A Hitchikers Guide To Parallel G As

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A Hitchikers Guide To Parallel G As

  1. 1. A Hitchiker’s guide to parallel GAs 3 key papers by Eric Cantu-Paz and David Golberg Presented by : Yann SEMET Universite de Technologie de Compiegne
  2. 2. Our 3 papers <ul><li>A survey of Parallel Genetic Algorithms , </li></ul><ul><li>E. Cantu-Paz, 1998 </li></ul><ul><li>On the scalability of Parallel GAs , </li></ul><ul><li>E. Cantu-Paz & David Golberg, 1999 </li></ul><ul><li>Markov Chain Models of Parallel GAs , </li></ul><ul><li>E. Cantu-Paz, 2000 </li></ul>
  3. 3. Roadmap <ul><li>General knowledge </li></ul><ul><ul><li>Toward parallel GAs </li></ul></ul><ul><ul><li>Categorization </li></ul></ul><ul><ul><li>Key issues </li></ul></ul><ul><li>Theory run for parameter sizing </li></ul><ul><ul><li>Bounding cases </li></ul></ul><ul><ul><li>Gambler’s Ruin model </li></ul></ul><ul><ul><li>Markov Model </li></ul></ul>
  4. 4. A good nest <ul><li>Illinois and parallelism </li></ul><ul><li>Illinois and GAs </li></ul><ul><li>An ideal nest for parallel GAs </li></ul>
  5. 5. Flynn’s taxonomy <ul><li>SISD : your PC </li></ul><ul><li>SIMD : not really relevant </li></ul><ul><li>MISD : multi processors </li></ul><ul><li>MIMD : super computers </li></ul>
  6. 6. GAs : 2 levels of parallelism <ul><li>Population-wise </li></ul><ul><li>Computation-wise </li></ul>
  7. 7. Taxonomy <ul><li>Master-slave GAs </li></ul><ul><li>Fine-grained GAs </li></ul><ul><li>Coarse-grained GAs </li></ul><ul><li>Hierarchical GAs </li></ul>
  8. 8. Master and Slaves <ul><li>Similar to a simple GA </li></ul><ul><li>Fitness/Communication tradeoff </li></ul><ul><li>Fitness distribution </li></ul><ul><li>Operator distribution </li></ul><ul><li>Efficient speedup </li></ul>
  9. 9. Fine-grained <ul><li>One population </li></ul><ul><li>Limited spatial interaction </li></ul><ul><li>Critical parameter : radius </li></ul><ul><li>Matches massively parallel computer </li></ul><ul><li>A potential alternative to Coarse-Grained </li></ul>
  10. 10. Multiple-Deme <ul><li>Key factors : </li></ul><ul><ul><li>Demes </li></ul></ul><ul><ul><li>Migration </li></ul></ul><ul><ul><li>Topology </li></ul></ul>
  11. 11. Hierarchical <ul><li>Three possibilities </li></ul><ul><li>The engineer’s choice </li></ul>
  12. 12. Non-Traditional GAs <ul><li>ECO </li></ul><ul><li>GENITOR </li></ul><ul><li>mGAs, fmGAs </li></ul><ul><li>GP </li></ul>
  13. 13. Engineering Summary 1 <ul><li>Categorization </li></ul><ul><li>Market Map </li></ul>
  14. 14. Engineering Summary 2 <ul><li>Key parameters : </li></ul><ul><ul><li>Demes </li></ul></ul><ul><ul><li>Migration </li></ul></ul><ul><ul><li>Topology </li></ul></ul><ul><li>Goal : remain panmictic </li></ul>
  15. 15. Milestone1 <ul><li>Up to now : </li></ul><ul><ul><li>Categorization </li></ul></ul><ul><ul><li>Key issues </li></ul></ul><ul><li>To come : </li></ul><ul><ul><li>Theoretical scaling </li></ul></ul><ul><ul><li>Markov models </li></ul></ul>
  16. 16. Theory Roadmap <ul><li>Goal : calculate optimal parameters </li></ul><ul><li>From Master-Slave to : </li></ul><ul><ul><li>Multiple deme </li></ul></ul><ul><ul><li>High Migration </li></ul></ul><ul><ul><li>Dense topology </li></ul></ul><ul><li>Markov models </li></ul>
