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Compactness in Spatial Decision Support
                                          A Literature Review


                  ...
Compactness in Spatial Decision Support
Contents




        1. Introduction
        2. Definitions
        3. Some Approac...
Compactness in Spatial Decision Support
Contents




        1. Introduction
        2. Definitions
        3. Some Approac...
Compactness in Spatial Decision Support
Contents




        1. Introduction
        2. Definitions
        3. Some Approac...
Compactness in Spatial Decision Support
Contents




        1. Introduction
        2. Definitions
        3. Some Approac...
Compactness in Spatial Decision Support
Contents




        1. Introduction
        2. Definitions
        3. Some Approac...
Problem Definition
Site Location Problem, Spatial Optimization


             Map represented by means of a matrix (set of ...
Problem Definition
Site Location Problem, Spatial Optimization


             Map represented by means of a matrix (set of ...
Problem Definition
Site Location Problem, Spatial Optimization


             Map represented by means of a matrix (set of ...
Problem Definition
Automatic Zoning Problem (AZP)


    Automatic Zoning Problem (AZP), Openshaw 1996

                    ...
Problem Definition
Automatic Zoning Problem (AZP)


    Automatic Zoning Problem (AZP), Openshaw 1996

                    ...
Problem Definition
Automatic Zoning Problem (AZP)


    Automatic Zoning Problem (AZP), Openshaw 1996

                    ...
Problem Definition
Applications




         Fischer et. al 2003       To reduce vulnerability of
                         ...
Problem Definition
Applications




    Church et. al 2003            Viable areas for the
                                ...
Problem Definition
Applications

                                                  Sediment Load at the Outlet




        ...
Problem Definition
Applications

                                                  Sediment Load at the Outlet




        ...
Problem Definition
Applications

                                                  Sediment Load at the Outlet




        ...
Problem Definition
Applications

                                                  Sediment Load at the Outlet




        ...
Problem Definition
Applications

                                                  Sediment Load at the Outlet




        ...
Problem Definition
Applications

                                                  Sediment Load at the Outlet




        ...
Problem Definition
Applications
   +Carbon Sequestration
   +Monetary Income                                              S...
Problem Definition
Applications
   +Carbon Sequestration
   +Monetary Income                               Sediment Load at...
Compactness in Spatial Decision Support




        1. Introduction
        2. Definitions
        3. Some Approaches
     ...
Topology
 TOPOLOGY

Relationship between an object and its neighbors. Abdul, 2008

Origin in the principles of object adja...
Topology
 TOPOLOGY

Relationship between an object and its neighbors. Abdul, 2008

Origin in the principles of object adja...
Methods


Exact Methods               High complexity

    · Mathematical Programming
    · Enumeration Methods


Heuristi...
Methods


Exact Methods               High complexity

    · Mathematical Programming
    · Enumeration Methods


Heuristi...
Methods


Exact Methods               High complexity

    · Mathematical Programming
    · Enumeration Methods


Heuristi...
Methods


Exact Methods               High complexity

    · Mathematical Programming
    · Enumeration Methods


Heuristi...
Methods


Exact Methods               High complexity

    · Mathematical Programming
    · Enumeration Methods


Heuristi...
Compactness in Spatial Decision Support




        1. Introduction
        2. Definitions
        3. Some Approaches
     ...
Exact Methods
 Integer Programming


Mathematical Programming

 ·     Attempt to maximize (or minimize) a linear function ...
Exact Methods
 Integer Programming


Mathematical Programming

 ·     Attempt to maximize (or minimize) a linear function ...
Exact Methods
 Integer Programming


Mathematical Programming

 ·     Attempt to maximize (or minimize) a linear function ...
Approximate Methods
Meta-heuristics


 Meta-heuristics

      Genetic Algorithms


  c(v1), … ,c(vi), ... ,c(vn)

      Co...
Approximate Methods
Meta-heuristics


 Meta-heuristics

      Genetic Algorithms


  c(v1), … ,c(vi), ... ,c(vn)

