Contiguity-Based Optimization Models for Political Redistricting Problems

Int. J. Appl. Geospat. Res. Pub Date : 2017-10-01 DOI:10.4018/IJAGR.2017100101

M. Kim, N. Xiao

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引用次数: 16

Abstract

Politicalredistrictingisaprocessusedtoredrawpoliticalboundariesbasedonanumberofcriteria thatincludepopulationequality,minorityrepresentation,contiguity,andcompactness.Redistricting planscanbedifficulttodrawmanuallyandsincethe1970stheuseofcomputersinthecreationof redistrictingplanshasincreaseddramatically.Thepurposeofthispaperistoformulatetheproblemof findingredistrictingplansasoptimizationproblemsonthebasisofpopulationequalityandcontiguity. Theauthorsspecificallyaddresstheproblemfromthecontiguityperspective.Theydevelopedtwo exactoptimalmodels:onebasedonaminimumspanningtreeandonebasedonnetworkflows.They discussthespatialrepresentationandtheformulationofcontiguityforbothmodelsandcompare theperformanceofthesetwomodels,alongwithathirdmodeldevelopedintheliterature,usinga varietyofsyntheticandrealdata.Theauthors’resultsconfirmthatsuchaproblemiscomputationally intensive and more efficient methods are needed for large size problems, but with appropriate formulationapproachestheycanobtainusefulbaselinesolutionstotheseproblemswithrelatively smallsize.Theyalsofindthatmultipleoptimalsolutionswithdifferentspatialconfigurationsmay existforthesameproblem,whichpresentsanewchallengetothedevelopmentofsolutionmethods forpoliticalredistrictingproblems. KeywORdS Land Acquisition Problems, Political Redistricting Problems, Spatial Contiguity, Spatial Optimization, Strict Equal Population

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基于邻接的政治区划优化模型

Politicalredistrictingisaprocessusedtoredrawpoliticalboundariesbasedonanumberofcriteria thatincludepopulationequality，minorityrepresentation，contiguity，andcompactness。Redistricting planscanbedifficulttodrawmanuallyandsincethe1970stheuseofcomputersinthecreationof redistrictingplanshasincreaseddramatically。Thepurposeofthispaperistoformulatetheproblemof findingredistrictingplansasoptimizationproblemsonthebasisofpopulationequalityandcontiguity。Theauthorsspecificallyaddresstheproblemfromthecontiguityperspective。Theydevelopedtwo exactoptimalmodels:onebasedonaminimumspanningtreeandonebasedonnetworkflows。They discussthespatialrepresentationandtheformulationofcontiguityforbothmodelsandcompare theperformanceofthesetwomodels，alongwithathirdmodeldevelopedintheliterature，usinga varietyofsyntheticandrealdata。Theauthors ' ' resultsconfirmthatsuchaproblemiscomputationally ' '需要' '密集' '和' '更有效' '的方法' '对于' '大' '尺寸' '的问题，' '需要' '适当' ' formulationapproachestheycanobtainusefulbaselinesolutionstotheseproblemswithrelatively smallsize。'Theyalsofindthatmultipleoptimalsolutionswithdifferentspatialconfigurationsmay existforthesameproblem，whichpresentsanewchallengetothedevelopmentofsolutionmethods forpoliticalredistrictingproblems。关键词征地问题，政治区划问题，空间连续性，空间优化，严格人口均等

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Int. J. Appl. Geospat. Res.

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