1. Predicting permit activity with cellular automata calibrated with genetic algorithms Sushil J. LouisGary Raines Department of Computer Science US Geological Survey sushil@cs.unr.edugraines@usgs.gov

2. 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 ?

3. 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

4. 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

5. http://gaslab.cs.unr.edu What is the problem?

6. 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

7. 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, …

8. http://gaslab.cs.unr.edu Genetic algorithm calibration

9. http://gaslab.cs.unr.edu What is a GA?  Randomized, parallel search  Models natural selection  Population based  Uses fitness to guide search

10. http://gaslab.cs.unr.edu Genetic algorithm search

11. 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

12. http://gaslab.cs.unr.edu Modified Annealed Voting Rule Probability of Life in Next Generation Number of Live Neighbors Status of Center Cell AliveDead > Annealing WindowVery LikelyLikely Annealing WindowLikelySomewhat Likely < Annealing WindowVery Somewhat Likely Unlikely

13. http://gaslab.cs.unr.edu Definitions of Parameters ParametersDefinition Very LikelySquare root of Likely (Larger) LikelyA high probability of life. Somewhat LikelyAn intermediate probability of life Very Somewhat LikelySquare root of Somewhat Likely (Larger) UnlikelyA low probability of life Resource ThresholdMinimum fuzzy membership defining where a reasonable explorationist would explore Anneal WindowPosition and width control response of CA

14. 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 bottomlikelyslikelyunlikely rt 447777

15. 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

16. 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

17. http://gaslab.cs.unr.edu Results

18. http://gaslab.cs.unr.edu Results

19. http://gaslab.cs.unr.edu Results

20. http://gaslab.cs.unr.edu Results

21. 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 ?

22. http://gaslab.cs.unr.edu Cross-Tabulation 1989-1998 Number of Cells CA Trace 01234567Sum Actual Trace 066364167126717650711068446 1354136767024420666 215442574918410325 3129691021334729203532 4333252783420161266 581115254231115148 68422342422143131 7174 34811257025373 Sum6696719696085993202421453770887