      Co...
Approximate Methods
Meta-heuristics


 Meta-heuristics

      Genetic Algorithms


  c(v1), … ,c(vi), ... ,c(vn)

      Co...
Approximate Methods
Heuristics


        Heuristics

    Brookes 2001

                   Region Growing




             ...
Approximate Methods
Heuristics


        Heuristics

    Brookes 2001

                   Region Growing




             ...
Approximate Methods
Heuristics


        Heuristics

    Brookes 2001

                   Region Growing




             ...
Approximate Methods
Heuristics
                                                                   1
                      ...
Compactness in Spatial Decision Support




        1. Introduction
        2. Definitions
        3. Some Approaches
     ...
Problem Definition
Site Location Problem, Spatial Optimization
                                         Referential     Siz...
Approximate Methods
Heuristics
          Heuristics

       Topological Relation
                +
           Interaction
...
Conclusions



             LP/IP formulations are not only adequate for situations when
             the problem can be r...
Conclusions



             LP/IP formulations are not only adequate for situations when
             the problem can be r...
Conclusions



             LP/IP formulations are not only adequate for situations when
             the problem can be r...
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Compactness in Spatial Decision Support A Literature Review - Pablo Vanegas

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Transcript of "Compactness in Spatial Decision Support A Literature Review - Pablo Vanegas"

