Phase transition in a random NK landscape model

An analysis for the phase transition in a random NK landscape model, NK ( n , k , z ) , is given. This model is motivated from population genetics and the solubility problem for the model is equivalent to a random ( k + 1 ) -SAT problem. Gao and Culberson [Y. Gao, J. Culberson, An analysis of phase...

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Bibliographic Details
Published in:Artificial intelligence 2008-02, Vol.172 (2), p.179-203
Main Authors: Choi, Sung-Soon, Jung, Kyomin, Kim, Jeong Han
Format: Article
Language:English
Subjects:
Applied sciences
Artificial intelligence
Computer science
control theory
systems
Exact sciences and technology
Fitness function
Learning and adaptive systems
NK landscape
Phase transition
Satisfiability problem
Solubility
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Summary:An analysis for the phase transition in a random NK landscape model, NK ( n , k , z ) , is given. This model is motivated from population genetics and the solubility problem for the model is equivalent to a random ( k + 1 ) -SAT problem. Gao and Culberson [Y. Gao, J. Culberson, An analysis of phase transition in NK landscapes, Journal of Artificial Intelligence Research 17 (2002) 309–332] showed that a random instance generated by NK ( n , 2 , z ) with z > z 0 = 27 − 7 5 4 is asymptotically insoluble. Based on empirical results, they conjectured that the phase transition occurs around the value z = z 0 . We prove that an instance generated by NK ( n , 2 , z ) with z < z 0 is soluble with positive probability by providing a polynomial time algorithm. Using branching process arguments, we prove again that an instance generated by NK ( n , 2 , z ) with z > z 0 is asymptotically insoluble. The results show the phase transition around z = z 0 for NK ( n , 2 , z ) . In the course of the analysis, we introduce a generalized random 2-SAT formula, which is of self interest, and show its phase transition phenomenon.
ISSN:0004-3702
1872-7921
DOI:10.1016/j.artint.2007.06.002