A Voronoi-based method for land-use optimization using semidefinite programming and gradient descent algorithm

The land-use optimization involves divisions of land into subregions to obtain spatial configuration of compact subregions and desired connections among them. Computational geometry-based algorithms, such as Voronoi diagram, are known to be efficient and suitable for iterative design processes to ac...

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Veröffentlicht in:International Journal of Geographical Information Science Jg. 35; H. 5; S. 999 - 1031
Hauptverfasser: Suppakitpaisarn, Vorapong, Ariyarit, Atthaphon, Chaidee, Supanut
Format: Journal Article
Sprache:Englisch
Japanisch
Veröffentlicht: Abingdon Taylor & Francis 04.05.2021
Informa UK Limited
Taylor & Francis LLC
Schlagworte:
Algorithms
Benchmarks
Computational geometry
Computer applications
Design optimization
Genetic algorithms
gradient descent method
interactive design
Iterative methods
Land use
Land-use optimization problem
Optimization
SDP-based graph drawing
Semidefinite programming
Voronoi diagram
Voronoi graphs
ISSN:1365-8816, 1362-3087, 1365-8824
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Abstract The land-use optimization involves divisions of land into subregions to obtain spatial configuration of compact subregions and desired connections among them. Computational geometry-based algorithms, such as Voronoi diagram, are known to be efficient and suitable for iterative design processes to achieve land-use optimization. However, such algorithms assume that generating point positions are given as inputs, while we usually do not know the positions in advance. In this study, we propose a method to automatically calculate the suitable point positions. The method uses (1) semidefinite programming to approximate locations while maintaining relative positions among locations; and (2) gradient descent to iteratively update locations subject to area constraints. We apply the proposed framework to a practical case at Chiang Mai University and compare its performance with a benchmark, the differential genetic algorithm. The results show that the proposed method is 28 times faster than the differential genetic algorithm, while the resulting land allocation error is slightly larger than that of the benchmark but still acceptable. Additionally, the output does not contain disconnected areas, as found in all evolutionary computations, and the compactness is almost equal to the maximum possible value.
AbstractList The land-use optimization involves divisions of land into subregions to obtain spatial configuration of compact subregions and desired connections among them. Computational geometry-based algorithms, such as Voronoi diagram, are known to be efficient and suitable for iterative design processes to achieve land-use optimization. However, such algorithms assume that generating point positions are given as inputs, while we usually do not know the positions in advance. In this study, we propose a method to automatically calculate the suitable point positions. The method uses (1) semidefinite programming to approximate locations while maintaining relative positions among locations; and (2) gradient descent to iteratively update locations subject to area constraints. We apply the proposed framework to a practical case at Chiang Mai University and compare its performance with a benchmark, the differential genetic algorithm. The results show that the proposed method is 28 times faster than the differential genetic algorithm, while the resulting land allocation error is slightly larger than that of the benchmark but still acceptable. Additionally, the output does not contain disconnected areas, as found in all evolutionary computations, and the compactness is almost equal to the maximum possible value.
Author Ariyarit, Atthaphon
Chaidee, Supanut
Suppakitpaisarn, Vorapong
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  orcidid: 0000-0002-7020-395X
  surname: Suppakitpaisarn
  fullname: Suppakitpaisarn, Vorapong
  organization: The University of Tokyo
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  givenname: Atthaphon
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  surname: Ariyarit
  fullname: Ariyarit, Atthaphon
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  givenname: Supanut
  orcidid: 0000-0002-2314-1397
  surname: Chaidee
  fullname: Chaidee, Supanut
  email: supanut.c@cmu.ac.th
  organization: CHE
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Snippet The land-use optimization involves divisions of land into subregions to obtain spatial configuration of compact subregions and desired connections among them....
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SubjectTerms Algorithms
Benchmarks
Computational geometry
Computer applications
Design optimization
Genetic algorithms
gradient descent method
interactive design
Iterative methods
Land use
Land-use optimization problem
Optimization
SDP-based graph drawing
Semidefinite programming
Voronoi diagram
Voronoi graphs
Title A Voronoi-based method for land-use optimization using semidefinite programming and gradient descent algorithm
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