• Geocomputational Approaches to Improve Problem Solution in Spatial Optimization: A Case Study of the p-Median Problem

      Tong, Daoqin; Mu, Wangshu; Tong, Daoqin; Plane, David A.; Christopherson, Gary L. (The University of Arizona., 2018)
      The p-Median problem (PMP) is one of the most widely applied location problems in urban and regional planning to support spatial decision-making. As an NP-hard problem, the PMP remains challenging to solve optimally, especially for large-sized problems. This research focuses on developing geocomputational approaches to improve the effectiveness and efficiency of solving the PMP. This research also examines existing PMP methods applied to choropleth mapping and proposes a new approach to address issues associated with uncertainty. Chapter 2 introduces a new algorithm that solves the PMP more effectively. In this chapter, a method called the spatial-knowledge enhanced Teitz and Bart heuristic (STB) is proposed to improve the classic Teitz and Bart (TB) heuristic.. The STB heuristic prioritizes candidate facility sites to be examined in the solution set based on the spatial distribution of demand and candidate facility sites. Tests based on a range of PMPs demonstrate the effectiveness of the STB heuristic. Chapter 3 provides a high performance computing (HPC) based heuristic, Random Sampling and Spatial Voting (RSSV), to solve large PMPs. Instead of solving a large-sized PMP directly, RSSV solves multiple sub-PMPs with each sub-PMP containing a subset of facility and demand sites. Combining all the sub-PMP solutions, a spatial voting strategy is introduced to select candidate facility sites to construct a PMP for obtaining the final problem solution. The RSSV algorithm is well-suited to the parallel structure of the HPC platform. Tests with the BIRCH dataset show that RSSV 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 or down when the availability of computing resources changes. Chapter 4 provides a new classification scheme to draw choropleth maps when data contain uncertainty. Considering that units in the same class on a choropleth map are assigned the same color or pattern, the new approach assumes the existence of a representative value for each class. A maximum likelihood estimation (MLE) based approach is developed to determine class breaks so that the overall within-class deviation is minimized while considering uncertainty. Different methods, including mixed integer programming, dynamic programming, and an interchange heuristic, are developed to solve the new classification problem. The proposed mapping approach is then applied to map two American Community Survey datasets. The effectiveness of the new approach is demonstrated, and the linkage of the approach with the PMP method and the Jenks Natural Breaks is discussed.