1. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
CALIBRATING THE SLEUTH
URBAN GROWTH MODEL
IN A MULTI-MODAL FITNESS
LANDSCAPE
William Veerbeek
Artificial Intelligence Section, Faculty of Sciences, Vrije Universiteit, Amsterdam

2. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
EXPLODING URBAN GROWTH
-1800: 3% of world population lived in cities
-2000: 47% of world population lived in cities
urbanization has a large impact on earth’s resources,
yet no general theory or model exists!

3. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
GAS: Geographic Automata Systems
1992: Urban growth models using Cellular Automata
Cellular Automata:
A CA is an array of identically programmed automata, or cells, which in-
teract with one another in a neighborhood and have a definate state
array cell interact neighborhood state starting
condition

4. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
early urban growth models using CA:
-attention to transition rules
-use spatially isotropic lattices
D.P. Ward et. al, ‘An Optimized Cellular Automata Approach for Sustainable urban Development in Rapidly
Urbanizing Regions (1999)

5. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
CA: SPATIALLY ISOTRIPIC ENVIRONMENT
spatial conditions of cities are almost never isotropic
mountains
river
sea
array cell interact neighborhood state starting
condition

6. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
1994: Human Induced Land Transformation (HILT) model
-first GAS to use geographic information as the envrionment
for the CA
Kirtland et. al, ‘An Analysis of Human Induced Land Transformations in the San Fransisco Bay/Sacramento
area (1994)

7. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
1997: Slope, Land-use, Exclusion, Urban Extent, Transpor-
tation and Hillshade model (SLEUTH)
Two Papers:
1. K.C. Clarke and S. Hoppen (1997), ‘A self-modyfying cellular automaton model of the histori-
ca urbanization in the San Fransisco Bay area’ ,planning and Design 24, 247-261
2. E. A. Silva and K. C. Clarke (2004), ‘Calibration of the SLEUTH urban growth model for Lisbon
and Porto’ , Computers, Environment and Urban systems 26 , 525-552

8. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
1. K.C. Clarke and S. Hoppen (1997), ‘A self-modyfying cellular automaton model of the his-
torica urbanization in the San Fransisco Bay area’ ,planning and Design 24, 247-261
The paper presents the SLEUTH-model. Features include:
-integration of GIS-layers as the operating environment
-different cell states (not binary as in game of life)
-complex set of transition rules
-set of coefficients that dictate outcome transition rules
-self-modifying rules
-calibration method

9. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
1. K.C. Clarke and S. Hoppen (1997), ‘A self-modyfying cellular automaton model of the his-
torica urbanization in the San Fransisco Bay area’ ,planning and Design 24, 247-261
1. Integration of GIS-layers
2. Roads 3. Seeds
1. Slope 4. Excluded Areas
-all layers except (roads layer) are cell-based (pixels)

10. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
1. K.C. Clarke and S. Hoppen (1997), ‘A self-modyfying cellular automaton model of the his-
torica urbanization in the San Fransisco Bay area’ ,planning and Design 24, 247-261
2. Different Cell-states
1. empty
2. seed cell
3. urbanized in current iteration
4. urbanized in previous iteration (any)

11. SOUP: Self in regional planning Planning
Oranizing Urban
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over decentralisatie, kritische grenzen en ai
1. K.C. Clarke and S. Hoppen (1997), ‘A self-modyfying cellular automaton model of the his-
torica urbanization in the San Fransisco Bay area’ ,planning and Design 24, 247-261
3. Complex set of transition rules
Composite rules composed of:
-rules on interaction with GIS-layers
-rules on cell-states of neighboring cells
For every cell {
count the #neighbors in the neighborhood
for every cell {
calculate individual_urbanization_probabilites of parameters
}
probability_of_urbanization = sum(normalized_parameter_values)/5 //(5 parameters)
if probability_of_urbanization>0.5 { //probability > 50%
cell becomes urbanized
}
}
neighborhood used is classic MOORE (8 neighbors)

12. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
1. K.C. Clarke and S. Hoppen (1997), ‘A self-modyfying cellular automaton model of the his-
torica urbanization in the San Fransisco Bay area’ ,planning and Design 24, 247-261
4. Set of Parameters
-diffussion (overall dispersiveness)
-breed (control of new development)
-spread (growth of urbanized areas)
-slope resistance (probability of urbanization depending on
slope values)
-road gravity (controls urban development alongside roads)
example spread:
if (#neighbors>2 || random_number<spread_coefficient) {
urbanize this cell
}

13. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
1. K.C. Clarke and S. Hoppen (1997), ‘A self-modyfying cellular automaton model of the his-
torica urbanization in the San Fransisco Bay area’ ,planning and Design 24, 247-261
5. Self modifying rules
Control of growth rate by positive feedback loops:
-boost rapid urban growth (resulting in dispersed growth)
-dampen slow urban growth (resulting in concentrated growth)
Calculate growth_rate for a time cycle
// Rapid growth: boost coefficients by 10%
If growth_rate>high_growth_treshold{
DIFFUSION +* 1.1
SPREAD +* 1.1
BREED by +* 1.1
}
-self modifying rules influnece effects of coefficients
-influence of positive feedback rules is moderated over time

14. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
1. K.C. Clarke and S. Hoppen (1997), ‘A self-modyfying cellular automaton model of the his-
torica urbanization in the San Fransisco Bay area’ ,planning and Design 24, 247-261
Examples
Remember this!
Simulated growth pattern of Washington DC (2000) generated by SLEUTH-model

15. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
1. K.C. Clarke and S. Hoppen (1997), ‘A self-modyfying cellular automaton model of the his-
torica urbanization in the San Fransisco Bay area’ ,planning and Design 24, 247-261
6. Calibration method
Adapt the model to specific local conditions!
2. E. A. Silva and K. C. Clarke (2004), ‘Calibration of the SLEUTH urban growth model for Lis-
bon and Porto’ , Computers, Environment and Urban systems 26 , 525-552
(description of the calibration process)
Calibration: Optimization of coefficient values
(diffusion, breed, spread, slope resistance, road gravity and self-modification)

16. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
2. E. A. Silva and K. C. Clarke (2004), ‘Calibration of the SLEUTH urban growth model for Lis-
bon and Porto’ , Computers, Environment and Urban systems 26 , 525-552
Brute force calibration (BFC):
3 steps: coarse, fine, final
1. generate permutation of coefficients
2. calculate simulations from seed-year
3. check if outcome is consistent with real data by using a set of 6 fitness
criteria
4. coefficients of model with best fit is used in new phase (smaller incre-
ments in permutations)
differences in coarse, fine, final are:
-amount of permutations used
-resolution of the input layers (GIS)

17. SOUP: Self in regional planning Planning
Oranizing Urban
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2. E. A. Silva and K. C. Clarke (2004), ‘Calibration of the SLEUTH urban growth model for Lis-
bon and Porto’ , Computers, Environment and Urban systems 26 , 525-552
BFC is adaptive refinement
1
�������������
0 .8
-take interval with best fitness value
0 .6
-use smaller increments within this
0 .4
interval for a new fitness calculation 0 .2
0
0 ���
�� �� �� �� �� �� �� �� ��
������������
����
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Assumptions:
����
-FITNESS FUNCTION IS MONOTONOUS!
����
-FITNESS IS UNI-MODAL!
����
����
����
�� �� �� �� �� �� �� �� �� ��
��
������������
adaptive refinement of a monotonous uni-modal fitness function

18. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
2. E. A. Silva and K. C. Clarke (2004), ‘Calibration of the SLEUTH urban growth model for Lis-
bon and Porto’ , Computers, Environment and Urban systems 26 , 525-552
Fitness criteria:
1. composite score (all scores together)
2. compare (ratio comparison urban areas)
3. r2 population (amount of urbanized cells)
4. edges r2 (total numer of edges)
5. cluster r2 (total numer of urban clusters)
6. LeeSalee (shape comparison)
Remember that the scores are a result of the coefficient values that influ-
ence the impact of the individual transistion rules !
(diffusion, breed, spread, slope resistance and road gravity)
Assumption: NO INTERACTION EFFECTS!

19. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
2. E. A. Silva and K. C. Clarke (2004), ‘Calibration of the SLEUTH urban growth model for Lis-
bon and Porto’ , Computers, Environment and Urban systems 26 , 525-552
For both Lisbon and Porto fitness values don’t gradu-
ally increase
AML AMP
Calibration phase final fine coarse final fine coarse
Score/resolution 784x836 392x418 196x209 347x563 173x281 86x140
Composite score 0.15 0.19 0.23 0.48 0.47 0.41
0.90 0.88 0.97 0.97 0.99 0.94
Compare
0.91 0.91 0.92 0.99 0.99 0.99
Population
0.78 0.99 0.98 0.98 0.99 0.98
Edges
0.85 0.85 0.93 0.99 0.95 0.97
Cluster
LeeSallee 0.35 0.34 0.32 0.58 0.57 0.53
Diffusion 16 20 1 20 40 1
Breed 57 51 100 20 1 100
Spread 50 50 50 40 35 50
Slope 25 25 25 45 40 50
Roads 30 30 20 20 25 75
wrong assumptions? BFC is not an appropriate calibration method?

20. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
2. E. A. Silva and K. C. Clarke (2004), ‘Calibration of the SLEUTH urban growth model for Lis-
bon and Porto’ , Computers, Environment and Urban systems 26 , 525-552
Conclusions (Silva and Clarke):
1. model performance improved with increase spatial and parameter resolution
2. biggest gains in fitness were made during coarse calibration phase
3. non-linear behavior of fitness-values is result of different spatial resolution
Critique:
Increasing spatial resolution should lower scores since:
-probability of false prediction increases (faulty urbanized cells)
-differentiation of information of input layers becomes larger
YET: SOME SCORES INCREASE, SOME SCORES DECREASE, SOME STAY FIXED
AND SOME BEHAVE NON-LINEARLY

21. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
2. E. A. Silva and K. C. Clarke (2004), ‘Calibration of the SLEUTH urban growth model for Lis-
bon and Porto’ , Computers, Environment and Urban systems 26 , 525-552
Check the results again:
AML AMP
Calibration phase final fine coarse final fine coarse
Score/resolution 784x836 392x418 196x209 347x563 173x281 86x140
Composite score 0.15 0.19 0.23 0.48 0.47 0.41
0.90 0.88 0.97 0.97 0.99 0.94
Compare
0.91 0.91 0.92 0.99 0.99 0.99
Population
0.78 0.99 0.98 0.98 0.99 0.98
Edges
0.85 0.85 0.93 0.99 0.95 0.97
Cluster
LeeSallee 0.35 0.34 0.32 0.58 0.57 0.53
Diffusion 16 20 1 20 40 1
Breed 57 51 100 20 1 100
Spread 50 50 50 40 35 50
Slope 25 25 25 45 40 50
Roads 30 30 20 20 25 75

22. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
2. E. A. Silva and K. C. Clarke (2004), ‘Calibration of the SLEUTH urban growth model for Lis-
bon and Porto’ , Computers, Environment and Urban systems 26 , 525-552
Possibility: non-monotonous multi-modal fitness curve
optimal value would not be found by using adaptive refinement!
could be caused by interaction effects between parameters

23. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
2. E. A. Silva and K. C. Clarke (2004), ‘Calibration of the SLEUTH urban growth model for Lis-
bon and Porto’ , Computers, Environment and Urban systems 26 , 525-552
Alternative regression methods to optimize coefficient
values:
STOCHASTIC METHODS:
-neural networks
-evolutionary algorithms (advantage: distribution)

24. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
2. E. A. Silva and K. C. Clarke (2004), ‘Calibration of the SLEUTH urban growth model for Lis-
bon and Porto’ , Computers, Environment and Urban systems 26 , 525-552
evolutionary algorithms (EA):
-population of candidate solutions moving through search space
(inspired by principle of ‘survival of the fittest as found in nature’
1 2 3

25. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
2. E. A. Silva and K. C. Clarke (2004), ‘Calibration of the SLEUTH urban growth model for Lis-
bon and Porto’ , Computers, Environment and Urban systems 26 , 525-552
evolutionary algorithms (general scheme):
BEGIN
INITIALIZE population iwth random candidate solutions
EVALUATE each candidate
REPEAT UNTIL (TERMINATION CONDITION is satisfied)
1 SELECT parents
2 RECOMBINE pairs of parents
3 MUTATE the resulting offspring
4 EVALUATE new candidate solutions
5 SELECT individuals for next generation;
0D
END

26. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
2. E. A. Silva and K. C. Clarke (2004), ‘Calibration of the SLEUTH urban growth model for Lis-
bon and Porto’ , Computers, Environment and Urban systems 26 , 525-552
evolutionary algorithms:
-information is stored in genes (different types of encoding)
-problem of representation: genotype to phenotype (mapping)
child1
parent1
child2
parent2
gray-coded bitstring sequence (7 bits = 128), 2-point recombination
IN SLEUTH, COEFFICIENTS COULD BE STORED AS 7 BIT LONG BITSTRINGS (genotypes)

27. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
2. E. A. Silva and K. C. Clarke (2004), ‘Calibration of the SLEUTH urban growth model for Lis-
bon and Porto’ , Computers, Environment and Urban systems 26 , 525-552
WHAT ARE EA’S GOOD AT?
-searching an non-monotonous multi-modal search space
-providing a sub-optimal sollution at anytime
-providing a sub-optimal sollution quickly
anytyme behavior of an EA

28. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
2. E. A. Silva and K. C. Clarke (2004), ‘Calibration of the SLEUTH urban growth model for Lis-
bon and Porto’ , Computers, Environment and Urban systems 26 , 525-552
EA for the SLEUTH-model:
Fitness criteria:
child1
child1
1. composite score
child1
child2
2. compare
child1
child2
child1
3. r2 population
child1
child2
child1
4. edges r2
child2
child1
child2
5. cluster r2
child2
child1
child2
child1
6. LeeSalee
child1
child2
child1
child2
child1
child2
child2
child1
child2
child1
child2
child2
child2
genotypes: coefficients phenotypes: models

29. SOUP: Self in regional planning Planning
Oranizing Urban
new directions
2. E. A. Silva and K. C. Clarke (2004), ‘Calibration of the SLEUTH urban growth model for Lis-
bon and Porto’ , Computers, Environment and Urban systems 26 , 525-552
POSSIBLE ADVANTAGES:
-quicker calibration (anytime behavior)
-better sollutions than through linear refinement
MODELS BECOMING MORE CONSISTENT WITH DATA
FURTHER RESEARCH:
-is search-space indeed non-monoutonous, multi-modal? (brute force)
-are there indeed interaction-effects?
-are fitness-functions bounded by different classes of cities?