Elsevier

Applied Soft Computing

Volume 12, Issue 9, September 2012, Pages 2790-2800
Applied Soft Computing

Using computational intelligence for large scale air route networks design

https://doi.org/10.1016/j.asoc.2012.03.063Get rights and content

Abstract

Due to the rapid development of air transportation, Air Route Networks (ARNs) need to be carefully designed to improve both efficiency and safety of air traffic service. The Crossing Waypoints Location Problem (CWLP) plays a crucial role in the design of an ARN. This paper investigates this problem in the context of designing the national ARN of China. Instead of adopting the single-objective formulation established in previous research, we propose to formulate CWLP as a bi-objective optimization problem. An algorithm named Memetic Algorithm with Pull–Push operator (MAPP) is proposed to tackle it. MAPP employs the Pull–Push operator, which is specifically designed for CWLP, for local search and the Comprehensive Learning Particle Swarm Optimizer for global search. Empirical studies using real data of the current national ARN of China showed that MAPP outperformed an existing approach to CWLP as well as three well-known Multi-Objective Evolutionary Algorithms (MOEAs). Moreover, MAPP not only managed to reduce the cost of the current ARN, but also improved the airspace safety. Hence, it has been implemented as a module in the software that is currently used for ARN planning in China. The data used in our experimental studies have been made available online and can be used as a benchmark problem for research on both ARN design and evolutionary multi-objective optimization.

Highlights

► We formulate a multi-objective optimization problem for air route networks design. ► We develop a novel Memetic Algorithm to tackle the large-scale optimization problem. ► The problem-specific Pull–Push operator is designed for local search. ► The proposed algorithm outperforms 3 well-known MOEAs.

Introduction

Due to the increase in air transportation and the limited airspace, how to improve the efficiency and safety of Air Traffic Services has become a major concern to both researchers and practitioners in the Air Traffic Management (ATM) domain. This problem is especially important to China, since the number of flight operations in China has doubled during the past 10 years [1].

Air Route Network (ARN), which determines the routes of every flight traveling from one city to another, is the backbone of ATM. The “hardware” basis of an ARN is the airports and the ground navaids, which have been deployed in advance all over the country. For each flight, the aircraft is required to fly along a sequence of navaids. The navigation system on the aircraft can receive signals from a navaid when approaching it, and thus keeps the pilot informed about the current position of the aircraft. Since the routes for different flights may share a common navaid in an ARN, there is a potential risk that two aircrafts approach the same navaid at the same time. In such a case, a flight conflict or even a collision may occur. Besides, even if two routes do not share a common navaid, it is still possible that the flights on them will come across each other in some region in the airspace. Fig. 1 demonstrates both of the above scenarios. In the ARN, the regions that two aircrafts may encounter each other are denoted as points, and thus are referred to as the Crossing Waypoints (CWs) [2]. The path between a pair of points (either CWs or airports) in the ARN is called an air route. Correspondingly, the path of a flight traveling from one airport to another along the ARN is called its trajectory.

Since the trajectories of all flights are determined based on the ARN, designing the topology of ARN is of great importance to ATM. Determining the location of CWs, which will be referred to as the Crossing Waypoints Location Problem (CWLP) hereafter, is the major step of designing an ARN. In early times, CWs were deployed solely based on human experience since the total numbers of CWs and flights were relatively small. However, with the rapid increase of air traffic demand, the number of CWs in an ARN has increased significantly, and manual design is no longer practical. More important, much more air routes are now sharing common CWs and more potential flight conflicts may emerge. Therefore, the location of CWs must be determined even more carefully than in the past so as to guarantee the airspace operational safety, and an automatic approach to CWLP is in great need.