  1. 1. Compactness in Spatial Decision Support A Literature Review Pablo Vanegas March 25, 2010 Compactness in Spatial Decision Support 1/19 Section:
  2. 2. Compactness in Spatial Decision Support Contents 1. Introduction 2. Definitions 3. Some Approaches 4. Discussion 5. Conclusions Compactness in Spatial Decision Support 2/19 Section: Introduction
  3. 3. Compactness in Spatial Decision Support Contents 1. Introduction 2. Definitions 3. Some Approaches 4. Discussion 5. Conclusions Compactness in Spatial Decision Support 2/19 Section: Introduction
  4. 4. Compactness in Spatial Decision Support Contents 1. Introduction 2. Definitions 3. Some Approaches 4. Discussion 5. Conclusions Compactness in Spatial Decision Support 2/19 Section: Introduction
  5. 5. Compactness in Spatial Decision Support Contents 1. Introduction 2. Definitions 3. Some Approaches 4. Discussion 5. Conclusions Compactness in Spatial Decision Support 2/19 Section: Introduction
  6. 6. Compactness in Spatial Decision Support Contents 1. Introduction 2. Definitions 3. Some Approaches 4. Discussion 5. Conclusions Compactness in Spatial Decision Support 2/19 Section: Introduction
  7. 7. Problem Definition Site Location Problem, Spatial Optimization Map represented by means of a matrix (set of cells) Identify a set of cells Multiple Criteria Compactness in Spatial Decision Support 3/19 Section: Introduction
  8. 8. Problem Definition Site Location Problem, Spatial Optimization Map represented by means of a matrix (set of cells) Identify a set of cells Multiple Criteria Compactness in Spatial Decision Support 3/19 Section: Introduction
  9. 9. Problem Definition Site Location Problem, Spatial Optimization Map represented by means of a matrix (set of cells) Identify a set of cells Multiple Criteria Compactness in Spatial Decision Support 3/19 Section: Introduction
  10. 10. Problem Definition Automatic Zoning Problem (AZP) Automatic Zoning Problem (AZP), Openshaw 1996 Hard optimization problem N building blocks aggregated into M zones Constraints on the topology of the M zones Analytic and computational techniques Compactness in Spatial Decision Support 4/19 Section: Introduction
  11. 11. Problem Definition Automatic Zoning Problem (AZP) Automatic Zoning Problem (AZP), Openshaw 1996 Hard optimization problem N building blocks aggregated into M zones Constraints on the topology of the M zones Analytic and computational techniques Compactness in Spatial Decision Support 4/19 Section: Introduction
  12. 12. Problem Definition Automatic Zoning Problem (AZP) Automatic Zoning Problem (AZP), Openshaw 1996 Hard optimization problem N building blocks aggregated into M zones Constraints on the topology of the M zones Analytic and computational techniques Compactness in Spatial Decision Support 4/19 Section: Introduction
  13. 13. Problem Definition Applications Fischer et. al 2003 To reduce vulnerability of elements like species, communities, and endemic plants Compactness in Spatial Decision Support 5/19 Section: Introduction
  14. 14. Problem Definition Applications Church et. al 2003 Viable areas for the reproduction and survival of some species Compactness in Spatial Decision Support 6/19 Section: Introduction
  15. 15. Problem Definition Applications Sediment Load at the Outlet Compact Area Objective: Identify a Set of Cells Environmental Performance -Carbon Sequestration -Nitrate Leaching Compactness in Spatial Decision Support 7/19 Section: Introduction
  16. 16. Problem Definition Applications Sediment Load at the Outlet Compact Area Objective: Identify a Set of Cells Environmental Performance -Carbon Sequestration -Nitrate Leaching Compactness in Spatial Decision Support 7/19 Section: Introduction
  17. 17. Problem Definition Applications Sediment Load at the Outlet Compact Area Objective: Identify a Set of Cells Environmental Performance -Carbon Sequestration -Nitrate Leaching Compactness in Spatial Decision Support 7/19 Section: Introduction
  18. 18. Problem Definition Applications Sediment Load at the Outlet Compact Area Objective: Identify a Set of Cells Intrinsic characteristics Environmental Performance -Carbon Sequestration -Nitrate Leaching Compactness in Spatial Decision Support 7/19 Section: Introduction
  19. 19. Problem Definition Applications Sediment Load at the Outlet Compact Area Objective: Identify a Set of Cells Intrinsic characteristics Environmental Performance -Carbon Sequestration -Nitrate Leaching Compactness in Spatial Decision Support 7/19 Section: Introduction
  20. 20. Problem Definition Applications Sediment Load at the Outlet Compact Area Objective: Identify a Set of Cells Intrinsic characteristics Environmental Performance -Carbon Sequestration -Nitrate Leaching Compactness in Spatial Decision Support 7/19 Section: Introduction
