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Predicting permit activity with cellular automata calibrated with
genetic algorithms
Sushil J. Louis Gary Raines
Department of Computer Science
US Geological Survey
http://gaslab.cs.unr.edu
Outline
What is the problem? Calibrating a CA
What is the technique? Genetic Algorithm
What are the issues? Discretization Encoding Evaluation
What are our results ?
http://gaslab.cs.unr.edu
What is the problem?
Project mineral-related activity on public land to 2010 Predicting permit activity in an area
Spatially explicit USGS and others have data on permit activity from 1989 – 1998
as well as data on natural resources Use cellular automata to model (predict) mineral activity over
next ten years Problem: Takes weeks to tune CA rules to match
available data
http://gaslab.cs.unr.edu
What is the problem?
Can we automate calibrating a cellular automaton As good as CA calibrated by human In the same or less time
http://gaslab.cs.unr.edu
What is the problem?
http://gaslab.cs.unr.edu
Model calibration as search
Search through the space of possible model parameters to find a parameter set that fits observed data
Many search methods We use genetic algorithms
http://gaslab.cs.unr.edu
Genetic Algorithms
Poorly understood problems (Holland, ‘75, Goldberg, ‘89) Empirical evidence to support their use in this kind of
problem Physics models
Physical Review Letters, Volume 88, Issue 4 Journal of Quantitative Spectroscopy and Radiative Transfer. Volume
75, 2002, Pgs. 625 - 636 Seismic models
Congress on Evolutionary Computing 1999, pages 855 - 861 Hydrology models
In progress Proceedings of GECCO, CEC, …
http://gaslab.cs.unr.edu
Genetic algorithm calibration
http://gaslab.cs.unr.edu
What is a GA?
Randomized, parallel search Models natural selection Population based Uses fitness to guide search
http://gaslab.cs.unr.edu
Genetic algorithm search
http://gaslab.cs.unr.edu
Genetic Algorithm
Randomly initialize P(0) with candidate parameter sets
Loop Select P(t+1) from P(t) Crossover and Mutate P(t+1) Evaluate P(t+1) run CA model t = t+1
http://gaslab.cs.unr.edu
Modified Annealed Voting Rule Probability of Life in Next Generation
Number of Live NeighborsStatus of Center Cell
Alive Dead
> Annealing Window Very Likely LikelyAnnealing Window Likely Somewhat
Likely< Annealing Window Very
Somewhat Likely
Unlikely
http://gaslab.cs.unr.edu
Definitions of Parameters
Parameters DefinitionVery Likely Square root of Likely (Larger)Likely A high probability of life.Somewhat Likely An intermediate probability of lifeVery Somewhat Likely Square root of Somewhat Likely (Larger)
Unlikely A low probability of lifeResource Threshold Minimum fuzzy membership defining where
a reasonable explorationist would exploreAnneal Window Position and width control response of CA
http://gaslab.cs.unr.edu
GA Encoding
GA usually works with string structures representing a candidate solution
2^36 = 64Gig possibilities Fitness = scaled match to observed data
top bottom likely slikely unlikely rt4 4 7 7 7 7
http://gaslab.cs.unr.edu
GA Parameters
Population sizes – 50 Elitist selection – next generation is best of
parents and offspring Probability of crossover – 1.00 Probability of mutation - 0.05 Fitness scaling – 1.05
http://gaslab.cs.unr.edu
Model parameters
496 X 503 = 249,488 cell CA 4 or 5 years (iterations) Average over 3 runs Cell data imported from GIS
http://gaslab.cs.unr.edu
Results
http://gaslab.cs.unr.edu
Results
http://gaslab.cs.unr.edu
Results
http://gaslab.cs.unr.edu
Results
http://gaslab.cs.unr.edu
GA produces good parameter values (20% better than human)
GA is a viable tool for model exploration
Many different parameter sets give about the same fit ?
Modeling rare events ?
http://gaslab.cs.unr.edu
Cross-Tabulation 1989-1998Number of
CellsCA Trace
0 1 2 3 4 5 6 7 Sum
ActualTrace
0 66364 1671 267 176 50 7 11 0 68446
1 354 136 76 70 24 4 2 0 666
2 154 42 57 49 18 4 1 0 325
3 129 69 102 133 47 29 20 3 532
4 33 32 52 78 34 20 16 1 266
5 8 11 15 25 42 31 11 5 148
6 8 4 22 34 24 22 14 3 131
7 17 4 17 34 81 125 70 25 373
Sum 66967 1969 608 599 320 242 145 37 70887