On solving large p-median problems

Abstract

Incorporating big data in urban planning has great potential for better modeling of urban dynamics and more efficiently allocating limited resources. However, big data may present new challenges for problem solutions. This research focuses on the p-median problem, one of the most widely used location models in urban and regional planning. Similar to many other location models, the p-median problem is non-deterministic polynomial-time hard (NP-hard), and solving large-sized p-median problems is difficult. This research proposes a high performance computing-based algorithm, random sampling and spatial voting, to solve large-sized p-median problems. Instead of solving a large p-median problem directly, a random sampling scheme is introduced to create smaller sub-p-median problems that can be solved in parallel efficiently. A spatial voting strategy is designed to evaluate the candidate facility sites for inclusion in obtaining the final problem solution. Tests with the Balanced Iterative Reducing and Clustering using Hierarchies (BIRCH) data set show that random sampling and spatial voting provides high-quality solutions and reduces computing time significantly. Tests also demonstrate the dynamic scalability of the algorithm; it can start with a small amount of computing resources and scale up and down flexibly depending on the availability of the computing resources.