Higher epistasis in genetic algorithms

We study the k-epistasis of a fitness function over a search space. This concept is a natural generalization of that of epistasis, previously considered by Davidor, Suys and Verschoren and Van Hove and Verschoren [Y.Davidor, in: Foundations of genetic algorithms, Vol. 1, (1991), pp. 2325; D. Suys and A. Verschoren, Proc Int. Conf. on Intelligent Technologies in Human-Related Sciences (ITHURS96), Vol. II (1996), pp. 251258; H. Van Hove and A. Verschoren ,Comput. Artificial Intell. 14 (1994), 271277], for example. We completely characterize fitness functions whose k-epistasis is minimal: these are exactly the functions of order k. We also obtain an upper bound for the k-epistasis of nonnegative fitness functions.

Publication year:2008