  21. 21. Problem Definition Applications +Carbon Sequestration +Monetary Income Sediment Load at the Outlet -Sediment Load 300 cells Cell Interaction 50 cells outlet Compact Area Objective: Identify a Set of Cells Intrinsic characteristics Environmental Performance -Carbon Sequestration -Nitrate Leaching Compactness in Spatial Decision Support 7/19 Section: Introduction
  22. 22. Problem Definition Applications +Carbon Sequestration +Monetary Income Sediment Load at the Outlet -Sediment Load Cell Interaction Compact Area Objective: Identify a Set of Cells Intrinsic characteristics Environmental Performance -Carbon Sequestration -Nitrate Leaching Compactness in Spatial Decision Support 7/19 Section: Introduction
  23. 23. Compactness in Spatial Decision Support 1. Introduction 2. Definitions 3. Some Approaches 4. Discussion 5. Conclusions Compactness in Spatial Decision Support 8/19 Section: Definitions
  24. 24. Topology TOPOLOGY Relationship between an object and its neighbors. Abdul, 2008 Origin in the principles of object adjacency and connectedness. VanOrshoven, 2007 Adjacency Compactness (Church 2003, Brookes 1997, Vanegas 2008, ...), Perforation (Shirabe 2004) Compactness in Spatial Decision Support 9/19 Section: Definitions
  25. 25. Topology TOPOLOGY Relationship between an object and its neighbors. Abdul, 2008 Origin in the principles of object adjacency and connectedness. VanOrshoven, 2007 Adjacency Compactness (Church 2003, Brookes 1997, Vanegas 2008, ...), Perforation (Shirabe 2004) Compactness in Spatial Decision Support 9/19 Section: Definitions
  26. 26. Methods Exact Methods High complexity · Mathematical Programming · Enumeration Methods Heuristics Problem specific way of directing problem solving · (Pure) Heuristics · Meta-heuristics: General-propose methods that can guide different problems · Simulated Annealing · Genetic Algorithms · Tabu Search Compactness in Spatial Decision Support 10/19 Section: Definitions
  27. 27. Methods Exact Methods High complexity · Mathematical Programming · Enumeration Methods Heuristics Problem specific way of directing problem solving · (Pure) Heuristics · Meta-heuristics: General-propose methods that can guide different problems · Simulated Annealing · Genetic Algorithms · Tabu Search Compactness in Spatial Decision Support 10/19 Section: Definitions
  28. 28. Methods Exact Methods High complexity · Mathematical Programming · Enumeration Methods Heuristics Problem specific way of directing problem solving · (Pure) Heuristics · Meta-heuristics: General-propose methods that can guide different problems · Simulated Annealing · Genetic Algorithms · Tabu Search Compactness in Spatial Decision Support 10/19 Section: Definitions
  29. 29. Methods Exact Methods High complexity · Mathematical Programming · Enumeration Methods Heuristics Problem specific way of directing problem solving · (Pure) Heuristics · Meta-heuristics: General-propose methods that can guide different problems · Simulated Annealing · Genetic Algorithms · Tabu Search Compactness in Spatial Decision Support 10/19 Section: Definitions
  30. 30. Methods Exact Methods High complexity · Mathematical Programming · Enumeration Methods Heuristics Problem specific way of directing problem solving · (Pure) Heuristics · Meta-heuristics: General-propose methods that can guide different problems · Simulated Annealing · Genetic Algorithms · Tabu Search Compactness in Spatial Decision Support 10/19 Section: Definitions
  31. 31. Compactness in Spatial Decision Support 1. Introduction 2. Definitions 3. Some Approaches 4. Discussion 5. Conclusions Compactness in Spatial Decision Support 11/19 Section: Some Approaches
  32. 32. Exact Methods Integer Programming Mathematical Programming · Attempt to maximize (or minimize) a linear function (objective decision variables) · Decision variables must satisfy a set of constraints (linear equation) Compactness in Spatial Decision Support 12/19 Section: Some Approaches
  33. 33. Exact Methods Integer Programming Mathematical Programming · Attempt to maximize (or minimize) a linear function (objective decision variables) · Decision variables must satisfy a set of constraints (linear equation) Compactness in Spatial Decision Support 12/19 Section: Some Approaches
  34. 34. Exact Methods Integer Programming Mathematical Programming · Attempt to maximize (or minimize) a linear function (objective decision variables) · Decision variables must satisfy a set of constraints (linear equation) Pij i j Compactness in Spatial Decision Support 12/19 Section: Some Approaches
  35. 35. Approximate Methods Meta-heuristics Meta-heuristics Genetic Algorithms c(v1), … ,c(vi), ... ,c(vn) Cost of every vertex i · Finds a movable vertex that can be removed from the site but avoiding non-contiguity. · Vertices are found which can be added to the site without resulting in a non-contiguous site. The mutation process selects the vertex in the site with the lowest cost à new seed to create another site. Compactness in Spatial Decision Support 13/19 Section: Some Approaches
