Phase transition in a random NK landscape model

Authors:
Sung-Soon Choi;Kyomin Jung;Jeong Han Kim
Affiliations:
Seoul National University, Seoul, Korea;Massachusetts Institute of Technology, Cambridge, MA;Microsoft Research, Redmond, WA
Venue:
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Year:
2005

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Abstract

An analysis for the phase transition in a random NK landscape model is given. For the fixed ratio model, NK(n,k,z), Gao and Culberson [17] showed that a random instance generated by NK(n,2,z) with z z0 = 27-7/√54 is asymptotically insoluble. Based on empirical results, they conjectured that the phase transition occurs around the value z = z0. We prove that an instance generated by NK(n,2,z) with z 0 is soluble with positive probability by providing a variant of the unit clause algorithm. Using branching process arguments, we also reprove that an instance generated by NK(n,2,z) with z z0 is asymptotically insoluble. The results show the phase transition around z = z0 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.