Computing epistasis through Walsh transforms

Iglesias, Marcos; Vidal, Concepción Martínez; Verschoren, A.

doi:10.1145/347127.347243

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A P R O O F S Of Some Auxiliary Results2

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2007

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“…The Walsh coefficients w 0 , w 2 i, calculated in [5], are given by (16) w 0 = [t -n + i)2('-2 ">/ 2 , { -2<'-2n >/ 2 (* + 1) if 0^i<£-n…”

Section: A P R O O F S Of Some Auxiliary Resultsmentioning

confidence: 99%

“…hence, for any pair of integers £ ^ n, the value of Fi = JZ ^ i s g i v e n by (see [5] for 3. if {i, k} DAj = 0 then ^(H*) = 2" n , w {Tj)2 i = io (r))2 * = 0 and u) (Tj)2 i +2 t = 0. So, it directly follows, from (17), that the Walsh coefficient w 2 x +2 k of T" is Finally, we need to determinate how many sets Aj contain {i, k).…”

Section: A P R O O F S Of Some Auxiliary Resultsmentioning

confidence: 99%

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The 2-epistasis of fitness functions

Iglesias

Peñaranda

Vidal

et al. 2007

Bull. Austral. Math. Soc.

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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.

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“…The Walsh coefficients w 0 , w 2 i, calculated in [5], are given by (16) w 0 = [t -n + i)2('-2 ">/ 2 , { -2<'-2n >/ 2 (* + 1) if 0^i<£-n…”

Section: A P R O O F S Of Some Auxiliary Resultsmentioning

confidence: 99%

Section: A P R O O F S Of Some Auxiliary Resultsmentioning

confidence: 99%