  36. 36. Approximate Methods Meta-heuristics Meta-heuristics Genetic Algorithms c(v1), … ,c(vi), ... ,c(vn) Cost of every vertex i · Finds a movable vertex that can be removed from the site but avoiding non-contiguity. · Vertices are found which can be added to the site without resulting in a non-contiguous site. The mutation process selects the vertex in the site with the lowest cost à new seed to create another site. Compactness in Spatial Decision Support 13/19 Section: Some Approaches
  37. 37. Approximate Methods Meta-heuristics Meta-heuristics Genetic Algorithms c(v1), … ,c(vi), ... ,c(vn) Cost of every vertex i · Finds a movable vertex that can be removed from the site but avoiding non-contiguity. · Vertices are found which can be added to the site without resulting in a non-contiguous site. The mutation process selects the vertex in the site with the lowest cost à new seed to create another site. Compactness in Spatial Decision Support 13/19 Section: Some Approaches
  38. 38. Approximate Methods Heuristics Heuristics Brookes 2001 Region Growing A shape-suitability score is determined by the distance and direction of the cell to the seed. Compactness in Spatial Decision Support 14/19 Section: Some Approaches
  39. 39. Approximate Methods Heuristics Heuristics Brookes 2001 Region Growing A shape-suitability score is determined by the distance and direction of the cell to the seed. Compactness in Spatial Decision Support 14/19 Section: Some Approaches
  40. 40. Approximate Methods Heuristics Heuristics Brookes 2001 Region Growing A shape-suitability score is determined by the distance and direction of the cell to the seed. Compactness in Spatial Decision Support 14/19 Section: Some Approaches
  41. 41. Approximate Methods Heuristics 1 2 3 (a) (b) 3 2 3 1 1 2 2 3 (c) (d) 3 3 2 2 1 1 (a) 2 (b) 2 (c) 2 (d) 3 3 3 3 3 Compactness in Spatial Decision Support 15/19 Section: Some Approaches
  42. 42. Compactness in Spatial Decision Support 1. Introduction 2. Definitions 3. Some Approaches 4. Discussion 5. Conclusions Compactness in Spatial Decision Support 16/19 Section: Discussion
  43. 43. Problem Definition Site Location Problem, Spatial Optimization Referential Size Predefined Time Time units size units seed Heuristics Mehrotra and Johnson 1998 46 counties N 5 minutes Brookes 2001 300 cells Y - - Church et al 2003 23000 cells Y - - Vanegas et al 2008 4900 cells N 1 second Metaheuristics Brookes 1997 6400 cells Y - - Brookes 2001 372890 cells Y 36 hours Xiao et al 2002 16384 cells N - - Aerts and Heuvelink 2002 2500 cells N few hours McDonnell et al 2002 2160 cells N Greedy 1 second Simulated Anealing 96 seconds Li and Yeh 2004 22500 cells Y 4 – 13.6 hours Venema 2004 162 patches N - - Stewart et al 2005 1600 cells N 15-18 minutes Xiao 2006 250000 cells N 2268 seconds Mathematical Programming Hof and Bevers 2000 1689 cells N - - Dimopoulou and Giannoikos 2001 160 cells N 1.5 minutes Fischer and Church 2003 776 planning units N 7 s – 98 h Seconds - hours Williams 2003 1024 cells Y 220 minutes Shirabe 2004 100 cells N 0.19 – 87882 wall clock Vanegas et al 2008 4900 cells N 540 - 28450 seconds Enumeration Methods Hof and Bevers 2000 900 cells N 16.8 seconds Compactness in Spatial Decision Support 17/19 Section: Discussion
  44. 44. Approximate Methods Heuristics Heuristics Topological Relation + Interaction Compactness in Spatial Decision Support 18/19 Section: Discussion
  45. 45. Conclusions LP/IP formulations are not only adequate for situations when the problem can be represented with an appropriate number of geographical entities, but they also play an important role in the evaluation of approximate solutions. Automatic generation of seed regions seems a crucial issue to increase the size of the analyzed problems. Population based metaheuristics can be improved through the exploration of the high quality seed solutions. Compactness in Spatial Decision Support 19/19 Section: Conclusions
  46. 46. Conclusions LP/IP formulations are not only adequate for situations when the problem can be represented with an appropriate number of geographical entities, but they also play an important role in the evaluation of approximate solutions. Automatic generation of seed regions seems a crucial issue to increase the size of the analyzed problems. Population based metaheuristics can be improved through the exploration of the high quality seed solutions. Compactness in Spatial Decision Support 19/19 Section: Conclusions
  47. 47. Conclusions LP/IP formulations are not only adequate for situations when the problem can be represented with an appropriate number of geographical entities, but they also play an important role in the evaluation of approximate solutions. Automatic generation of seed regions seems a crucial issue to increase the size of the analyzed problems. Population based metaheuristics can be improved through the exploration of the high quality seed solutions. Compactness in Spatial Decision Support 19/19 Section: Conclusions
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