A Multistart Heuristic Approach to Spatial Aggregation Problems

Abstract

GIScience 2016 Short Paper Proceedings A Multistart Heuristic Approach to Spatial Aggregation Problems Ningchuan Xiao 1 , Peixuan Jiang 2 , Myung Jin Kim 3 , Anuj Gadhave 4 Department of Geography, Ohio State University, Columbus, OH 43210 Email: xiao.37@osu.edu 2 Esri, Redlands, CA, 92373 3 Gyeonggi Institute of Science and Technology Promotion, Suwon, Gyeonggi, Korea 4 Department of Computer Science and Engineering, Ohio State University, Columbus, OH 43210 Abstract In this paper, we present a heuristic method that can be used to search for a diverse set of solutions to spatial aggregation problems. The algorithm is developed using a multistart strategy. Computational experiments are conducted to test the effectiveness of the algorithm. Spatial data are often aggregated for different purposes. The census data in the United States, for example, are aggregated into levels such as blocks, block groups, and tracts. In another example, political redistricting requires the aggregation of spatial units into districts such that some objectives can be optimized. Though aggregation is a common exercise in the use of spatial data, it has been noted that many of the aggregations are arbitrary and may not provide effective spatial units for applications (Martin, 1998; Cockings and Martin, 2005), which often leads to the modifiable areal unit problem (Openshaw, 1983). Equally important is the multiplicity of spatial aggregations: given an aggregation of spatial units, many equivalent schemes may also exist. For example, there often exist many perfect political redistricting plans when population equality is the only objective (Kim and Xiao, 2016). Subsequently, it is important to explore a diverse set of aggregation schemes in order to fully understand the complexity of aggregation. Researchers have developed a wide range of methods that can be used to solve aggregation problems (Openshaw and Rao, 1995; Xiao, 2008). However these methods are designed for specific purposes and they generally do not aim to explore the complexity of aggregation. The purpose of this paper is to develop a heuristic method that can be used to find, not one, but a diverse set of high quality solutions to an aggregation problem. This method first uses a search algorithm to find a set of good solutions. These solutions are stored in a pool and another algorithm is developed to improve the solutions in the pool by recombining them into new solutions. This method is heuristic, meaning it cannot guarantee optimal solutions be found, and we test its effectiveness using a set of benchmark problems. We have tested the multistart algorithm with a wide range of data. Due to the page limit of this abstract, we discuss the first data set of Iowa congressional redistricting for year 2000. The Iowa Constitution dictates that the counties shall not be split for political redistricting purposes, which make it a problem of aggregating 99 spatial units into 5 regions. The official 2000 plan has an objective function value of 0.0080, and the literature has documented a number of redistricting