On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
Upper and Lower Bounds for Randomized Search Heuristics in Black-Box Optimization
Theory of Computing Systems
Black-box search by unbiased variation
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Faster black-box algorithms through higher arity operators
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Theory of Randomized Search Heuristics: Foundations and Recent Developments
Theory of Randomized Search Heuristics: Foundations and Recent Developments
Towards a complexity theory of randomized search heuristics: ranking-based black-box complexity
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Reducing the arity in unbiased black-box complexity
Proceedings of the 14th annual conference on Genetic and evolutionary computation
Black-box complexity: from complexity theory to playing mastermind
Proceedings of the 15th annual conference companion on Genetic and evolutionary computation
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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 log(n) / loglogn). This shows that the recent natural looking O(nlogn) 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. 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).