calibrating sleuth

SOUP: Self Oranizing Urban Planningnew directions in regional planning

CALIBRATING THE SLEUTH URBAN GROWTH MODEL

IN A MULTI-MODAL FITNESS LANDSCAPE

William VeerbeekArtif icial Intelligence Section, Faculty of Sciences, Vrije Universiteit, Amsterdam


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!

SOUP: Self Oranizing Urban Planningnew directions in regional planningGAS: Geographic Automata Systems1992: 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 def inate state

array cell interact neighborhood state starting condition

SOUP: Self Oranizing Urban Planningnew directions in regional planningearly 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)

SOUP: Self Oranizing Urban Planningnew directions in regional planningCA: SPATIALLY ISOTRIPIC ENVIRONMENTspatial conditions of cities are almost never isotropic

array cell interact neighborhood state starting condition

sea

mountains

river


1994: Human Induced Land Transformation (HILT) model-f irst 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)


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

SOUP: Self Oranizing Urban Planningnew directions in regional planning1. 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 coeff icients that dictate outcome transition rules-self-modifying rules-calibration method


1. Integration of GIS-layers1. Slope 4. Excluded Areas2. Roads 3. Seeds

-all layers except (roads layer) are cell-based (pixels)

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

SOUP: Self Oranizing Urban Planning


new directions in regional planning

2. Different Cell-states

1. empty

2. seed cell

3. urbanized in current iteration

4. urbanized in previous iteration (any)

over decentralisatie, kritische grenzen en ai SOUP: Self Oranizing Urban Planningnew directions in regional planning

2. Different Cell-states 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)



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

}


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

}

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 inf lunece effects of coeff icients-inf luence of positive feedback rules is moderated over time



Examples

Simulated growth pattern of Washington DC (2000) generated by SLEUTH-model

Remember this!


Examples 6. Calibration method

Adapt the model to specif ic 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 coeff icient values(diffusion, breed, spread, slope resistance, road gravity and self-modif ication)


SOUP: Self Oranizing Urban Planningnew directions in regional planning2. 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, f ine, f inal1. generate permutation of coeff icients2. calculate simulations from seed-year3. check if outcome is consistent with real data by using a set of 6 f itness criteria4. coeff icients of model with best f it is used in new phase (smaller incre-ments in permutations)

differences in coarse, f ine, f inal are:-amount of permutations used-resolution of the input layers (GIS)


BFC is adaptive ref inement

-take interval with best f itness value-use smaller increments within this interval for a new f itness calculation

Assumptions:-F ITNESS FUNCTION IS MONOTONOUS!-F ITNESS IS UNI-MODAL!

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

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adaptive ref inement of a monotonous uni-modal f itness function


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 coeff icient values that inf lu-ence the impact of the individual transistion rules !(diffusion, breed, spread, slope resistance and road gravity)

Assumption: NO INTERACTION EFFECTS!


For both Lisbon and Porto f itness values don’t gradu-ally increase


AML AMPCalibration phase final fine coarse final fine coarseScore/resolution 784x836 392x418 196x209 347x563 173x281 86x140Composite score 0.15 0.19 0.23 0.48 0.47 0.41Compare 0.90 0.88 0.97 0.97 0.99 0.94 Population 0.91 0.91 0.92 0.99 0.99 0.99Edges 0.78 0.99 0.98 0.98 0.99 0.98Cluster 0.85 0.85 0.93 0.99 0.95 0.97LeeSallee 0.35 0.34 0.32 0.58 0.57 0.53Diffusion 16 20 1 20 40 1Breed 57 51 100 20 1 100Spread 50 50 50 40 35 50Slope 25 25 25 45 40 50Roads 30 30 20 20 25 75

wrong assumptions? BFC is not an appropriate calibration method?


Conclusions (Silva and Clarke):1. model performance improved with increase spatial and parameter resolution2. biggest gains in f itness were made during coarse calibration phase3. non-linear behavior of f itness-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



Check the results again:


AML AMPCalibration phase final fine coarse final fine coarseScore/resolution 784x836 392x418 196x209 347x563 173x281 86x140Composite score 0.15 0.19 0.23 0.48 0.47 0.41Compare 0.90 0.88 0.97 0.97 0.99 0.94 Population 0.91 0.91 0.92 0.99 0.99 0.99Edges 0.78 0.99 0.98 0.98 0.99 0.98Cluster 0.85 0.85 0.93 0.99 0.95 0.97LeeSallee 0.35 0.34 0.32 0.58 0.57 0.53Diffusion 16 20 1 20 40 1Breed 57 51 100 20 1 100Spread 50 50 50 40 35 50Slope 25 25 25 45 40 50Roads 30 30 20 20 25 75


Possibility: non-monotonous multi-modal f itness curve

optimal value would not be found by using adaptive ref inement!

could be caused by interaction effects between parameters


Alternative regression methods to optimize coeff icient values:

STOCHASTIC METHODS:-neural networks-evolutionary algorithms (advantage: distribution)



evolutionary algorithms (EA):-population of candidate solutions moving through search space(inspired by principle of ‘survival of the f ittest as found in nature’

1 2 3


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


evolutionary algorithms:-information is stored in genes (different types of encoding)-problem of representation: genotype to phenotype (mapping)

parent1

parent2

child1

child2

gray-coded bitstring sequence (7 bits = 128), 2-point recombination

IN SLEUTH, COEFFICIENTS COULD BE STORED AS 7 BIT LONG BITSTRINGS (genotypes)


anytyme behavior of an EA

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



EA for the SLEUTH-model:

genotypes: coeff icients phenotypes: models

parent1

parent2

child1

child2

parent1

parent2

child1

child2

parent1

parent2

child1

child2

parent1

parent2

child1

child2

parent1

parent2

child1

child2

parent1

parent2

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child2

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child2

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parent2

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parent1

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child1

child2

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child2

Fitness criteria:1. composite score 2. compare 3. r2 population 4. edges r2 5. cluster r2

6. LeeSalee


POSSIBLE ADVANTAGES:-quicker calibration (anytime behavior)-better sollutions than through linear ref inement

MODELS BECOMING MORE CONSISTENT WITH DATA

FURTHER RESEARCH:-is search-space indeed non-monoutonous, multi-modal? (brute force)-are there indeed interaction-effects?-are f itness-functions bounded by different classes of cities?


calibrating sleuth

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