Compactness in Spatial Decision Support A Literature Review - Pablo Vanegas

Compactness in Spatial Decision SupportA Literature Review

Pablo Vanegas

March 25, 2010

Compactness in Spatial Decision Support 1/19 Section:

Compactness in Spatial Decision SupportContents

1. Introduction

2. Definitions

3. Some Approaches

4. Discussion

5. Conclusions

Compactness in Spatial Decision Support 2/19 Section: Introduction


1. Introduction

2. Definitions

3. Some Approaches

4. Discussion

5. Conclusions



1. Introduction

2. Definitions

3. Some Approaches

4. Discussion

5. Conclusions



1. Introduction

2. Definitions

3. Some Approaches

4. Discussion

5. Conclusions



1. Introduction

2. Definitions

3. Some Approaches

4. Discussion

5. Conclusions


Problem DefinitionSite Location Problem, Spatial Optimization

I Map represented by means of a matrix (set of cells)I Identify a set of cells

I Multiple Criteria




I Multiple Criteria




I Multiple Criteria


Problem DefinitionAutomatic 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
















Problem DefinitionApplications

Fischer et. al 2003 To reduce vulnerability of

elements like species,

communities, and endemic

plants



Church et. al 2003 Viable areas for the

reproduction and survival

of some species



Objective:

Identify a Set of CellsCompact Area

Environmental Performance

-Carbon Sequestration

-Nitrate Leaching

Sediment Load at the Outlet



Objective:




-Nitrate Leaching




Objective:




-Nitrate Leaching




Objective:




-Nitrate Leaching


Intrinsic characteristics



Objective:




-Nitrate Leaching





Objective:




-Nitrate Leaching





Objective:




-Nitrate Leaching



300 cells

outlet50 cells

+Carbon Sequestration

+Monetary Income

-Sediment Load

Cell Interaction



Objective:




-Nitrate Leaching



+Carbon Sequestration

+Monetary Income

-Sediment Load

Cell Interaction


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

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)

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)

TOPOLOGY


Methods

Exact Methods

· Mathematical Programming

· Enumeration Methods

Heuristics

· (Pure) Heuristics

· Meta-heuristics:

· Simulated Annealing

· Genetic Algorithms

· Tabu Search

Problem specific way of directing problem solving

High complexity

General-propose methods that can guide different problems


Methods

Exact Methods



Heuristics


· Meta-heuristics:



· Tabu Search


High complexity



Methods

Exact Methods



Heuristics


· Meta-heuristics:



· Tabu Search


High complexity



Methods

Exact Methods



Heuristics


· Meta-heuristics:



· Tabu Search


High complexity



Methods

Exact Methods



Heuristics


· Meta-heuristics:



· Tabu Search


High complexity




1. Introduction

2. Definitions

3. Some Approaches

4. Discussion

5. Conclusions

Compactness in Spatial Decision Support 11/19 Section: Some Approaches

Exact MethodsInteger Programming

Mathematical Programming

· Attempt to maximize (or minimize) a linear function (objective decision variables)

· Decision variables must satisfy a set of constraints (linear equation)











i jijP


Approximate MethodsMeta-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.



Meta-heuristics

Genetic Algorithms

c(v1), … ,c(vi), ... ,c(vn)




site.





Meta-heuristics

Genetic Algorithms

c(v1), … ,c(vi), ... ,c(vn)




site.




Approximate MethodsHeuristics

Heuristics

Brookes 2001

Region Growing

A shape-suitability score is determined by the distance

and direction of the cell to the seed.



Heuristics

Brookes 2001

Region Growing





Heuristics

Brookes 2001

Region Growing





1

2

3 3

2

3 3 3

2(a) (b) (c) (d)

1

12

2

2

2

33

3

3

2

3

2

3

1

1

(a) (b)

(c) (d)



1. Introduction

2. Definitions

3. Some Approaches

4. Discussion

5. Conclusions

Compactness in Spatial Decision Support 16/19 Section: Discussion


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


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



Heuristics

Topological Relation

+

Interaction


Conclusions

I LP/IP formulations are not only adequate for situations whenthe problem can be represented with an appropriate numberof geographical entities, but they also play an important rolein the evaluation of approximate solutions.

I Automatic generation of seed regions seems a crucial issue toincrease the size of the analyzed problems.

I Population based metaheuristics can be improved through theexploration of the high quality seed solutions.

Compactness in Spatial Decision Support 19/19 Section: Conclusions

Conclusions





Conclusions





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Compactness in Spatial Decision Support A Literature Review - Pablo Vanegas