The binary value function, or BinVal, has appeared in several studies in
theory of evolutionary computation as one of the extreme examples of linear
pseudo-Boolean functions. Its unbiased black-box complexity was previously
shown to be at most βlog2βnβ+2, where n is the problem
size. We augment it with an upper bound of log2βn+2.42141558βo(1),
which is more precise for many values of n. We also present a lower bound of
log2βn+1.1186406βo(1). Additionally, we prove that BinVal is an easiest
function among all unimodal pseudo-Boolean functions at least for unbiased
algorithms.Comment: 24 pages, one figure. An extended two-page abstract of this work will
appear in proceedings of the Genetic and Evolutionary Computation Conference,
GECCO'1