Enhanced region aggregation modeling using improved shape constraints

Robert M Wallace, Purdue University

Abstract

A subset of the general spatial optimization problem is the land acquisition or region aggregation problem. If a particular region is thought of as a continuous surface of non-overlapping parcels, then the region aggregation problem combines individual parcels into a contiguous and well-formed subset that meets the objectives of the user. Region aggregation modeling was applied by Lin and Kao (1999) on a vector data set and Yen (1999) on a raster data set to find the optimal location for a landfill. Brookes (1997) used a type of region aggregation modeling to locate optimal sites for habitat restoration on a raster data set. A necessary requirement in region aggregation modeling is the application of a constraint on the shape of the region. The shape constraint should guide the model to find regions that are both contiguous and generally convex. Without this constraint, the problem degenerates into the more general knapsack problem and the solution is not acceptable. The conventional method of constraining shape in region aggregation modeling is limited, however, and cannot find regions with specific desirable shapes. The research described in this dissertation presents an enhanced formulation of the regional aggregation model that uses a geometric variation of five simple shape descriptors introduced in the field of map analysis by Peura and Iivarinen in 1997. Their technique uses standard two-dimensional polygon descriptors, such as elliptic variance, compactness, and convexity, to distinguish between two planar polygon regions. By geometrically varying these five simple shape descriptors, a more complete mechanism for controlling shape in region aggregation modeling has been developed which can now identify and evaluate regions with specific shape properties. Using the “greedy” principle, a heuristic algorithm has been formulated that is able to find solution regions with specific shape properties and non-inferior cost values for problems represented by either raster or vector data sets. An evaluation demonstrating the capabilities of this algorithm in finding regions with specific shape properties for both the raster and vector data sets is also presented.

Degree

Ph.D.

Advisors

Wright, Purdue University.

Subject Area

Civil engineering|Operations research

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