Identifying vital edges in Chinese air route network via memetic algorithm

📝 Abstract

Due to its rapid development in the past decade, air transportation system has attracted considerable research attention from diverse communities. While most of the previous studies focused on airline networks, here we systematically explore the robustness of the Chinese air route network, and identify the vital edges which form the backbone of Chinese air transportation system. Specifically, we employ a memetic algorithm to minimize the network robustness after removing certain edges hence the solution of this model is the set of vital edges. Counterintuitively, our results show that the most vital edges are not necessarily the edges of highest topological importance, for which we provide an extensive explanation from the microscope of view. Our findings also offer new insights to understanding and optimizing other real-world network systems.

💡 Analysis

Due to its rapid development in the past decade, air transportation system has attracted considerable research attention from diverse communities. While most of the previous studies focused on airline networks, here we systematically explore the robustness of the Chinese air route network, and identify the vital edges which form the backbone of Chinese air transportation system. Specifically, we employ a memetic algorithm to minimize the network robustness after removing certain edges hence the solution of this model is the set of vital edges. Counterintuitively, our results show that the most vital edges are not necessarily the edges of highest topological importance, for which we provide an extensive explanation from the microscope of view. Our findings also offer new insights to understanding and optimizing other real-world network systems.

📄 Content

Identifying vital edges in Chinese air route network via memetic algorithm Wen-Bo Dua,b, Bo-Yuan Lianga,b, Gang Yanc, Oriol Lordand, Xian-Bin Caoa,b* aSchool of Electronic and Information Engineering, BeihangUniversity, Beijing 100191, P.R.China bBeijing Key Laboratory for Network-based Cooperative Air Traffic Management, Beijing 100191, P.R.China c School of Physics Science and Engineering, Tongji University, Shanghai 200092, P. R. China dUniversitat Politècnica de Catalunya-BarcelonaTech, C/Colom no. 11, Terrassa 08222, Spain Abstract Due to its rapid development in the past decade, air transportation system has attracted considerable research attention from diverse communities. While most of the previous studies focused on airline networks, here we systematically explore the robustness of the Chinese air route network, and identify the vital edges which form the backbone of Chinese air transportation system. Specifically, we employ a memetic algorithm to minimize the network robustness after removing certain edges hence the solution of this model is the set of vital edges. Counterintuitively, our results show that the most vital edges are not necessarily the edges of highest topological importance, for which we provide an extensive explanation from the microscope of view. Our findings also offer new insights to understanding and optimizing other real-world network systems.

Keywords: vital edges; air route network; memetic optimization.

1. Introduction1 With the increasing people and goods transport demand during the accelerating globalization process, the air transportation system plays a more and more important role than ever before due to its high-speed and high-security advantages. For example, the air transport volume of China grows at an average annual speed of over 10% in the past decades, and now it possesses over one seventh of the total comprehensive transport volume (including roadways, railways, shipping and air transport), which was only 7.9% in 2000. Hence the air transportation system has been drawing much attention from different research communities. One of the most interesting directions is to analyze the structure and function of air transportation systems within the framework of complex network theory. The air transportation system can be represented as a network, in which nodes denote airport and an edge will be created if there is a direct flight between two airports. In the vast majority of previous literature, the air transport network (ATN) was primarily classified into two scales: worldwide and national.
   For the worldwide scale, Amaral et al. firstly found worldwide ATN is a small-world network with a power-law degree distribution, and the highest-degree airport is not necessarily the most central node, prompting them to propose a network model where both geographical and political factors are taken into account[1-2]. Barrat et al. investigated the worldwide ATN from a perspective of complex weighted networks and found the nonlinear positive correlation between flight flow and topology properties[3-4]. They proposed a weighted network model, enlightening the understanding of weighted feature of complex systems. Verma et al. decomposed the worldwide ATN into three distinct layers via k-core decomposition and found that this network is robust to the removal of long distance edges, but fragile to the disconnectivity of short and apparently insignificant edges[5-6].
   For the national scale, ATNs of several major nations, such as US, Brazil, India and China, are extensively studied[3, 7-11], and the national ATNs usually exhibit different features from the worldwide ATN. Gautreau et al. studied US ATN during 1990–2000[3]. A remarkable result they presented is that although most statistical properties are stationary, an intense activity takes place at the local level. Fleurquin et al. proposed a delay propagation model via quantifying the network congestion for US ATN, revealing that even under normal operating condition the systemic instability risk is

*Corresponding author. Tel.: +86-10-82314318 E-mail address: xbcao@buaa.edu.cn

non-negligible[11]. Rocha investigated the Brazilian ATN during 1995-2006, and found that it shrank in topology but grew in traffic volume [7]. Bagler et al. studied the Indian ATN, and found its signature of hierarchy feature[12]. As the most active economy, the Chinese aviation industry ranks second to US in the past decade and keeps a high increase rate. Consequently, Chinese ATN attracts continuous attention in different aspects, from topology to dynamics and evolution [8-10, 13-14], one of which is to investigate the backbone of ATN, the air route network (ARN). ATN is actually a logic network with Origin-Destination (OD) relationships. In real air traffic operation, a flight does not straightly fly from departure airport to landing a

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