  17. 17. Paramaters to be tuned <ul><li>Populations : </li></ul><ul><ul><li>Size </li></ul></ul><ul><ul><li>Number </li></ul></ul><ul><li>Migration : </li></ul><ul><ul><li>Rate </li></ul></ul><ul><ul><li>Frequency </li></ul></ul><ul><li>Topology : </li></ul><ul><ul><li>Density </li></ul></ul><ul><ul><li>Shape </li></ul></ul>
  18. 18. Single Population 1 <ul><li>Assumptions </li></ul><ul><ul><li>Distributed population </li></ul></ul><ul><ul><li>Modified operators to ensure panmictism </li></ul></ul><ul><li>Why ? </li></ul><ul><ul><li>Straightforward and intuitive </li></ul></ul><ul><ul><li>Close to Multiple-deme bounding case </li></ul></ul>
  19. 19. Single Population 2 <ul><li>Computation time : </li></ul><ul><li>Optimal chunk size : </li></ul>
  20. 20. Multi Populations 1 <ul><li>2 Bounding cases : </li></ul><ul><ul><li>Lower Bound on migration and connectivity </li></ul></ul><ul><ul><li>Upper bound : “deja vu)” but : </li></ul></ul><ul><ul><ul><li>At most one migration per generation </li></ul></ul></ul><ul><ul><ul><li>Picking the migrants </li></ul></ul></ul>
  21. 21. The Gambler’s ruin model <ul><li>A random walk to absorbative barriers </li></ul><ul><li>Predicts solution quality </li></ul><ul><li>Yields population sizing </li></ul><ul><li>A conservative model </li></ul>
  22. 22. Multiple demes <ul><li>Relaxation : </li></ul>
  23. 23. Regular topologies <ul><li>Over two epochs </li></ul>
  24. 24. Optimal parameters <ul><li>Deme size : </li></ul><ul><li>Optimal connectivity : </li></ul>
  25. 25. Topology considerations <ul><li>Efficiency depends on connectivity </li></ul><ul><li>Extented Neighborhoods </li></ul><ul><li>After several epochs : </li></ul>
  26. 26. Derivation… <ul><li>Dimensional analysis gives : </li></ul><ul><li>The GRM then gives : </li></ul>
  27. 27. Derivation… <ul><li>Optimal connectivity : </li></ul><ul><li>Optimal number of epochs obtained similarly </li></ul>
  28. 28. The long run <ul><li>At the end : </li></ul>
  29. 29. Finally <ul><li>Solving the time equation : </li></ul><ul><li>Similar to single population ! </li></ul>
  30. 30. Markov Chains <ul><li>Transient and closed states </li></ul><ul><li>M : transition matrix </li></ul><ul><li>N :fundamental matrix : </li></ul><ul><ul><li>T : time </li></ul></ul><ul><ul><li>V : distribution </li></ul></ul><ul><ul><li>A : Pbb on the long run </li></ul></ul>
  31. 31. Upper Bounding case <ul><li>Full migration </li></ul><ul><li>Dense topology </li></ul><ul><li>V is a binomial distribution </li></ul>
  32. 32. Arbitrary Migration <ul><li>Different rates : might not converge </li></ul><ul><li>Yields more state </li></ul><ul><li>V is again binomial but with a disjunction </li></ul>
  33. 33. Arbitrary Topologies <ul><li>Even more states ! </li></ul><ul><li>Which demes actually converged ? </li></ul><ul><li>Each state is a binary string </li></ul>
  34. 34. Conclusions on Markov Chains <ul><li>Predictive models </li></ul><ul><li>Panmictism on the long run </li></ul><ul><li>Prefer : </li></ul><ul><ul><li>High migration rates </li></ul></ul><ul><ul><li>Dense topologies </li></ul></ul>
  35. 35. General Summary <ul><li>Categorization </li></ul><ul><li>Key issues </li></ul><ul><li>Parameter sizing </li></ul><ul><li>Accurate Predictive Models </li></ul><ul><li>Tradeoff Practical Guidelines </li></ul>
  36. 36. Discussion

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