An exponential lower bound for the runtime of the compact genetic algorithm on jump functions
Benjamin Doerr · 2019
In the first runtime analysis of an estimation-of-distribution algorithm (EDA) on the multimodal jump function class, Hasenöhrl and Sutton (GECCO 2018) proved that the runtime of the compact genetic algorithm with suitable parameter 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 is super-logarithmic. The exponential runtime guarantee was achieved with a hypothetical population size that is also exponential in the jump size. Consequently, this setting cannot lead to a better runtime.