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neighboring basic units in order of decreasing distance until the desired district size
is reached. Variations exist with respect to the selection of seeds, whether districts
grow simultaneously or sequentially around the seeds, and how to deal with enclaves
of unassigned basic units which typically occur at the end of this greedy process
(Bodin and Levy
1991
; Williams
1995
; Mehrotra et al.
1998
; Bozkaya et al.
2003
).
The resulting districting plans are not always connected or balanced and typically
serve as a starting point for a meta heuristic.
A different approach treats each basic unit initially as a single district and then
merges iteratively pairs of districts until the prescribed number of districts is reached
(Deckro
1977
).
23.5.5
Meta Heuristics
There exists a wide range of meta heuristics that have been applied to districting
problems: Simulated Annealing (D'Amico et al.
2002
), Tabu Search (Ricca and
Simeone
2008
; Bozkaya et al.
2003
), GRASP (Ríos-Mercado and Fernández
2009
;
Salazar-Aguilar et al.
2013b
), and Genetic algorithms (Forman and Yue
2003
;
Bergey et al.
2003
; Bação et al.
2005
), just to name a few. A major advantage
of these methods is their flexibility to include almost any practical criterion and
measure for the design of districts.
23.6
Conclusions
Despite the large number of publications, it is striking that only few authors consider
the districting problem independently from a practical background. Moreover, there
is no consensus on which criteria are eligible and important and, on how to
measure them appropriately. Thus, instead of devising yet another (variant of a)
meta heuristic for a districting model with yet another measure for compactness
or additional constraint, research should foremost concentrate on a common and
generic framework for districting problems. And it should try to categorize the
suitability of criteria and measures based on the availability of data, the geometric
representation of the basic units, and the different types of applications.
Acknowledgements
This work was partly supported by grant NI 521/6-1 of the German Research
Foundation (DFG). This support is gratefully acknowledged.