In spite of its importance to the real world, research on CWLP and even the design problem of ARN are still in their infancy. A pioneer work that brought the ARN design problem to academia was conducted by Siddiquee [3]. In that paper, a number of mathematical models were formally established to quantify various attributes of an ARN, such as the number and duration of potential flight conflicts at CWs and the capacity of air routes. These attributes can be employed as criteria for measuring the quality of an ARN, and thus defined the target for later investigations. However, to the best of our knowledge, it was not until recently that some effort had been devoted to developing advanced computational methods to address CWLP. In [4], Mehadhebi proposed an approach in the free route scenario. Aiming at minimizing the total airlines cost subject to the air traffic control constraints, the approach contains two main steps: one is merging two or more CWs, and the other is moving the merged nodes to the optimal locations in order to reduce the density of congested airspace. More recently, Rivière [5], [6] introduced Simulated Annealing (SA) algorithm [7] into the design of ARN in the context of Sector-Less ATM. Specifically, SA is employed to fine-tune the positions of CWs so that the total airlines cost is minimized.

This paper investigates the application of computational intelligence approaches to CWLP in the context of real-world ARN design in China. Briefly speaking, an ARN can be defined as a planar graph, the nodes of which represent the airports and the CWs. The edge between a pair of nodes stands for the air route between them, and the trajectory of a flight is denoted by the path connecting the departure airport, the arrival airport, and all the CWs it passes by. CWLP aims at fine-tuning the location of the nodes corresponding to CWs, so that some criterion measuring the quality of the ARN is maximized/minimized. The challenges brought by the CWLP are mainly two-fold: first, a typical CWLP may involve a large number of design variables. For our case, the ARN of China includes more than 100 airports and several hundred CWs (see Fig. 2 for an illustration). When representing it with a planar graph, the position of each CW is defined by two design variables. Hence, the CWLP to be solved is a large scale continuous optimization problem with hundreds of design variables. Second, the objective functions of CWLP are all non-differentiable or even non-continuous [3], [4], [5], [6]. Therefore, many conventional optimization techniques that are capable of handling large scale problems (e.g., such as Newton/Quasi-Newton method and conjugate gradient method [8], [9]), are not applicable for the CWLP.

The criteria used for measuring the quality of ARNs arise from two major considerations, that is, the operational cost and safety of airspace. For example, total airline cost was employed in both [4] and [5]. In addition, the safety issue has also been taken into account by pre-defining an upper-bound for the flights density at every CW (a criterion measuring the safety at a CW) [4]. Such a scheme may cause difficulties in practice because it is usually hard to determine an appropriate upper-bound for the density in practice. Furthermore, enhancing the airspace safety may inevitably induce more cost. Hence, it is more appropriate to simultaneously consider both total airlines cost and safety and try to seek a good trade-off between them. Motivated by this consideration, we propose formulating CWLP as a bi-objective optimization problem, and solve it using Multi-Objective Evolutionary Algorithms (MOEAs). However, a direct application of existing MOEAs to CWLP might lead to poor performance due to the scale of the problem. Hence, we further developed a novel algorithm, namely Memetic Algorithm with Pull–Push operator (MAPP) to tackle our CWLP. The MAPP employs the Pull–Push (P-P) operator for local search, while the Comprehensive Learning Particle Swarm Optimizer (CLPSO) [10] is utilized to carry out global search. The P-P operator is designed on the basis of specific problem characteristics of CWLP and thereby leads to a more effective problem-solving process. The efficacy of MAPP has been evaluated on real data generated from the national ARN of China. MAPP was shown to be not only capable of improving the current layout of the national ARN of China, but also superior to a number of relevant approaches (including three MOEAs). The major contributions of this work are summarized as below:

  • For the first time, CWLP is formulated as a bi-objective optimization problem, and the MAPP algorithm is proposed to solve it. Although the new CWLP formulation is a natural extension of the existing ones, it will benefit real-world applications significantly.

  • The proposed algorithm has been evaluated in a real-world scenario. The data used in our empirical study have been made available online. Given the lack of benchmark CWLP problems in the literature, we hope our data can serve as a common test-bed for future studies in this domain.

