the absolute centers andmedians of a graph,1964,450-459.
[8] Campbell J F. Integer programming formulations of discrete hub location problems.European Journal of Operational Research,1994,72:387-405.
[9] O'Kelly M E. A quadratic integer program for the location of interacting hub facilities.European Journal of Operational Research,1987,32(3): p.393-404.
[10] Davidovi T, Ramljak D, elmi M and et al. Bee colony optimization for the p-centerproblem. Computers&Operations Research,2011,38(10):1367-1376.
[11] O’Kelly M,Skorin-Kapov D, Skorin-Kapov J. Lower bounds for the hub locationproblem1. Manggement Science,1995,41(4)713-721.
[12] Skorin-Kapov D, Skorin-Kapov J, O'Kelly M. Tight linear programming relaxations ofuncapacitated p-hub median problems. European Journal of Operational Research,1996,94(3):582-593.
[13] Ernst A T, Krishnamoorthy M. Efficient algorithms for the uncapacitated single allocationp-hub median problem, Location Science,1996,4(3): p.139-154.
[14] Ebery J. Solving large single allocation p-hub problems with two or three hubs. EuropeanJournal of Operational Research,2001,128(2):447-458.
[15] O'Kelly M E, BRYAN D, SKORIN-KAPOV D and et al. Hub network design withsingle and multiple allocation: A computational study. Location Science,1996,4(3):125-138.
[16] Sohn J, Park S. Efficient solution procedure and reduced size formulations for p-hublocation problems. European Journal of Operational Research,1998,118-126.
[17] Skorin-Kapov D, Skorin-Kapov J.On tabu search for the location of interacting hubfacilities,1994.73:502-509.
[18] Campbell J F. Hub location and the p-hub median problem. Operations Research,1996,44(6):923-935.
[19] Ernst A T, Krishnamoorthy M. An exact solution approach based on shortest-paths forp-hub median problems. Informs Journal on Computing,1998,10(2):149-162.
[20] Pirkul H, Schilling D A.An efficient procedure for designing single allocation hub andspoke systems. Management Science,1998,44(12):235-242.
[21] Smith K, Krishnamoorthy M, Palaniswami M. Neural versus traditional approaches to thelocation of interacting hub facilities. Location Science,1996.4(3):155-171.
[22] Sohn J, Park S. A linear program for the two-hub location problem. European Journal ofOperational Research,1997,100(3):617-622.
[23] Ili A, Aleksandar, Uro evi D,Brimberg J and et al.A general variable neighborhoodsearch for solving the uncapacitated single allocation p-hub median problem. EuropeanJournal of Operational Research,2010,206(2):289-300.
[24] Contreras I, Diaz J a, Fernandez E.Branch and Price for Large-Scale Capacitated HubLocation Problems with Single Assignment. INFORMS Journal on Computing,2011,23(1):41-55.
[25] Campbell J F. Location and allocation for distribution systems with transshipments andtransportation economies of scale. Annals of Operations Research,1992,40:77-99.
[26] Ernst A T, Krishnamoorthy M.Exact and heuristic algorithms for the uncapacitatedmultiple allocation p-hub median problem. European Journal of Operational Research,1998,104:100-112.
[27] Sasaki M, Suzuki A, Drezner Z.On the selection of hub airports for an airlinehub-and-spoke system. Computers&Operations Research,1999,26:1411-1422.
[28] Ernst A T, Krishnamoorthy M. Solution algorithms for the capacitated single allocationhub location problem. Annals of Operations Research,1999,86:141-159.
[29] Ebery J, Krishnamoorthy M, Ernst A and et al. The capacitated multiple allocation hublocation problem: Formulations and algorithms. European Journal of Operational Res-earch,2000,120(3):614-631.
[30] Boland N, Krishnamoorthy M, Ernst A T and et al. Preprocessing and cutting for multipleallocation hub location problems. European Journal of Operational Research,2004,155(3):638-653.
[31] Marín A. Formulating and solving splittable capacitated multiple allocation hub locationproblems. Computers&Operations Research,2005,32(12):3093-3109.
