Black-Box Complexity: Breaking the O(n n) Barrier of LeadingOnes

10/24/2012

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by   Benjamin Doerr, et al.

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We show that the unrestricted black-box complexity of the n-dimensional XOR- and permutation-invariant LeadingOnes function class is O(n (n) / n). This shows that the recent natural looking O(n n) bound is not tight. The black-box optimization algorithm leading to this bound can be implemented in a way that only 3-ary unbiased variation operators are used. Hence our bound is also valid for the unbiased black-box complexity recently introduced by Lehre and Witt (GECCO 2010). The bound also remains valid if we impose the additional restriction that the black-box algorithm does not have access to the objective values but only to their relative order (ranking-based black-box complexity).