Cooperative Co-evolution with Weighted Random Grouping for Large-Scale Crossing Waypoints Locating in Air Route Network

The large-scale Crossing Waypoints Location Problem (CWLP) is a crucial problem in the design of Air Route Network (ARN). CWLP is fully non-separable and non-differentiable, and thus traditional algorithms can hardly deal with it. This paper proposes an algorithm named Cooperative Co-evolution with Weighted Random Grouping (CCWR) to tackle it. CCWR employs the weighted random (WR) grouping strategy, which is specifically designed for CWLP, to divide the large-scale Crossing Waypoints (CWs) into small sub-groups and an Evolutionary Algorithm (EA) to solve the smaller scale CWs location problem in each sub-group. Experiments on the database of the ARN in China have been carried out to evaluate the performance of CCWR. The results showed that CCWR is superior to a number of state-of-the-art algorithms, and the advanced performance of CCWR is mainly due to the WR grouping strategy.

I. Introduction

Air Route Network (ARN) plays an important role in transporting air traffic in the airspace. The maximum air traffic flow [1] and the cost of flights are mainly dependent on the structure of ARN. Crossing waypoints (CWs), the intermediate nodes linking the origin and destination airports in an ARN, are of great importance to the performance of an ARN [2]. Firstly, positions of CWs directly determine the Euclidean distance of airlines and thereby determine the total airlines cost. Secondly, as the intersections of air routes, potential flight conflicts will emerge when two aircrafts approach the same CW at the same time. Hence, CWs restrict the safety operation of the whole airspace. For these reasons, it is important to seek the optimal positions of CWs so that the total cost of flights can be minimized and the airspace safety is maintained at a satisfactory level. In [3], this problem is referred to as the Crossing Waypoints Location Problem (CWLP).