[32] Mar n A, Cánovas L, Landete M. New formulations for the uncapacitated multipleallocation hub location problem. European Journal of Operational Research,2006,172(1):274-292.
[33] Labb M, Yaman H, Gourdin E. A branch and cut algorithm for hub location problems.Math. Program., Ser. A,2005,102:371-405.
[34] Costa M G,Captivo M E, Clímaco J. Capacitated single allocation hub locationproblem—A bi-criteria approach. Computers&Operations Research,2008,35(11):3671-3695.
[35] Contreras I, Cordeau J F, Laporte G.Benders decomposition for large-scale uncapacitatedhub location. Operations Research,2011,59(6):1477-1490.
[36] Hamacher H W, Labbe M, Nickel S and et al. Adapting polyhedral properties fromfacility to hub location problems. Discrete Applied Mathematics,2004,145:104-116.
[37] Ernst A T, Hamacher H, Jiang H and et al.Uncapacitated single and multiple allocationp-hub center problems. Computers&Operations Research,2009,36(7):2230-2241.
[38] Campbell A M, Lowe T J, Zhang L. The p-hub center allocation problem. EuropeanJournal of Operational Research,2007,176(2):819-835.
[39] Meyer T, Ernst A T, Krishnamoorthy M. A2-phase algorithm for solving the singleallocation p-hub center problem. Computers and Operations Research,2009,36(12):3143-3151.
[40] Kara B Y, Tansel B C.The single-assignment hub covering problem: Models andlinearizations. Journal of the Operational Research Society,2003,59-64.
[41] Aykin T. Networking policies for hub-and-spoke systems with application to the airtransportation system,1995,29(3):201-221.
[42] O’Kelly M E, Bryan D L.Hub location with flow economies of scale. TransportationResearch Part B: Methodological,1998,32(8):605-616.
[43] Campbell J F, Ernst A T, Krishnamoorthy M. Hub arc location problems: part I:introduction and results. Management Science,2005,51(10):1540-1555.
[44] Campbell J F. Designing Hub Networks with Connected and Isolated Hubs. Proceedingsof the43rd Hawaii International Conference on System Sciences,2010:1-10.
[45] Kim H. Reliable p-hub location problems and protection models for hub networkdesign[博士学位论文]2008.
[46] Kim H, O'Kelly M E. Reliable p-Hub Location Problems in TelecommunicationNetworks. Geographical Analysis,2009,41(3):283-306.
[47] Sim T, Lowe T J, Thomas B W. The stochastic-hub center problem with service-levelconstraints. Computers& Operations Research,2009,36(12):3166-3177.
[48] Contreras I, Cordeau J F, Laporte G.Stochastic uncapacitated hub location. EuropeanJournal of Operational Research,2011,212(3):518-528.
[49] Yang T H. Stochastic air freight hub location and flight routes planning. AppliedMathematical Modelling,2009,33(12):4424-4430.
[50] Lium A G, Crainic T G, Wallace S W.A Study of Demand Stochasticity in ServiceNetwork Design. Transportation Science,2009,43(2):144-157.
[51] Alumur S A, Nickel S, Saldanha-da-Gama F.Hub location under uncertainty.Transportation Research Part B: Methodological,2012,46(4):529-543.
[52] Kouvelis P, Y G. Robust discrete optimization and its applications. KluwerA cadem icPublishers,Boston,1997.
[53] Guti6rrez G J, Kouvelis P,Kurawarwala A A. A robustness approach to uncapacitatednetwork design problems. European Journal of Operational Research,1996,94:362-376.
[54]姜涛,朱金福.非严格的中枢辐射航线网络设计的鲁棒优化方法.信息与控制，2007，36(5):539-545.
[55]姜涛,朱金福，覃义.基于最短路的中枢辐射航线网络鲁棒优化方法.系统工程，2007，25(1):53-59.
[56]姜涛,朱金福，覃义.中枢辐射航线网络的鲁棒优化方法研究.小型微型计算机系统,2008,29(7):1366-1371.
