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# Compactness in Spatial Decision Support A Literature Review - Pablo Vanegas

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Compactness in Spatial Decision Support A Literature Review - Pablo Vanegas

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### 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