2016/04/08 by Doerr, Carola, Lengler, Johannes · 1 citation
#Computational Complexity (cs.CC) #F.2.2 #FOS: Computer and information sciences #Neural and Evolutionary Computing (cs.NE)
paper · doi:10.48550/arxiv.1604.02355
One important goal of black-box complexity theory is the development of complexity models allowing to derive meaningful lower bounds for whole classes of randomized search heuristics. Complementing classical runtime analysis, black-box models help us understand how algorithmic choices such as the population size, the variation operators, or the selection rules influence the optimization time. One example for such a result is the Ω(n log n) lower bound for unary unbiased algorithms on functions with a unique global optimum [Lehre/Witt, GECCO 2010], which tells us that higher arity operators or biased sampling strategies are needed when trying to beat this bound. In lack of analyzing techniques, almost no non-trivial bounds are known for other restricted models. Proving such bounds therefore remains to be one of the main challenges in black-box complexity theory. With this paper we contribute to our technical toolbox for lower bound computations by proposing a new type of information-theoretic argument. We regard the permutation- and bit-invariant version of LeadingOnes and prove that its (1+1) elitist black-box complexity is Ω(n2), a bound that is matched by (1+1)-type evolutionary algorithms. The (1+1) elitist complexity of LeadingOnes is thus considerably larger than its unrestricted one, which is known to be of order nloglog n [Afshani et al., 2013].