Sectorization and Configuration Transition in Airspace Design

Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2016, Article ID 6048326, 21 pages http://dx.doi.org/10.1155/2016/6048326 Research Article Sectorization and Configuration Transition in Airspace Design Xiang Zou, Peng Cheng, Bang An, and Jingyan Song Department of Automation, Tsinghua University, Beijing 100084, China Correspondence should be addressed to Peng Cheng; Received 20 February 2016; Accepted 24 May 2016 Academic Editor: Babak Shotorban Copyright © 2016 Xiang Zou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Current airspace is sectorized according to some predefined rules that are not flexible. To facilitate utilizing the airspace more efficiently, methods to design sectors need to be promoted. In this paper, we propose an undirected graph cut-based approach that employs a memetic local search-embedded constrained evolution algorithm, NSGA-II, to generate nondominated airspace configurations. We also propose a new concave hull-based method to automatically depict sector boundaries. In addition, we also study the configuration transition problem. We define the similarity of the two different configurations and calculate their similarity with a bisection diagram and a minimum cost flow algorithm. We build a forward network to represent configuration transitions across several consecutive time periods and use multiobjective dynamic programming to determine a series of nondominated configuration links from the first period to the end. We test our approaches by simulation in high-altitude airspace controlled by Beijing Area Control Center. The results show that our sectorization method outperforms the current configuration in practice, providing a lower sector number, lower intersector flow, more balanced workload distribution among the different sectors, and no constraint violations, so that the proposed approach shows its significant potential as practical applications for dynamic airspace configuration. 1. Introduction and Literature Review Airspace sectors are basic controlling units in Air Transportation Systems (Figure 1). They were originally designed according to some predefined rules such as historical or geographic considerations or just according to experience. Sectors have essentially remained unchanged in terms of geometric shape and the total number of sectors inside a specific airspace. However, along with rapidly increasing air transportation, fixed sectors cannot accommodate varying traffic flows anymore; several problems have arisen, such as unbalanced workload distribution across different sectors, with overload in some sectors and very sparse flow density in others, and improper sector numbers, which means too many open sectors in off-peak time periods and too few sectors during busy times or too little flight time in a single sector for some flights. Original ideas to deal with the problem of fixed airspace structure is the “Merge and Divide” operation, meaning combining two or more adjacent sectors together when the traffic flow is low and splitting one sector into several during peak hours or choosing one airspace structure from a predefined experienced structure set [1–4]. However, this approach is not flexible enough because the boundaries of these sectors remain unchanged across different time periods. A more advanced concept, called Dynamic Airspace Configuration (DAC), was therefore proposed [5]. In DAC, both the boundaries of the sectors and the number of sectors are allowed to change according to varying traffic situations. One key issue in DAC is the sectorization problem, that is, how to divide an airspace into several sectors. The solution of a sectorization problem is always called the airspace configuration. To the best of our knowledge, the work by Delahaye et al. [6] may be one of the earliest studies to systematically research the sectorization problem, in which the author utilized a genetic algorithm to generate an optimal airspace configuration. Since then, many approaches have been developed. To summarize, relevant methods can be sorted into three categories [7]: (i) Methods based on geometric computation. (ii) Methods by cells (grids) growth (gathering) or by directly clustering trajectory points. 2 Mathematical Problems in Engineering Figure 1: Configuration of Beijing Area Control. (iii) Methods based on undirected graph cuts. In the geometric computation category [8–13], approaches combining Voronoi diagrams with genetic algorithms were proposed in [8–10]. Tang et al. [11] used several kinds of geometric cuts such as bisection cuts and kd trees to split the airspace and compare different cutting methods. In the cell-growth category [11, 14–20], Brinton directly clustered trajectory points to form sectors [14]. Yousefi and Donohue divided an airspace into three layers with different altitude ranges [16, 17]. Each layer was discretized into hexagonal cells, with information about the controller workload. The hexagonal cells were then gathered into sectors. Based on [16], Drew utilized a boundary-smoothing method to eliminating jagged boundary segments [18]. Klein also divided an airspace into hexagonal cells [19], but, in his approach, sectors grew up from a set of seeding cells. The third category [20–24] is in fact another kind of clustering approach, but it is based on a weighted undirected graph and uses one subgraph to represent a sector. Li et al. constructed a weighted graph model that accurately represents the air-route network [21]. The sectorization problem was then formulated as a graph cut problem and solved by iterative spectral bisection. Martinez et al. proposed a method based on a weighted graph and a grid [22] and also utilized spectral bisection to cut the graph. Chen and Zhang proposed a spectral clustering-based approach to clustering vertices [23]. The spectral clustering solution was further refined by the ODLB algorithm and another heuristic algorithm to get better performance in terms of workload balancing. Trandac et al. proposed a method based on Constraint Programming [24]. In [25], Zelinski gave a comprehensive comparison of different approaches. The results showed completely different sector shapes according to the different approaches. The performance of these approaches was evaluated, which revealed their strengths and weaknesses. To summarize, methods using geometric computation are simple and straightforward, but they are optimally inferior because the methods used to cut the plane or space are limited. Although the second category may be the best in terms of workload balancing, it can hardly handle other objectives or constraints in sectorization problems. Approaches based on undirected graph cuts show great potential in managing multiple objectives and constraints. However, the (...truncated)