Balanced Allocation of Multi-criteria Geographic Areas by a Genetic Algorithm
The balanced partitioning of geographic space into regions is a common problem. This Territory Design Problem (TDP) of assigning smaller areas to larger regions with equal potential is a task mainly done manually. Therefore, the result becomes subjective and provides only a roughly approximated balanced result. This work presents an automated allocation of independent areas to regions using the Genetic Algorithm (GA) , which finds an optimally balanced configuration of regions based on multiple criteria. Thereby, spatial constraints are fully respected as (1) all areas remain contiguous within a region and (2) the automated allocation facilitates a compact region shape. The developed algorithm was tested on a case study in the field of sales territory planning. The target of sales territory planning is the optimal distribution of balanced and fair sales areas based on market potentials. Results of our case study demonstrate the effectiveness of our proposed technique to find an optimal structure of sales territories in a reasonable time. The distance that salesmen need to travel is 16% lower than the existing sales territory configuration. This means that the regions are more balanced and more compact. Due to the independent nature of the GA, this method demonstrates a high flexibility to the optimization problem. It can be easily altered to any objective in territory planning as well as to familiar multi-criteria spatial allocation problems in other disciplines.
KeywordsTerritory design problem Combinatorial optimization Graph partitioning Genetic algorithm
This research was supported by the WIGeoGIS GmbH. We wish to thank WIGeoGIS for kindly providing the case study data. We specially thank Michael Steigemann for insightful discussions in the conception of this work.
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