This document summarizes research into using evolutionary algorithms to solve the Mastermind puzzle more efficiently than exhaustive search or naive algorithms. The researchers tested canonical genetic algorithms and estimation of distribution algorithms on the problem, finding that these evolutionary approaches obtained results comparable or better than exhaustive search with less computational effort. Their approach involved using distance-to-consistency as the fitness function and scoring and selecting consistent combinations to guide the search. The evolutionary algorithms were able to defeat exhaustive search with similar running times to naive approaches.

1. J. J. Merelo , T. P. Runarsson U. Granada (Spain) & U. Iceland Finding better solutions to the Mastermind puzzle using evolutionary algorithms

2. Game of MasterMind

3. Why should I care? I want to frag!

5. NP-Complete

6. Differential cryptanalisis

7. Circuit and program test

8. Genetic profiling

9. Minimize guesses

10. Minimize evaluations

11. Let's play, then

12. Consistent combinations

16. Some will reduce the remaining search space more.

17. But scoring them is an open issue

18. Score consistent set

19. Enter partitions Most parts. Score = 5 Best worst case. Score = -3 Entropy. Score = 1.67 1.31 0.96 0.96 1.58 1.52 1.67 1.42 1.52 1.67

22. Score them using partitions

23. Play best score

25. Naïve algorithms obtain ~ 4.6

26. Problem : exhaustive search needed

28. What we do in this paper Evolutionary algorithm Fitness = Distance-to-consistency Gather a set of consistent combinations Score using most-parts Play the best score

30. Population = ¼ of search space

31. Reset after stagnation

32. Run until 20 consistent combinations are found or 3 generations without change

33. 10 * 1296 runs (10 for each combination AAAA .. FFFF)

37. Evolutionary algorithm acting on final stages

39. Evolutionary algorithm acting on final stages

40. Mostly exploratory regime.

42. Running time similar to naïve evolutionary algorithm

44. Running time similar to naïve evolutionary algorithm

45. Conclusions in exhaustive search can be translated to EAs. Concluding...

46. That's all Thanks for your attention