T. P. Runarsson, J. J. Merelo, U. Iceland & U. Granada (Spain) NICSO 2010 Adapting Heuristic Mastermind Strategies to Evolutionary Algorithms

Evolutionary Mastermind - Merelo/Runarsson 2 Game of MasterMind

Evolutionary Mastermind - Merelo/Runarsson 3 But that's just a game!

Evolutionary Mastermind - Merelo/Runarsson 4 1.Donald Knuth 2.NP-Complete 3.Differential cryptanalisis 4.Circuit and program test 5.Genetic profiling 6.Minimize guesses 7.Minimize evaluations 7 reasons why you should

Evolutionary Mastermind - Merelo/Runarsson 5 Let's play, then

Evolutionary Mastermind - Merelo/Runarsson 6 Consistent combinations

Evolutionary Mastermind - Merelo/Runarsson 7 Naïve Algorithm Repeat Find a consistent combination and play it.

Evolutionary Mastermind - Merelo/Runarsson 8 Looking for consistent solutions Optimization algorithm based on distance to consistency (for all combinations played) D = 2

Evolutionary Mastermind - Merelo/Runarsson 9 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

Evolutionary Mastermind - Merelo/Runarsson 10 Score consistent set

Evolutionary Mastermind - Merelo/Runarsson 11 Enter partitions Most parts. Score = 5Best worst case. Score = Entropy. Score = 1.67

Evolutionary Mastermind - Merelo/Runarsson 12 Less Naïve Algorithm Play initial combination Repeat until end Eliminate non- consistent combinations Score the rest using partitions Play best score

Evolutionary Mastermind - Merelo/Runarsson 13 And the (exhausted) winner is... Entropy & Most Parts obtains the best results ~ combinations played Naïve algorithms obtain ~ 4.6 Problem: exhaustive search needed

Evolutionary Mastermind - Merelo/Runarsson 14 We want to do better than exhaustive search Berghman et al.'s used only a subset of the set of consistent combinations with an evolutionary algorithm: non-exhaustive Better scaling In this paper, we want first to compute the size of the set which obtains the same result as exhaustive search.

Evolutionary Mastermind - Merelo/Runarsson 15 What we do in this paper Check exhaustive search strategies Improve EAs Minimize set with same results

Evolutionary Mastermind - Merelo/Runarsson 16 Comparison of exhaustive search strategies

Evolutionary Mastermind - Merelo/Runarsson 17 Since entropy is good, let's try on EDAs Rank-based GA did not yield good results Available as Algorithm::Mastermind::EDA Population = 1/6 of search space Replacement rate: 50% 10 * 1296 runs (10 for each combination AAAA.. FFFF)

Evolutionary Mastermind - Merelo/Runarsson 18 How fit are combinations Combinations evolved directly Fitness: Distance-to- consistency Play random consistent combination (f) Play highest local entropy (f l )

Evolutionary Mastermind - Merelo/Runarsson 19 Are EDAs any good?

Evolutionary Mastermind - Merelo/Runarsson 20 Can we avoid exhaustive search? Instead of finding all consistent combinations, how many are needed? Most-parts & entropy methods need only ~20 (10-25% of total) Could be used for EDAs Not in this paper!

Evolutionary Mastermind - Runarsson/Merelo 21 Exhaustive search algorithms examined Comparison with EDAs yield better- than-random results We can use just a subset of consistent combinations Concluding... Exhaustive search algorithms examined Comparison with EDAs yield better- than-random results We can use just a subset of consistent combinations

Evolutionary Mastermind - Merelo/Runarsson 22 Open source your science!

Evolutionary Mastermind - Merelo/Runarsson 23 That's all Thanks for your attention Any questions?