IEEE Transactions On Evolutionary Computation
N-K fitness landscapes have been widely used as examples and test functions in the field of evolutionary computation. Thus, the computational complexity of these landscapes as optimization problems is of interest. We investigate the computational complexity of the problem of optimizing the N-K fitness functions and related fitness functions. We give an algorithm to optimize adjacent-model N-K fitness functions which is polynomial in N. We show that the decision problem corresponding to optimizing random-model N-K fitness functions is NP-complete for K > 1 and is polynomial for K = 1. If the restriction that the ith component function depends on the ith bit is removed, then the problem is NP-complete even for K = 1. We also give a polynomial-time approximation algorithm for the arbitrary-model N-K optimization problem.
© 2000 IEEE
A. H. Wright, R. K. Thompson and Jian Zhang, "The computational complexity of N-K fitness functions," in IEEE Transactions on Evolutionary Computation, vol. 4, no. 4, pp. 373-379, Nov 2000.