Entropy-Driven Evolutionary Approaches to the Mastermind Problem
•Download as ODP, PDF•
0 likes•190 views
Poster for PPSN 2010 at Krakow, presenting a new coevolutionary method for finding solutions to the Mastermind puzzle
![Entropy-Driven Evolutionary Approaches to the Mastermind Problem C. Cotta J.J. Merelo A. Mora T.P. Runarsson University of Málaga University of Granada University of Iceland M ASTERMIND Find the secret combination of colors using the information provided by the codemaker, e.g., h ( , ) = hidden combination played combination 1 correct peg 2 pegs of the right colot but out of place Mastermind is a dynamic constraint satisfaction problem. Consistency is the key. Assume these are the available colors: and let the hidden combination be ... 1 st guess 64 combinations are initially possible 12 combinations remain feasible after 1 st move 2 nd guess Only 2 possible combinations remained after 2 nd move 3 rd guess A combination c is feasible iff h( c , g i ) = h( g i ,c h ) for all i , where g i are previous guesses and c h is the secret combination. Let Φ={ c 1 ,... c k } be a collection of feasible combinations, given the information gathered in previous moves. We compute the partition matrix Ξ Ξ ibw = |{c Φ | h( c , c i ) = < b , w > }| We pick c i such that the entropy of Ξ i[··] is maximal , i.e., we maximize the information obtained when playing a combination. An EA tries to find feasible solutions (1st-level goal) maximizing entropy (2nd-level goal). Experiments The algorithms have been tested on instances with 4 pegs and 6 or 8 colors . A comparison is done with EvoRank , a state-of-the-art EA for this problem. E GAs perform comparably to EvoRank with a much lower computational effort . E GAC M is the best E GA, statistically indistinguishable of EvoRank in number of guesses. Seeded initialization is essential for good performance.](https://image.slidesharecdn.com/postermastermind-101008045426-phpapp01/85/Entropy-Driven-Evolutionary-Approaches-to-the-Mastermind-Problem-1-320.jpg)
Recommended
Recommended
More Related Content
What's hot
What's hot (20)
Similar to Entropy-Driven Evolutionary Approaches to the Mastermind Problem
Similar to Entropy-Driven Evolutionary Approaches to the Mastermind Problem (20)
More from Juan J. Merelo
More from Juan J. Merelo (20)
Recently uploaded
Recently uploaded (20)
Entropy-Driven Evolutionary Approaches to the Mastermind Problem
- 1. Entropy-Driven Evolutionary Approaches to the Mastermind Problem C. Cotta J.J. Merelo A. Mora T.P. Runarsson University of Málaga University of Granada University of Iceland M ASTERMIND Find the secret combination of colors using the information provided by the codemaker, e.g., h ( , ) = hidden combination played combination 1 correct peg 2 pegs of the right colot but out of place Mastermind is a dynamic constraint satisfaction problem. Consistency is the key. Assume these are the available colors: and let the hidden combination be ... 1 st guess 64 combinations are initially possible 12 combinations remain feasible after 1 st move 2 nd guess Only 2 possible combinations remained after 2 nd move 3 rd guess A combination c is feasible iff h( c , g i ) = h( g i ,c h ) for all i , where g i are previous guesses and c h is the secret combination. Let Φ={ c 1 ,... c k } be a collection of feasible combinations, given the information gathered in previous moves. We compute the partition matrix Ξ Ξ ibw = |{c Φ | h( c , c i ) = < b , w > }| We pick c i such that the entropy of Ξ i[··] is maximal , i.e., we maximize the information obtained when playing a combination. An EA tries to find feasible solutions (1st-level goal) maximizing entropy (2nd-level goal). Experiments The algorithms have been tested on instances with 4 pegs and 6 or 8 colors . A comparison is done with EvoRank , a state-of-the-art EA for this problem. E GAs perform comparably to EvoRank with a much lower computational effort . E GAC M is the best E GA, statistically indistinguishable of EvoRank in number of guesses. Seeded initialization is essential for good performance.