Regionalization Revisited: An Explicit Optimization Approach

Owsinski, J.W. (1980). Regionalization Revisited: An Explicit Optimization Approach. IIASA Collaborative Paper. IIASA, Laxenburg, Austria: CP-80-026

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Abstract

This paper presents an optimization framework for the regionalization problem. Having a set of regions for which an allocation problem is defined in the presence of nonlinear spatial characteristics related to grouping of the regions, one has to solve the allocation-and-grouping problem.

Indications are given as to the nature of nonlinear spatial characteristics, making the grouping aspect of the problem appear together with an exemplary form of the model.

The complexity of a problem thus conceived makes the direct application of complete enumeration, dynamic programming and branch-and-bound impossible. Thus, an iterative scheme is proposed in which the partial and simplified problems are solved at each step of the iterative procedure.

In order to follow this procedure, a method was required that would yield groupings or clusters optimizing a certain objective function. A new, general, objective function for clustering is formulated, providing both optimal partitions and the number of clusters. It is presented along with the method in the second part of the paper in which other methods of solving the regionalization problem are also reviewed.

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