Finding an evolutionary solution to the game of Mastermind with good scaling behavior

Finding an evolutionary solution to the game of Mastermind with good scaling behavior

By Merelo, Mora, Cotta, Fernández

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Juan Julián Merelo Guervós

February 05, 2013
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  1. J. J. Merelo, A. Mora, C. Cotta, A. Fernández U.

    Granada & Málaga (Spain) http://geneura.wordpress.com http://twitter.com/geneura Finding an evolutionary solution to the game of Mastermind with good scaling behavior
  2. Faster Mastermind Merelo/Mora/Cotta/Fernández 2 Game of MasterMind G R Y

    B R B Y P DB G Y B R Y G Y
  3. Faster Mastermind Merelo/Mora/Cotta/Fernández 3 Let's play, then

  4. Faster Mastermind Merelo/Mora/Cotta/Fernández 4 Consistent combinations

  5. Faster Mastermind Merelo/Mora/Cotta/Fernández 5 Naïve Algorithm  Repeat  Find

    a consistent combination and play it.
  6. Faster Mastermind Merelo/Mora/Cotta/Fernández 6 Looking for consistent solutions  Optimization

    algorithm based on distance to consistency (for all combinations played) Y DB Y P D = 2
  7. Faster Mastermind Merelo/Mora/Cotta/Fernández 7 Not all consistent combinations are born

    the same  There's at least one better than the others (the solution).  Some will reduce the remaining search space more.  But scoring them is an open issue.
  8. Faster Mastermind Merelo/Mora/Cotta/Fernández 8 What we did What we did

    before before Minimize Minimize consistent set consistent set size to speed up size to speed up solutions solutions
  9. Faster Mastermind Merelo/Mora/Cotta/Fernández 9 What we do now Test this

    smaller (and unique) consistent-set size over a range of problem sizes
  10. Faster Mastermind Merelo/Mora/Cotta/Fernández 10  Use consistent set- Use consistent

    set- size == 10. size == 10.
  11. Faster Mastermind Merelo/Mora/Cotta/Fernández 11 Number of evaluations

  12. Faster Mastermind Merelo/Mora/Cotta/Fernández 12 Proportion of search space explored

  13. Faster Mastermind Merelo/Mora/Cotta/Fernández 13 Evaluatios vs. population

  14. Faster Mastermind Merelo/Mora/Cotta/Fernández 14 Three times as fast! #Evaluations decreased

    up to 70%! #Evaluations decreased up to 70%! (Game performance more or less the same for (Game performance more or less the same for smaller sizes) smaller sizes)
  15. Faster Mastermind Merelo/Mora/Cotta/Fernández 15 Open source your science!

  16. Faster Mastermind Merelo/Mora/Cotta/Fernández 16 Thank you very much Questions?

  17. J. J. Merelo, A. Mora, C. Cotta, A. Fernández U.

    Granada & Málaga (Spain) http://geneura.wordpress.com http://twitter.com/geneura Finding an evolutionary solution to the game of Mastermind with good scaling behavior Image from Just a Prairie Boy at http://www.flickr.com/photos/justaprairieboy/4565153930/in
  18. Faster Mastermind Merelo/Mora/Cotta/Fernández 2 Game of MasterMind G R Y

    B R B Y P DB G Y B R Y G Y
  19. Faster Mastermind Merelo/Mora/Cotta/Fernández 3 Let's play, then How would you

    play mastermind? It's not easy to do, since possible branches are many more than for Sudoku or even chess. In fact, this is the kind of game that can be played more easily by a machine than by a person. CC picture from http://www.flickr.com/photos/unloveable/239993254 9/
  20. Faster Mastermind Merelo/Mora/Cotta/Fernández 4 Consistent combinations One of the possible

    ways to find solutions. Could be others, of course, but this is a good one.
  21. Faster Mastermind Merelo/Mora/Cotta/Fernández 5 Naïve Algorithm  Repeat  Find

    a consistent combination and play it.
  22. Faster Mastermind Merelo/Mora/Cotta/Fernández 6 Looking for consistent solutions  Optimization

    algorithm based on distance to consistency (for all combinations played) Y DB Y P D = 2
  23. Faster Mastermind Merelo/Mora/Cotta/Fernández 7 Not all consistent combinations are born

    the same  There's at least one better than the others (the solution).  Some will reduce the remaining search space more.  But scoring them is an open issue. Like the birds. They look the same, but one of them has a bad hair day. Or rather a bad feather day. Let's just say that what we do is, once a solution is consistent, we find a scoring based on how the set of consistent solutions is partitioned by comparing consistent solutions with each other. In other papers we tested different ways of doing it, and we're fixing it here. Ideally, anyways, the solution should have always the maximum fitness, but I'm not sure it does (it will have to be checked)
  24. Faster Mastermind Merelo/Mora/Cotta/Fernández 8 What we did What we did

    before before Minimize Minimize consistent set consistent set size to speed up size to speed up solutions solutions Creative commons image from Okinawa Soba at http://www.flickr.com/photos/24443965@N08/3606831198/ This was published in NICSO, Evostar, CIG, GECCO (as a póster) and eventually PPSN
  25. Faster Mastermind Merelo/Mora/Cotta/Fernández 9 What we do now Test this

    smaller (and unique) consistent-set size over a range of problem sizes CC Picture from San Diego Shooter http://www.flickr.com/photos/nathaninsandiego/375898830 New is always better. And better is also always better. Mostly.
  26. Faster Mastermind Merelo/Mora/Cotta/Fernández 10  Use consistent set- Use consistent

    set- size == 10. size == 10. Picture from Philip James Claxton at http://www.flickr.com/photos/philipclaxton/4076919342/in/pho
  27. Faster Mastermind Merelo/Mora/Cotta/Fernández 11 Number of evaluations

  28. Faster Mastermind Merelo/Mora/Cotta/Fernández 12 Proportion of search space explored

  29. Faster Mastermind Merelo/Mora/Cotta/Fernández 13 Evaluatios vs. population

  30. Faster Mastermind Merelo/Mora/Cotta/Fernández 14 Three times as fast! #Evaluations decreased

    up to 70%! #Evaluations decreased up to 70%! (Game performance more or less the same for (Game performance more or less the same for smaller sizes) smaller sizes) Image from John Traynor at http://www.flickr.com/photos/trainor/3028243647/in/photost
  31. Faster Mastermind Merelo/Mora/Cotta/Fernández 15 Open source your science! All source,

    data sets, experiment results for this paper are available from Sourceforge (in fact, they were while we were doing it). Source is also available from the CPAN Perl module server worldwide, in two separate modules: the algorithm itself as the module Algorithm::Mastermind (along with other algorithms; for instance, Knuth's algorithm), and the EA in the shape of the Evolutionary Algorithm library.
  32. Faster Mastermind Merelo/Mora/Cotta/Fernández 16 Thank you very much Questions?