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Extra info for Foundations of Genetic Algorithms: 9th International Workshop, FOGA 2007, Mexico City, Mexico, January 8-11, 2007, Revised Selected Papers
However, it is important to notice that generally the curves have a tendency to increase, thus showing that for this landscape recombination is aiding the evolution in ﬁnding optimal BBs or schemata. 6 Conclusions In this paper we have shown how a selecto-recombinative EA can be most naturally understood in terms of Building Blocks that form a basis for the description of the dynamics and which, in distinction to the notion of building block inherent in the BBH and HST, can be given a complete and rigorous mathematical characterization.
For any set X, an m-parent transmission function [14,1,18] over X is an element of the set m+1 X → [0, 1] ∀x1 , . . , xm ∈ X, T : T (x, x1 , . . , xm ) = 1 x∈X 1 Extending the notation introduced above, we denote this set by ΛX m . Following , we use conditional probability notation in our denotation of transmission functions. Thus an m-parent transmission function T (x, x1 , . . , xm ) is denoted T (x|x1 , . . , xm ). A transmission function can be used to model the individual-level eﬀect of mutation, which operates on one parent and produces one child, and indeed the individual-level eﬀect of any variation operation which operates on any numbers of parents and produces one child.
4 NIAH blocks. N =4, p =0. 02 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 t Fig. 5. Graph of PI (s + r)/PI (s) as a function of time for N = 4, 4 NIAH blocks and one-point crossover not all order-one BBs have the same evolution, BBs associated with loci at the boundary being preferred to those away from the boundary. This is not a direct eﬀect of recombination, as pc does not explicitly enter in the equations for the order-one BBs, but rather an indirect one, in that it enters in the schema ﬁtness of the BBs.