Computational methods for airspace sectorisation

A problem of combining elementary sectors of an airspace region is considered, in which a minimum number of combined sectors must be obtained with restrictions on their load and feasibility of combinations such as the requirement of the space connectivity or the membership of a given set of permissible combinations. Computational methods are proposed and tested to be used for solution of general problems of airspace sectorization. In particular, two types of combinatorial algorithms are proposed for constructing partitions of a finite set with specified element weights and graph-theoretical relationships between the elements. Partitions are constructed by use of a branch and bound method to minimize the number of subsets in the final partition, while limiting the total weight of elements in the subset. In the first type algorithm, ready-made components of the final partition are formed in each node of the branch and bound tree. The remaining part of the original set is further divided at the lower nodes. In the second type algorithm, the entire current partition is formed in each node, the components of which are supplemented at the lower nodes. When comparing algorithms performance, the problems are divided into two groups, one of which contains a connectivity requirement, and the other does not. Several integer programming formulations are also presented. Computational complexity of two problem variants is established: a bin packing type problem with restrictions on feasible combinations, and covering type problem.