[57]柏明国,姜涛，朱金福.基于禁忌算法的中枢辐射航线网络鲁棒优化方法.数学的实践和认识,2008,38(13):60-69.
[58] Averbakh I. On the complexity of a class of combinatorial optimization problems withuncertainty. Mathematical Programming,2001,90(2):263-272.
[59] Averbakh I, Lebedev V.Interval data minmax regret network optimization problems.Discrete Applied Mathematics,2004,138(3):289-301.
[60] Kasperski A, Zieliński P.An approximation algorithm for interval data minmax regretcombinatorial optimization problems. Information Processing Letters,2006,97(5):177-180.
[61] Pereira J, Averbakh I. Exact and heuristic algorithms for the interval data robustassignment problem. Computers&Operations Research,2011,38(8):1153-1163.
[62]周涛.复杂网络研究概述.物理，2005，34(1):31-36.
[63] Baggio R, Scott N, Cooper C.Network science: a review focused on tourism. Annals ofTourism Research,2010:1-24.
[64] Erdos P, RBNYI A. On the evolution of random graphs. Transactions of the AmericanMathematical Society,1960,286(1):343-347.
[65] Erdos P, Renyi A. On random graphs,Publications Mathematicae,6,290.,1959.
[66] Watts D J, Strogatz S H.Collective dynamics of 'small-world' networks. Nature,1998,393:440-442.
[67] Barabasi A, Albert R.Emergence of Scaling in Random Networks. Science,1999,286:509-512.
[68]王文旭.复杂网络的演化动力学及网络上的动力学过程研究[博士学位论文]2007.
[69] Newman M. Assortative Mixing in Networks. Physical Review Letters,2002,89(20):1-4.
[70] Goh K.-I, Oh E, Kahng B and et al. Betweenness centrality correlation in social networks.Physical Review E,2003,67(1):1-4.
[71] Ravasz E, Barabási A.-L.Hierarchical organization in complex networks. Physical ReviewE,2003,67(2):1-7.
[72] Barabasi A, Albert R, Jeong H. Mean-field theory for scale-free random networks.1999,272:173-187.
[73] Barrat A, Barthélemy M, Vespignani A. Modeling the evolution of weighted networks.Physical Review E,2004,70(6):1-12.
[74] Barrat A, Barthélemy M, Vespignani A. Weighted Evolving Networks: CouplingTopology and Weight Dynamics. Physical Review Letters,2004,92(22):2-5.
[75] Ebel H,Mielsch L.-I, Bornholdt S.Scale-free topology of e-mail networks. PhysicalReview E,2002,66(3):1-4.
[76] Zhou T, Wang B H.Topological properties of integer networks. Physica A: StatisticalMechanics,2006:12-14.
[77] Amaral L A N, Scala A, Barthelemy M and et al.Classes of small-world networks.Proceedings of the National Academy of Sciences of the United States of America,2000,97(21):11149-11152.
[78] Wang M, Wu B Q, Wu X and et al.The Topological and Statistical Analysis of PublicTransport Network Based on Fuzzy Clustering.2:1183-1191.
[79]刘宏鲲,张效莉,曹崀等.中国城市航线网络航线连接机制分析.中国科学G辑:物理学、力学、天文学,2009,39(7):935-942.
[80]王姣娥,莫辉辉,金凤君.中国航线网络空间结构的复杂性.2009,64(8):899-910.
[81] CHI Li-Ping, WANG Ru, SU Hang and et al. Structural properties of US flight network.Chinese physics,2003,20(8):1393-1396.
[82] Li W, Cai X.Statistical analysis of airport network of China. Physical Review E,2004,69(4):1-6.
[83] Guimer R, Amaral L A N. Modeling the world-wide airport network. The EuropeanPhysical Journal B:Condensed Matter,2004,38(2):381-385.
[84]高峰，党亚茹.世界航空客运网络的节点度分布特征.科学学与科学技术管理,2009,7:75-80.
[85]党亚茹,李雯静.基于网络视角的航空客流结构分析.交通运输系统工程与信息,2010,10:167-174.