The rest of this paper is organized as follows: Section 2 introduces the problem formulation of the investigated bi-objective CWLP. Section 3 describes the proposed P-P operator as well as the MAPP in detail. The experimental study is presented in Section 4 to analyze P-P operator and to evaluate the effectiveness of our algorithm. Finally, Section 5 concludes this paper and discusses directions for further research.

Section snippets

Problem formulation

In this section, we will present a mathematical formulation of the bi-objective CWLP. Following previous work [3], our formulation is defined on the basis of the three assumptions and principles:

  • 1.

    The ARN is defined as a planar graph, without considering aircrafts’ climbing or descending between different flight levels.

  • 2.

    The trajectory chosen for each flight is always the shortest one on the ARN.

  • 3.

    The required communication, surveillance and navigation service are adequate to support the flight

Memetic Algorithm with Pull–Push operator for CWLP

From Section 2, we may find that calculating the objective function values of CWLP involves solving a combinatorial problem (i.e., determining the trajectories of the flights). Hence, many traditional optimization methods that are based on the derivatives of objective functions are not applicable for CWLP. Instead, black-box optimization methods such as SA and Evolutionary Algorithms (EAs) appear to be promising alternatives. Given the bi-objective formulation of CWLP, basically any existing

Experimental studies

To evaluate the efficacy of the P-P operator and MAPP, three experiments have been carried out. First, the performance of the P-P operator was analyzed with different settings for issues mentioned at the end of Section 3.1. The purpose is to identify appropriate default parameter settings and implementation details for the P-P operator. After that, MAPP with the default parameter settings was evaluated on real data generated from the national ARN of China, and was compared with a conventional

Conclusion and discussions

The design of ARN is of great significance to the real world and can benefit from advanced computational techniques. This paper presented a successful application of computational intelligence to this domain. The CWLP, a major sub-problem of ARN design, has been investigated in the real-world scenario of re-designing the national ARN of China. Unlike previous work, we first formulated CWLP as a bi-objective optimization problem. Then the MAPP algorithm, which is equipped with a novel local

Acknowledgments

This work is partially supported by the National Basic Research Program of China (Grant No. 2011CB707004), and Key Project in the National Science & Technology Pillar Program (Grant No. 2011BAH24B01), and the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 60921001).

Kaiquan Cai was born in Fujian Province, China, in 1981. He received his B.S. degree at Beihang University in 2004, and is currently a Ph.D. candidate there. His specialty is traffic information and control engineering and his research interests include airspace design and air traffic optimization.

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    Kaiquan Cai was born in Fujian Province, China, in 1981. He received his B.S. degree at Beihang University in 2004, and is currently a Ph.D. candidate there. His specialty is traffic information and control engineering and his research interests include airspace design and air traffic optimization.

    Jun Zhang was born in Anhui Province, China, in 1965 and received his M.S. and Ph.D. degrees at Beihang University in 1990 and 2001, respectively. He is currently a Professor of School of Electronic and Information Engineering, Beihang University. His research interests cover modern air traffic management theory and application, traffic information engineering and control.

    Chi Zhou was born in Anhui Province, China, in 1987. She received her B.S. degree at Beihang University in 2009, and is currently a M.S. candidate there. Her research interests include air traffic management and intelligent optimization methods.

    Xianbin Cao was born in Anhui Province, China, in 1969. He received his Ph.D. degree at University of Science and Technology of China in 1996 and currently he is a Professor of Department of Electronic and Information Engineering, Beihang Universit. His research interests include but not limited to intelligent computing, machine learning and pattern analysis and information security.

    Ke Tang was born in Hubei Province, China, in 1981. He received his Ph.D. degree at Nanyang Technological University in Republic of Singapore and currently he is a Professor of School of Computer Science and Technology in University of Science and Technology of China. His research interests cover evolutionary computation, meta-heuristic algorithms and various real-world applications

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