In this note about Genetic Algorithms(GA-), we study the2-epistasisof a fitness function over a search space. This concept is a natural generalisation of that ofepistasis, previously considered by Davidor in 1991 Suys and Verschoren in 1996 and Van Hove and Verschoren in 1994 for example. We completely characterise fitness functions whose 2-epistasis is minimal: these are exactly the second order functions. The validity of 2-epistasis as a measure of hardness with respect to genetic algorithms is checked over some classical laboratory functions. Finally, we obtain an upper bound of the maximal value of the 2-epistasis when we restrict attention to non-negative functions.
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 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.2000 Mathematics subject classification: 68R99.
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