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  - 
TY  - JOUR
A1  - Doerr, Benjamin
A1  - Krejca, Martin S.
T1  - Significance-based estimation-of-distribution algorithms
JF  - IEEE transactions on evolutionary computation
N2  - Estimation-of-distribution algorithms (EDAs) are randomized search heuristics that create a probabilistic model of the solution space, which is updated iteratively, based on the quality of the solutions sampled according to the model. As previous works show, this iteration-based perspective can lead to erratic updates of the model, in particular, to bit-frequencies approaching a random boundary value. In order to overcome this problem, we propose a new EDA based on the classic compact genetic algorithm (cGA) that takes into account a longer history of samples and updates its model only with respect to information which it classifies as statistically significant. We prove that this significance-based cGA (sig-cGA) optimizes the commonly regarded benchmark functions OneMax (OM), LeadingOnes, and BinVal all in quasilinear time, a result shown for no other EDA or evolutionary algorithm so far. For the recently proposed stable compact genetic algorithm-an EDA that tries to prevent erratic model updates by imposing a bias to the uniformly distributed model-we prove that it optimizes OM only in a time exponential in its hypothetical population size. Similarly, we show that the convex search algorithm cannot optimize OM in polynomial time.
KW  - heuristic algorithms
KW  - sociology
KW  - statistics
KW  - history
KW  - probabilistic
KW  - logic
KW  - benchmark testing
KW  - genetic algorithms
KW  - estimation-of-distribution
KW  - algorithm (EDA)
KW  - run time analysis
KW  - theory
Y1  - 2020
U6  - https://doi.org/10.1109/TEVC.2019.2956633
SN  - 1089-778X
SN  - 1941-0026
VL  - 24
IS  - 6
SP  - 1025
EP  - 1034
PB  - Institute of Electrical and Electronics Engineers
CY  - New York, NY
ER  -