Boundary-Constrained Max-p-Regions Problem and Its Heuristic Algorithm

The boundary-constrained max-p-regions problem is proposed to tackle the automatic regionalization problem in urban space with respect to constraining regions by boundaries. On the premise of maximized the number of regions p, a weighted objective function considering the subordinate uncertainfy of spatial elements is designed to deal with the subordinat uncertainty caused by the intersectiou of elements and multiple boundaries. Besides a threshold constraint and other constraints in the max-p-regions problem, several boundary constraints are incorporated as well. A region would normally be within a certain boundary. If a region crosses boundaries, these boundaries must be encompassed by the region. A Tabu-search based heuristic algorithm is designed and implemented to solve this NP-hard problem. The effectiveness are evaluated through a simulation dataset and a real-world dataset. The results show that the proposed model allows researchers and practitioners flexibly incorporate boundary constraints in real-world problems into the model specification, thus exerts more practical control over the regionalization results.