Predicting permit activity with cellular automata calibrated with

genetic algorithms

Sushil J. Louis Gary Raines

Department of Computer Science

US Geological Survey

sushil@cs.unr.edu graines@usgs.gov

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 ?

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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

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What is the problem?

Can we automate calibrating a cellular automaton As good as CA calibrated by human In the same or less time

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What is the problem?

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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

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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, …

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Genetic algorithm calibration

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What is a GA?

Randomized, parallel search Models natural selection Population based Uses fitness to guide search

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Genetic algorithm search

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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

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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

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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

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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

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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

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Model parameters

496 X 503 = 249,488 cell CA 4 or 5 years (iterations) Average over 3 runs Cell data imported from GIS

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Results

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Results

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Results

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Results

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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 ?

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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