[86] Bagler G. Analysis of the airport network of India as a complex weighted network.Physica A,2008,387:2972-2980.
[87] Han D D. Network Topology of the Austrian Airline Flights. Arxiv preprintphysics/0703193,2007(1):1-7.
[88] Newman M E J, Watts D J.Scaling and percolation in the small-world network model.Physical review E,1999,60(6):7332-7342.
[89]章忠志,荣莉莉. BA网络的一个等价演化模型.系统工程，2005，23（2）：1-5.
[90]陈禹，宗骁，郝杰等. BA模型的三种扩展.系统工程学报，2005，20（2）：120-127.
[91] Li X, Chen G. A local-world evolving network model. Physica A: Statistical Mechanicsand its Applications,2003,328:274-286.
[92] Cao Y J, Wang G Z, Jiang Q Y and et al. A neighbourhood evolving network model,2006,349:462-466.
[93] Jost J, Joy M.Evolving networks with distance preferences. Physical Review E,2002,66(3):1-7.
[94] Chen Q, Shi D.The modeling of scale-free networks. Physica A: Statistical Mechanics andits Applications,2004,335:240-248.
[95]李增扬,韩秀萍,陆君安等.内部演化的BA无标度网络模型.复杂系统与复杂性科学,2005,2(2):1-6.
[96]蒋品群,罗晓曙,汪秉宏等.一个新的演化网络模型中节点的吸引力研究.广西师范大学学报,2009,27(4):15-18.
[97]李季,汪秉宏,蒋品群等.节点数加速增长的复杂网络生长模型.物理学报，2006，55（8）：4051-4057.
[98] Zhang X, Zhao Q. Degree distribution of a new model for evolving.2010，74(3):469-474.
[99] Xu X.-J, Hu X.-M, Zhang L.-J.Network evolution by nonlinear preferential rewiring ofedges. Physica A: Statistical Mechanics and its Applications,2011,390(12):2429-2434.
[100] Wang W X, Wang B H, Hu B and et al. General Dynamics of Topology and Traffic onWeighted Technological Networks. Physical Review Letters,2005,94(18):1-4.
[101]汪秉宏,王文旭,周涛.交通流驱动的含权网络.物理，2006,35(4):304-310.
[102]钱江海,韩定定.基于预期流优化的空间网络引力模型.物理学报，2009,58(5):3028-3033.
[103] Qian J.-H, Han D.-D.A spatial weighted network model based on optimal expected traffic.Physica A: Statistical Mechanics and its Applications,2009,88(19):4248-4258.
[104] Zhao H, Gao Z Y. Weighted Networks Model Based on Traffic Dynamics with LocalPerturbation. Communications in Theoretical Physics,2007,48(5):953-956.
[105] Wang W.-X, Hu B, Zhou T and et al.Mutual selection model for weighted networks. Phy-sical Review E,2005,72(4):1-8.
[106] Pan Z, Li X, Wang X.Generalized local-world models for weighted networks. PhysicalReview E,2006,73(5):1-9.
[107] Sun X, Feng E, Li J.From unweighted to weighted networks with local information.Physica A: Statistical Mechanics and its Applications,2007,385(1):370-378.
[108] Antal T, Krapivsky P. Weight-driven growing networks. Physical Review E,2005.71(2):1-6.
[109] Yang X, Jiang F, Chen S. Modeling Evolution of Weighted Clique Networks. Commu-nications in Theoretical Physics,2011,56(5):952-956.
[110] Cholvi V, Laderas V, López L and et al. Self-adapting network topologies in congestedscenarios. Physical Review E,2005,71(3):1-4.
[111] Guimerà R, Díaz-Guilera A, Vega-Redondo F and et al. Optimal Network Topologies forLocal Search with Congestion. Physical Review Letters,2002,89(24):1-4.
[112] Wang W.-X, Wang B H, Yin C Y and et al. Traffic dynamics based on local routingprotocol on a scale-free network. Physical Review E,2006,73(2):1-7.
