Dynamic airspace sectorization via improved genetic algorithm

J. Mod. Transport. (2013) 21(2):117–124 DOI 10.1007/s40534-013-0010-2 Dynamic airspace sectorization via improved genetic algorithm Yangzhou Chen • Hong Bi • Defu Zhang • Zhuoxi Song Received: 4 February 2013 / Revised: 15 March 2013 / Accepted: 20 March 2013 / Published online: 7 June 2013 Ó The Author(s) 2013. This article is published with open access at Springerlink.com Abstract This paper deals with dynamic airspace sectorization (DAS) problem by an improved genetic algorithm (iGA). A graph model is first constructed that represents the airspace static structure. Then the DAS problem is formulated as a graph-partitioning problem to balance the sector workload under the premise of ensuring safety. In the iGA, multiple populations and hybrid coding are applied to determine the optimal sector number and airspace sectorization. The sector constraints are well satisfied by the improved genetic operators and protect zones. This method is validated by being applied to the airspace of North China in terms of three indexes, which are sector balancing index, coordination workload index and sector average flight time index. The improvement is obvious, as the sector balancing index is reduced by 16.5 %, the coordination workload index is reduced by 11.2 %, and the sector average flight time index is increased by 11.4 % during the peak-hour traffic. Keywords Dynamic airspace sectorization (DAS)  Improved genetic algorithm (iGA)  Graph model  Multiple populations  Hybrid coding  Sector constraints 1 Introduction In air traffic management, airspace is often partitioned into sectors, and each of the sectors is controlled by one or several controllers. Airspace sectorization is to determine reasonable sector number and sector structure such that air Y. Chen  H. Bi (&)  D. Zhang  Z. Song College of Electronic Information and Control Engineering, Beijing University of Technology, Beijing 100124, China e-mail: traffic safety and efficiency are ensured. Dynamic airspace sectorization (DAS) is to divide the airspace into several sectors according to the traffic situation. Recently, DAS becomes an important issue, and many approaches have been proposed to solve the problem. Traffic safety and efficiency are ensured by balancing the controller’s workloads between sectors and making them within a reasonable threshold on the basis of traffic situation. Apart from this, the sectors are required to meet the convexity constraint, connectivity constraint, minimum distance constraint, and minimum sector crossing time constraint [1, 2]. Up to now, genetic algorithm (GA) has been applied in DAS approaches. It was first attempted by Delahaye et al. [3, 4], who proposed two approaches, one based on weighted graph and the other using Voronoi diagram model of the airspace. Xue [5] further improved the GA efficiency by combining the algorithm with an iterative deepening algorithm, and then directly applied it to a real flight track data. In recent years, the study of DAS has been extended from 2D airspace to 3D airspace [6–8]. They used Voronoi diagram, cells and agent-based models to establish the airspace model. These models are based on the generating points or seed points, and point locations are optimized by applying GAs to realize optimal sectors. As to 3D airspace. Tang et al. [9, 10] proposed an improved agentbased model (iABM), and combined it with GA to achieve the optimized sectorization. He also identified the gaps in the iABM and three additional models such as KD-tree, graph bisection, and Voronoi diagram in 3D, and evaluated their constraints and objective indices. The aforementioned researches used GA in a way similar to Ref. [4] and made improvements in different aspects. However, one limitation of these works is that in each generation the fitness of every individual must be calculated on 123 118 Y. Chen et al. the basis of the new partitions. These new partitions are produced by performing the model algorithm time and again after accomplishing GA operators, resulting in lower algorithm efficiency. Another limitation is that in the design of GA the emphasis was to establish a relation between the multi-objectives of DAS and the fitness function, while the sector constraints were not considered. In fact, the sector constraints cannot be completely satisfied because of the limitation of model algorithm (see [9] for the details). Figure 1 shows an example of Voronoi diagram. Although the safety distance and residence time are taken into account in the fitness function, boundaries may superimpose on the airroutes or key-points, and it is hard to satisfy the minimum distance constraint. This is because the airspace structure is taking into account when establishing model. In this paper, we discuss the feasibility of full application of GA in DAS by improving the method in Ref. [3]. The improved GA (iGA) can overcome the aforementioned shortages in the previous works. By using several populations competed genetic algorithm (SPCGA) [11], the optimal sector number and airspace sectorization can be determined. We also studied the search capability by adding a crossover operator and designed a repair strategy to meet the convexity constraint. 2 Weighed graph model of airspace In this section, we will first set up an airspace model by using a weighed graph. The model is limited to 2D airspace, because the DAS in 2D airspace is easily extended to the one in 3D airspace. The vertices of the weighed graph consist of key-points of the airspace such as airports, waypoints, conflict points, etc., and its edges describe the air-routes between these key-points. Both of the vertices and edges are endowed with weighed values representing workloads of controllers in the airspace. 2.1 Establishing the weighed graph Static structural information in airspace includes air-routes, locations of key-points (airports, waypoints, conflict points), etc. The key-points are described as the vertices of an undirected graph. The air-routes between airports and waypoints are described as the edges of the undirected graph. That is, we set up a graph G = {V, E} with the set of vertices V and the set of edges E to describe the airspace structure. Most of the air-routes in China airspace are fixed. Figure 2 shows the distribution of air-routes and key-points of North China airspace. We choose the main airspace of North China based on Fig. 2 to establish the undirected graph as shown in Fig. 3. Next, we endow the vertices and edges of the graph with workloads of controllers. Workloads consist of the three styles, i.e., monitoring workload, coordination workload, and conflict avoidance workload [12]. Each style is calculated on the basis of airspace complexity and then added to the undirected graph. Monitoring workload and conflict avoidance workload are endowed to vertices, and coordination workload is to the edges. Thus, we have the final weighted graph that describes both of static structural informat (...truncated)