Compactness in Spatial Decision Support A Literature Review - Pablo Vanegas

1. Compactness in Spatial Decision Support
A Literature Review
Pablo Vanegas
March 25, 2010
Compactness in Spatial Decision Support 1/19 Section:

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Approximate Methods
Heuristics
Heuristics
Topological Relation
+
Interaction
Compactness in Spatial Decision Support 18/19 Section: Discussion

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. 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. 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