[113] Wang W.-X, Yin C Y, Yan G and et al. Integrating local static and dynamic informationfor routing traffic. Physical Review E,2006,74(1):1-5.
[114] Hu M B, Jiang R, Wu Y H and et al. Routing on a weighted scale-free network. PhysicaA: Statistical,2008,387:4967-4972.
[115] Yan G, Zhou T, Hu B and et al. Efficient routing on complex networks. Physical Review E,2006,73(4):1-5.
[116] Ling X, Hu M B, Jiang R and et al. Pheromone routing protocol on a scale-free network.Physical Review E,2009,80(6):3-7.
[117] Newman M E J. Spread of epidemic disease on networks. Physical Review E,2002,66(1):1-11.
[118] Hufnagel L, Brockmann D, Geisel T.Forecast and control of epidemics in a globalizedworld. Proceedings of the National Academy of Sciences of the United States of America,2004,101(42):15124-15129.
[119] Pastor-Satorras R, Vespignani A. Epidemic Spreading in Scale-Free Networks. PhysicalReview Letters,2001,86(14):3200-3203.
[120] Ni S, Weng W, Shen S and et al. Epidemic outbreaks in growing scale-free networks withlocal structure. Physica A: Statistical Mechanics and its Applications,2008,387(21):5295-5302.
[121] Ni S, Weng W, Fan W. Threshold of sis epidemics. Acta physica polonica B,2008,39(3):739-749.
[122] Barthélemy M, Barrat A, Pastor-Satorras R and et al. Velocity and Hierarchical Spread ofEpidemic Outbreaks in Scale-Free Networks. Physical Review Letters,2004,92(17):18-21.
[123] Yan G, Zhou T, Wang J and et al. epidemic spreading in weighted scale free networks.Chinese Physics Letters,22(2):510-513.
[124] Motter A, Lai Y.-C.Cascade-based attacks on complex networks. Physical Review E,2002,66(6):2-5.
[125] Motter A E. Cascade Control and Defense in Complex Networks. Physical Review Letters,2004,93(9):1-4.
[126] Wang J.-W, Rong L.-L.Cascade-based attack vulnerability on the US power grid. SafetyScience,2009,47(10):1332-1336.
[127]谢丰,程苏琦,陈冬青等.基于级联失效的复杂网络抗毁性.清华大学学报，2011，51(10):1252-1257.
[128] Bao Z. J, Y. J. Cao,L. J. Ding and et al.Comparison of cascading failures in small-worldand scale-free networks subject to vertex and edge attacks. Physica A: StatisticalMechanics and its Applications,2009,388(20):4491-4498.
[129]李勇,吴俊,谭跃进.容量均匀分布的物流保障网络级联失效抗毁性.系统工程学报，2010，25(6):853-860.
[130] Wang W.-X, Chen G.Universal robustness characteristic of weighted networks againstcascading failure. Physical Review E,2008,77(2):1-5.
[131] Mirzasoleiman B, Babaei M, Jalili M and et al.Cascaded failures in weighted networks.Physical Review E,2011,84(4):1-8.
[132]吴金闪,狄增如.从统计物理学看复杂网络研究.物理学进展，2004，24（1）：18-46.
[133]侯振霆，孔祥星，史定华等.BA模型的数学基础.数学物理进展，2010，30A(5):1313-1321.
[134]史定华.网络-探索复杂性的新途径.系统工程学报,2005,20(2):115-120.
[135]史定华.复杂网络的随机刻画和演化规律.力学进展,2008,38(6):679-691.
[136]何大韧,刘宗华，汪秉宏.杂网络研究的一些统计物理学方法及其背景.力学进展，2008，38(6):692-701.
[137]吕琳媛,陆君安,张子柯等.复杂网络观察.复杂系统与复杂性科学,2010,7(2-3):173-186.
[138]章忠志,周水庚,方锦清.复杂网络确定性模型研究的最新进展.复杂系统与复杂性科学,2008,5(4):29-46.
[139] Evans T S. Complex Networks. arxiv.org/cond-mat/0405123v1,2004:1-31.
