50 Transportation Research Record: Journal of the Transportation Research Board, No. 2214, Transportation Research Board of the National Academies, Washington, D.C., 2011, pp. 50–58. DOI: 10.3141/2214-07 no-frills, low-price basis. Low-cost carriers do not need the cost advan- tages of hub-and-spoke networks because they have low marginal costs per passenger (5). Modeling airline route networks is a crucial step for a system- atic study of the effects of these changes and has attracted the attention of many researchers. For example, to measure the level of spatial concentration of a network, the coefficient of variance, the Herfindahl index, Theil’s entropy measure, the C4-firm concen- tration ratio, and the Gini index are used in the literature (3, 6, 7 ); Williams presents a model to calculate the costs that drive airline route network development from a skeletal network focused on major gateway hubs to a more connected network with secondary hubs bypassing the initial gateways (5); Veldhuis introduces the so-called connectivity matrix to analyze the competitive position of airline networks (8). Complex network theory has also been used to study some aspects of aviation network systems, such as the power laws exhibited by unequal traffic of the passengers in airline networks (9–11). This study will shed some light on the modeling of airline route net- works with complex network techniques. More than modeling, the focus of the study is to develop an effective and efficient genetic algo- rithm (GA) to optimize the topology of airline route networks, which is a major concern of airline companies. Complex networks—that is, networks whose structure is irregular, complex, and dynamically evolving in time—are all common in daily life (12). As a recently developed mathematical framework, complex network theory has good potential for systematically studying airline route networks. Actually, one could consider that the two main categories of today’s airline route networks, point-to-point and hub-and-spoke networks, are engineering examples of the small-world network and the scale- free network, respectively. Therefore, the corresponding concepts, measures, and algorithms developed in complex network theory are likely to be useful in the systematic study of airline route networks. The first objective of this study is to introduce some complex net- work properties suitable for the modeling of airline route networks. On the basis of these ideas, the second objective is to develop an effective and efficient algorithm to optimize the topology of airline route networks. Many algorithms are reported to improve traffic performance based on a given transportation network topology, for example, itinerary planning (13) and traffic flow prediction (14), whereas few are for optimizing the network topology itself. This sit- uation is probably because as the main infrastructure in a transporta- tion system, network topology is usually extremely expensive to change. However, topology optimization is relatively more practi- cable in the case of airline route networks because there is no phys- ical route network as in the road or railway system. As is well known, the optimization of network topology is an NP-hard problem. As large-scale parallel stochastic search and optimization algorithms, GAs, if properly designed, have the capability of producing high- Application of Complex Network Theory and Genetic Algorithm in Airline Route Networks Hao Liu, Xiao-Bing Hu, Saini Yang, Ke Zhang, and Ezequiel Di Paolo To cope with increasing customer demand and market changes, airline companies need to organize and manage their route networks in a more cost-efficient way. In addition, the robustness of flight operations against unpredictable accidents such as terrorist attacks and natural disasters has become more important to airlines. In this study, the con- cepts and techniques from complex network theory are used to model airline route networks, and then an effective and efficient genetic algo- rithm is developed to optimize airline route networks in terms of net- work properties that may have crucial roles to play in improving the cost-effectiveness and reliability of airspace systems. The simulation results illustrate that the work reported in this study has a good poten- tial to improve the topology of airline route networks in terms of given network properties such as operating costs and network robustness. Every airline company needs to organize its service to cover a set of cities of interest by providing either direct or indirect flight connections. An airline route network is a complete set of direct flights provided by the company to cover its targeted destinations. In the past two decades, aviation traffic volume around the world has continued to soar, and the competition between airline compa- nies has become more and more fierce (1). To survive and to make more profit, airline companies have to constantly plan and reorga- nize their route networks in cost-efficient and reliable ways. Par- ticularly after the deregulation of the passenger aviation market at the end of the last century, many trunk-line carriers took advan- tage of the possibilities of the liberalized market and reorganized their networks from point-to-point into hub-and-spoke topologies (2, 3) The hub-and-spoke network requires a concentration of air traffic in both space and time, and consequently flights between medium-sized and small airports were increasingly replaced by indirect flights via central airports, or hubs. These hub-and-spoke networks allow airlines to benefit from cost and demand advan- tages (4). In contrast, some new or recently started airline compa- nies continued operating point-to-point networks on a low-cost, H. Liu and S. Yang, State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University, 19 Xinjiekouwaidajie, Haidian District, Beijing 100875, China. Current affiliation for H. Liu: National ITS Center of Engineering and Technology, Research Institute of Highway, Ministry of Transport, No. 8 Xi Tu Cheng Road, Haidian District, Beijing 100088, China. X.-B. Hu, School of Engineer- ing, University of Warwick, Coventry CV4 7AL, United Kingdom. K. Zhang, National ITS Center of Engineering and Technology, Research Institute of Highway, Ministry of Transport, No. 8 Xi Tu Cheng Road, Haidian District, Beijing 100088, China. E. Di Paolo, Centre for Computational Neuroscience and Robotics, University of Sussex, Brighton BN1 9QH, United Kingdom. Corresponding author: H. Liu, hao.liu@rioh.cn.