Zone design using graph partitioning algorithm with multiple criteria, a EDA-based zone design

Abstract

Zone design is a powerful concept in Geographic Information Analysis. It allows data analysts to develop a model not only for displaying zones by selected attributes but more interestingly for discovering hidden pattern within the extent of the zones. In brief, given a zonal data comprises a number of contiguous basic zonal units within a study area, zone design is to aggregate the basic spatial units into given number of regions subject to constraints and objective functions, whereas the objective functions is a series of pattern sensor, each can measure the presence of particular characteristics of interest in the zonal data and can be changed whenever required. This allows analyst to transform the zonal data to regions so that effects of the objective functions and constraints can be visualized on the map. Unfortunately, zone design is a NP-complete problem that polynomial time algorithm is not available and exhaustive search is also impractical to solve the problem. Alternatively, heuristic approach is commonly adopted to tackle the problem within reasonable time. Common heuristic approaches include Hill-climbing, Tabu search and Simulated Annealing. In recent years, new approach like agglomerative clustering, which forms regions by cutting a minimum spanning tree is also introduced. To tackle the zone design problem, this study investigate the use of Estimation of Distribution Algorithms (EDAs), and explore how it can be used to cope with the problem. EDAs are generic evolutionary searching methods that make use of probabilistic models to learn the structure and statistical parameters of a problem domain. Since the models in EDA can handle variables with multiple dependencies, it is common when dealing with variables in spatial data. By adding spatial handling procedure to EDA, this study presents a new way to handle zone design problem and at the same time, overcomes previous limitations in common heuristic approaches. To test the EDA based zone design method, a zonal data based on Large Street Block Groups covering an entire Wan Chai district of Hong Kong is developed. Two encoding methods are used to model zone design solution for searching purpose: group-number encoding, and regional centre encoding. Meanwhile, GA-based zone design is developed for comparison purpose. The EDA-based zone design is compared with the GA-based zone design for finding equal population regions. On the other hand, it is compared with SKATER (regionalization based on removal of edges from a minimum spanning tree) for finding homogenous regions with minimum internal variation. Test results show that the EDA-based zone design manages to generate solutions with better quality in homogeneity and compactness. In reality, zone design problem is naturally a multiple-objective optimization problem. The difficulty to solve this kind of problem is that the objective functions are always conflicting with each other. Therefore, finding a single solution that can fit all the objectives simultaneously is an impossible task. Further to the EDA-based zone design, a variant based on the multiple-objective evolutionary paradigm is developed. Different from its predecessor that can find single optimum only, this variant is aimed to find the Pareto Optimal Set of the problem disregarding any subjective preference. The Pareto Optimal Set allows decision makers to decide which solution to go for that demonstrates a pragmatic way to tackle the zone design problem in reality.