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T. P. Runarsson, J. J. Merelo,
U. Iceland & U. Granada (Spain)
NICSO 2010
Adapting Heuristic Mastermind Strategies to
Evolutionary Algorithms
Evolutionary Mastermind - Merelo/R unarsson 2
Game of MasterMind
Evolutionary Mastermind - Merelo/R unarsson 3
But that's just a game!
Evolutionary Mastermind - Merelo/R unarsson 4
7 reasons why you should
Donald Knuth
NP-Complete
Differential cryptanalisis
Circuit and program test
Genetic profiling
Minimize guesses
Minimize evaluations
Evolutionary Mastermind - Merelo/R unarsson 5
Let's play, then
Evolutionary Mastermind - Merelo/R unarsson 6
Consistent combinations
Evolutionary Mastermind - Merelo/R unarsson 7
Naïve Algorithm
Repeat
Find a consistent combination and play it.
Evolutionary Mastermind - Merelo/R unarsson 8
Looking for consistent solutions
Optimization algorithm based on distance to consistency (for all combinations played)
D = 2
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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
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Score consistent set
AAA BBB CCC ABC CBA AAB AAC AAD BCAAAA 3b-0w 0b-0w 0b-0w 1b-0w 1b-0w 2b-0w 2b-0w 2b-0w 1b-0wBBB 0b-0w 3b-0w 0b-0w 1b-0w 1b-0w 1b-0w 0b-0w 0b-0w 1b-0wCCC 0b-0w 0b-0w 3b-0w 1b-0w 1b-0w 0b-0w 1b-0w 0b-0w 1b-0wABC 1b-0w 1b-0w 1b-0w 3b-0w 1b-2w 1b-1w 2b-0w 1b-0w 0b-3wCBA 1b-0w 1b-0w 1b-0w 1b-2w 3b-0w 0b-2w 0b-2w 0b-1w 1b-2wAAB 2b-0w 1b-0w 0b-0w 1b-1w 0b-2w 3b-0w 2b-0w 2b-0w 0b-2wAAC 2b-0w 0b-0w 1b-0w 2b-0w 0b-2w 2b-0w 3b-0w 2b-0w 0b-2wAAD 2b-0w 0b-0w 0b-0w 1b-0w 0b-1w 2b-0w 2b-0w 3b-0w 0b-1wBCA 1b-0w 1b-0w 1b-0w 0b-3w 1b-2w 0b-2w 0b-2w 0b-1w 3b-0w
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Enter partitions
0b-0w 0b-1w 0b-2w 0b-3w 1b-0w 1b-1w 1b-2w 2b-0wAAA 2 0 0 0 3 0 0 3BBB 4 0 0 0 4 0 0 0CCC 4 0 0 0 4 0 0 0ABC 0 0 0 1 4 1 1 1CBA 0 1 2 0 3 0 2 0AAB 1 0 2 0 1 1 0 3AAC 1 0 2 0 1 0 0 4AAD 2 2 0 0 1 0 0 3BCA 0 1 2 1 3 0 1 0
Most parts. Score = 5 Best worst case. Score = -3
1.31
0.96
0.96
1.58
1.52
1.67
1.42
1.52
1.67
Entropy. Score = 1.67
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Less Naïve Algorithm
Play initial combination
Repeat until end
Eliminate non-consistent combinations
Score the rest using partitions
Play best score
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And the (exhausted) winner is...
Entropy & Most Parts obtains the best results ~ 4.408 combinations played
Naïve algorithms obtain ~ 4.6
Problem: exhaustive search needed
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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.
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What we do in this paper
Check exhaustive search strategies
Make small improvements
Find out minimum set with same results
Incorporate heuristic into EA
Play the best score
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Comparison of exhaustive search strategies
Strategy min mean median max st.dev. max guesses
Entropy 4.38 4.41 4.41 4.42 0.01 6
Most parts 4.38 4.41 4.41 4.43 0.01 7
Expected size 4.45 4.47 4.47 4.49 0.02 7
Worst case 4.46 4.48 4.47 4.51 0.02 6
Random 4.57 4.61 4.61 4.65 0.03 8
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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)
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How fit are combinations
Combinations evolved directly
Fitness: Distance-to-consistency
Play random consistent combination (f)
Play highest local entropy (f
l)
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Strategy min mean median max st. dev, max guesses
Entropy 4.38 4.41 4.41 4.42 0.01 6
Most parts 4.38 4.41 4.41 4.43 0.01 7
Expected size 4.45 4.47 4.47 4.49 0.02 7
Worst case 4.46 4.48 4.47 4.51 0.02 6
LocalEntropy 4.53 4.57 4.57 4.61 0.02 7
EDA+fl 4.52 4.57 4.58 4.6 0.03 7
EDA+f 4.56 4.62 4.62 4.67 0.03 7
Random 4.57 4.61 4.61 4.65 0.03 8
Are EDAs any good?
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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!
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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
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Open source your science!
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That's allThat's all
Thanks for your attentionAny questions?
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