The paper focuses on a case study of delineating census tracts (CTs) in the Census Metropolitan area of London, Ontario, Canada. The procedure for defining the actual pattern of CTs by a local committee and Statistics Canada has involved such consideration as the compactness of CTs and their population-based and area-based uniformity as well as some subjective aspects. The actual pattern shows that compactness of CTs has been achieved at the expense of uniformity in population and areal sizes. The paper proposes an integer-coded multiobjective genetic algorithm for aggregating census units with the expectation of obtaining a higher level of compactness and population/area uniformity of CTs through an optimization technique. Square-shape and circular-shape compactness of CTs are examined under different scenarios. The results indicate that the proposed genetic algorithm can provide solutions that are considerably better in terms of the Pareto-optimality principle than the actual pattern of CTs.
AertsJ C J HHeuvelinkG B M, 2002, “Using simulated annealing for resource allocation”International Journal of Geographical Information Science16571–587
2.
AertsJ C J Hvan HerwijnenMJanssenRStewartT J, 2005, “Using genetic algorithms and simulated annealing for solving a multisite land use allocation problem”Journal for Environmental Management and Planning48121–142
3.
AlvanidesSOpenshawSReesP, 2002, “Designing your own geographies”, in The Census Data System Eds ReesPMartinDWilliamsonP (John Wiley, New York) pp 47–65
BongC WWangY C, 2004, “A multiobjective hybrid metaheuristic approach for GIS-based spatial zoning model”Journal of Mathematical Modelling and Algorithms3245–261
6.
BozkayaBErkutELaporteG, 2003, “Discrete optimization: A tabu search heuristic and adaptive memory procedure for political districting”European Journal of Operational Research14412–26
7.
CockingsSHarfootAHornbyD, 2009, “Towards 2011 output geographies: Exploring the need for, and challenges involved in, maintenance of the 2001 output geographies”Population Trends13838–39
8.
CohonJ L, 1978Multiobjective Programming and Planning (Academic Press, London)
9.
DamicoS JWangS JBattaRRumpC M, 2002, “A simulated annealing approach to police district design”Computers and Operations Research29667–684
10.
DattaDFigueiraJ R, 2011, “Graph partitioning by multi-objective real-valued metaheuristics: A comparative study”Applied Soft Computing113976–3987
11.
DattaDFigueiraJ RFonsecaC MTavares-PereiraF, 2008, “Graph partitioning through a multi-objective evolutionary algorithm: A preliminary study”, in Proceedings of Genetic and Evolutionary Computation Conference (GECCO-2008) 12–16 July, Atlanta, GA, pp 625–632, doi: 10.1145/1389095.1389222
12.
DebK, 2000, “An efficient constraint handling method for genetic algorithms”Computer Methods in Applied Mechanics and Engineering186311–338
13.
DebKAgarwalSPratapAMeyarivanT, 2002, “A fast and elitist multi-objective genetic algorithm: NSGA-II”IEEE Transactions on Evolutionary Computation6182–197
FigueiraJ RGrecoSMousseauVSłowińskiR, 2008, “Interactive multiobjective optimization using a set of additive value functions”, in Multiobjective Optimization: Interactive and Evolutionary Approaches (Springer, Berlin) pp 97–119, doi: 10.1007/978-3-540-88908-3_4
16.
GuoJ YTrinidadGSmithN, 2001, “MOZART: A Multi-objective Zoning and AggRegation Tool”, paper presented at the TRB 80th Annual Meeting, Transportation Research Board, Washington, DC
17.
HessS WWeaverJ BSiegfeldtJ NWhelanJ NZhitlauP A, 1965, “Nonpartisan political districting by computer”Operations Research13998–1006
18.
HornM E T, 1995, “Solution techniques for large regional partitioning problems”Geographical Analysis27230–248
19.
MacEachrenA M, 1985, “Compactness of geographic shape: Comparison and evaluation of measures”Geografiska Annaler: Series B, Human Geography6753–67
20.
MacmillanWPierceT, 1994, “Optimization modelling in a GIS framework: The problem of political redistricting”, in Spatial Analysis and GIS Eds FotheringhamSRogersonP (Taylor and Francis, London) pp 221–246
21.
MalczewskiJ, 1999GIS and Multicriteria Decision Analysis (John Wiley, New York)
22.
MalczewskiJ, 2006, “GIS-based multicriteria decision analysis: A survey of the literature”International Journal of Geographical Information Science20249–268
23.
MalczewskiJOgryczakW, 1995, “The multiple criteria location problem: 1. A generalized network model and the set of efficient solutions”Environment and Planning A271931–1960
24.
MartinD, 1997, “From enumeration districts to output areas: Experiments in the automated creation of a census output geography”Population Trends8836–42
25.
MartinDNolanATranmerM, 2001, “The application of zone-design methodology in the 2001 UK census”Environment and Planning A331949–1962
26.
MorillR L, 1973, “Ideal and reality in reapportionment”Annals of the Association of American Geographers63463–477
27.
MorillR L, 1976, “Redistricting revisited”Annals of the Association of American Geographers66548–556
28.
OpenshawS, 1977, “A geographical solution to scale and aggregation problems in regionbuilding, partitioning and spatial modelling”Transactions of the Institute of British Geographers, New Series2459–472
29.
OpenshawSAbrahartR J, 2004Geocomputation: A Primer (John Wiley, Chichester, Sussex)
30.
OpenshawSRaoL, 1995, “Algorithms for reengineeering 1991 census geography”Environment and Planning A27425–446
31.
OpenshawSWymerC, 1995, “Classifying and regionalizing census data”, in Census Users Handbook (GeoInformation International, Cambridge) pp 239–270
32.
RalphsMAngL, 2009, “Optimised geographies for data reporting: Zone design tools for census output geographies”, WP 09–0, Statistics New Zealand, Wellington
33.
SchillingD AMcGarityAReVelleC, 1982, “Hidden attributes and the display of information in multiobjective analysis”Management Science28236–242
34.
ShirabeT, 2005, “A model of contiguity for spatial unit allocation”Geographical Analysis372–16
35.
ShirabeT, 2009, “Districting modeling with exact contiguity constraints”Environment and Planning B: Planning and Design361053–1066
Statistics Canada, 2007bCensus of Canada, 2006: Cartographic Boundary File Map of Census Metropolitan Areas: London, Ontario at the Census Tract (CT) Level computer file, Statistics Canada, Ontario, Ottawa
38.
SteuerR E, 1986Multiple Criteria Optimization: Theory, Computation and Application (John Wiley, New York)
39.
Tavares-PereiraFFigueiraJ RMousseauVRoyB, 2007, “Multiple criteria districting problems: The public transportation network pricing system of the Paris region”Annals of Operations Research15469–92
40.
VanegasPCattrysseDvan OrshovenJ, 2010, “Compactness in spatial decision support: A literature review”, in Computational Science and its Applications: ICCSA 2010 (Part I) (Springer, Berlin) pp 414–429
41.
WilliamsJ C, 1995, “Political districting: A review”Papers in Regional Science7413–40
42.
XiaoN, 2006, “An evolutionary algorithm for site search problems”Geographical Analysis38227–247
43.
XiaoN, 2008, “A unified conceptual framework for geographical optimization using evolutionary algorithms”Annals of the Association of American Geographers98795–817
44.
YeatesM H, 1963, “Hinterland delimitation: A distance minimizing approach”The Professional Geographer157–10
45.
ZhangXArmstrongM P, 2008, “Genetic algorithms and the corridor location problem: Multiple objectives and alternative solutions”Environment and Planning B: Planning and Design35148–168