[140] Dorogovtsev S N, Mendes J F F.Evolution of networks. arXiv:cond-mat/0106144,2001:67-67.
[141] Rodríguez-Martín I, Salazar-González J J.Solving a capacitated hub location problem.European Journal of Operational Research,2008,184(2):468-479.
[142]中国民用航空总局科技规划司.从统计看民航,北京：中国民航出版社,1996-2011.
[143]陈欣.机场空侧容量评估与优化方法研究[博士学位论文]2007.
[144]胡明华，刘松，苏兰根.基于统计分析的单跑道容量估计模型研究.数据采集与处理,2000,15(1):74-77.
[145] Alumur S, Kara B Y.Network hub location problems: The state of the art. EuropeanJournal of Operational Research,2008,190(1):1-21.
[146] Aykin T.The hub location and routing problem. European Journal of Operational Research,1995,83:200-219.
[147] Chen J.-F.A hybrid heuristic for the uncapacitated single allocation hub location problem.Omega,2007,35(2):211-220.
[148]柏明国,朱金福,姚韵.枢纽航线网络的构建方法及应用.系统工程，2006，24(5):29-34.
[149] Sim T, Lowe T J, Thomas B W.The stochastic-hub center problem with service-levelconstraints. Computers&Operations Research,2009,36(12):3166-3177.
[150] Kouvelis P, Y G.Robust Discrete Optimization and its Applications. Boston： KluwerAcademic Publishers，1997．
[151]吴小欢,朱金福，吴薇薇.航线网络区间相对鲁棒优化设计.系统工程学报，2012，27(1):69-78.
[152] Faloutsos M, Faloutsos P, Faloutsos C.On power-law relationships of the internettopology. ACM SIGCOMM Computer Communication Review,1999,251-262.
[153] Zhang J, Cao X, Du W and et al. Evolution of Chinese airport network. Physica A:Statistical Mechanics and its Applications,2010,389(18):3922-3931.
[154] Xu X, Hu J, Liu F and et al.Scaling and correlations in three bus-transport networks ofChina. Physica A: Statistical Mechanics and its Applications,2007,374(1):441-448.
[155] Liu H.-K, Zhang X.-L, Zhou T.Structure and external factors of chinese city airlinenetwork. Physics Procedia,2010,3(5):1781-1789.
[156] Xue T, Chen J, He Y and et al. Complex network properties of Chinese power grid. Intern-ational Journal of Modern Physics B,2010,18(17):2599-2603.
[157] Moreno Y, G′omez J B, Pacheco A F.Instability of scale-free networks under node-bre-aking avalanches. Europhysics Letters,2002,58(4):630-636.
[158] Callaway D S, Newman M E J, Strogatz S H and et al. Network robustness and fragility:Percolation on random graphs. arXiv:cond-mat/0007300,2000:1-4.
[159] Korniss G.Synchronization in weighted uncorrelated complex networks in a noisyenvironment: Optimization and connections with transport efficiency. Physical Review E,2007,75(5):38-41.
[160] Li C, Chen G.A comprehensive weighted evolving network model. Physica A: StatisticalMechanics and its Applications,2004,343:288-294.
[161] Cao Y J, Wang G Z, Jiang Q Y and et al. A neighborhood evolving network model.Physics Letters A,2006,349:462-466.
[162] Zheng J.-F, Gao Z.-Y.A weighted network evolution with traffic flow. Physica A:Statistical Mechanics and its Applications,2008,387(24):6177-6182.
[163] Yin B.-B, Zhu L.-Z, Cai K.-Y.The BA model with finite-precision preferential attachment.Physica A: Statistical Mechanics and its Applications,2009,388(14):2806-2814.
[164] Han D D, Qian J H, Ma Y G.Emergence of double scaling law in complex systems.Europhysics Letters,2011,94(2):1-6.
[165] Ferretti L, Cortelezzi M.Preferential attachment in growing spatial networks. PhysicalReview E,2011,84(1):1-8.
