TY  - JOUR
A1  - Krejca, Martin S.
A1  - Witt, Carsten
T1  - Lower bounds on the run time of the Univariate Marginal Distribution Algorithm on OneMax
JF  - Theoretical computer science : the journal of the EATCS
N2  - The Univariate Marginal Distribution Algorithm (UMDA) - a popular estimation-of-distribution algorithm - is studied from a run time perspective. On the classical OneMax benchmark function on bit strings of length n, a lower bound of Omega(lambda + mu root n + n logn), where mu and lambda are algorithm-specific parameters, on its expected run time is proved. This is the first direct lower bound on the run time of UMDA. It is stronger than the bounds that follow from general black-box complexity theory and is matched by the run time of many evolutionary algorithms. The results are obtained through advanced analyses of the stochastic change of the frequencies of bit values maintained by the algorithm, including carefully designed potential functions. These techniques may prove useful in advancing the field of run time analysis for estimation-of-distribution algorithms in general.
KW  - estimation-of-distribution algorithm
KW  - run time analysis
KW  - lower bound
Y1  - 2020
U6  - https://doi.org/10.1016/j.tcs.2018.06.004
SN  - 0304-3975
SN  - 1879-2294
VL  - 832
SP  - 143
EP  - 165
PB  - Elsevier
CY  - Amsterdam [u.a.]
ER  -