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In the first runtime analysis of an estimation-of-distribution algorithm(EDA) on the multi-modal jump function class, Hasen\"ohrl and Sutton (GECCO2018) proved that the runtime of the compact genetic algorithm with suitableparameter choice on jump functions with high probability is at most polynomial(in the dimension) if the jump size is at most logarithmic (in the dimension),and is at most exponential in the jump size if the jump size issuper-logarithmic. The exponential runtime guarantee was achieved with ahypothetical population size that is also exponential in the jump size.Consequently, this setting cannot lead to a better runtime.  In this work, we show that any choice of the hypothetical population sizeleads to a runtime that, with high probability, is at least exponential in thejump size. This result might be the first non-trivial exponential lower boundfor EDAs that holds for arbitrary parameter settings.

An Exponential Lower Bound for the Runtime of the cGA on Jump Functions