[166] Tong J, Zhang Z, Dai R.Weighted scale-free networks induced by group preferentialmechanism. Physica A: Statistical Mechanics and its Applications,2011,390(10):1826-1833.
[167] Guo W.-P, Li X, Wang X.-F.Epidemics and immunization on Euclidean distance preferredsmall-world networks. Physica A: Statistical Mechanics and its Applications,2007,380:684-690.
[168] Yoo J, Lee J.S, Kahng B.Disease spreading on fitness-rewired complex networks. PhysicaA: Statistical Mechanics and its Applications,2011,390(23):4571-4576.
[169] Lacasa L, Cea M, Zanin M.Jamming transition in air transportation networks. Physica A:Statistical Mechanics and its Applications,2009,388(18):3948-3954.
[170] Guimerà R, Arenas A, D′az-Guilera A and et al. Dynamical properties of modelcommunication networks. Physical Review E,2002,66(2):1-8.
[171] Pu C L, Zhou S Y, Wang K and et al.Efficient and robust routing on scale-free networks.Physica A: Statistical Mechanics and its Applications,2012,391(3):866-871.
[172] Yin C Y, Wang B H, Wang W X and et al. Efficient routing on scale-free networks basedon local information. Physics Letters A,2006,351:220-224.
[173] Tang M, Zhou T. Efficient routing strategies in scale-free networks with limitedbandwidth. Physical Review E,2011,84(2):1-5.
[174] Echenique P, Gómez-Garde es J, Moreno Y.Improved routing strategies for Internettraffic delivery. Physical Review E,2004,70(5):1-4.
[175] Guan Z.-H, Chen L, Qian T.-H.Routing in scale-free networks based on expandingbetweenness centrality. Physica A: Statistical Mechanics and its Applications,2011,390(6):1131-1138.
[176]陈华良,刘忠信,陈增强等.复杂网络的一种加权路由策略研究.物理学报，2009，58(9):6068-6073.
[177] Arenas A, Díaz-Guilera A,Guimerà R.Communication in Networks with HierarchicalBranching. Physical Review Letters,2001,86(14):3196-3199.
[178] Pastor-Satorras R, Vespignani A.Epidemic dynamics and endemic states in complexnetworks. Physical Review E,2001,63(6):1-8.
[179] Bibb Latan′e J H L. Personality Social Psych.1995，21：795.
[180] Wu J J, Sun H J, Gao Z Y.Cascading failures on weighted urban traffic equilibriumnetworks. Physica A: Statistical Mechanics and its Applications,2007,386(1):407-413.
[181] Wang J, Rong L, Zhang L and et al. Attack vulnerability of scale-free networks due tocascading failures. Physica A: Statistical Mechanics and its Applications,2008,387(26):6671-6678.
[182] Wu Z.-X, Peng G, Wang W.-X and et al. Cascading failure spreading on weightedheterogeneous networks. Journal of Statistical Mechanics: Theory and Experiment,2008.2008(5):1-15.
[183] Wang J.-W, Rong L.-L. Effect Attack on Scale-Free Networks due to Cascading Failures.Chinese Physics Letters,2008,25(10):3826-3829.
[184]窦炳琳，张世永.复杂网络上级联失效的负载容量模型.系统仿真学报，2011.23(7):1459-1464.
[185]徐立新，杨建梅，姚灿中等.基于加权网络模型的电网连锁故障分析.控制理论与应用,2011,28(11):1607-1612.
[186] Sun H J, Zhao H, Wu J J.A robust matching model of capacity to defense cascadingfailure on complex networks. Physica A: Statistical Mechanics and its Applications,2008,387:6431-6435.
[187] Ash J, Newth D.Optimizing complex networks for resilience against cascading failure.Physica A: Statistical Mechanics and its Applications,2007,380:673-683.
[188] Zhao H, Gao Z Y.Cascade defense via navigation in scale free networks. The EuropeanPhysical Journal B,2007,57(1):95-101.
[189] Wang B, Kim B J.A high-robustness and low-cost model for cascading failures.Europhysics Letters,2007,78:1-6.