TY  - JOUR
A1  - Doerr, Benjamin
A1  - Kötzing, Timo
A1  - Lagodzinski, Gregor J. A.
A1  - Lengler, Johannes
T1  - The impact of lexicographic parsimony pressure for ORDER/MAJORITY on the run time
JF  - Theoretical computer science : the journal of the EATCS
N2  - While many optimization problems work with a fixed number of decision variables and thus a fixed-length representation of possible solutions, genetic programming (GP) works on variable-length representations. A naturally occurring problem is that of bloat, that is, the unnecessary growth of solution lengths, which may slow down the optimization process. So far, the mathematical runtime analysis could not deal well with bloat and required explicit assumptions limiting bloat. 
In this paper, we provide the first mathematical runtime analysis of a GP algorithm that does not require any assumptions on the bloat. Previous performance guarantees were only proven conditionally for runs in which no strong bloat occurs. Together with improved analyses for the case with bloat restrictions our results show that such assumptions on the bloat are not necessary and that the algorithm is efficient without explicit bloat control mechanism. 
More specifically, we analyzed the performance of the (1 + 1) GP on the two benchmark functions ORDER and MAJORITY. When using lexicographic parsimony pressure as bloat control, we show a tight runtime estimate of O(T-init + nlogn) iterations both for ORDER and MAJORITY. For the case without bloat control, the bounds O(T-init logT(i)(nit) + n(logn)(3)) and Omega(T-init + nlogn) (and Omega(T-init log T-init) for n = 1) hold for MAJORITY(1).
KW  - genetic programming
KW  - bloat control
KW  - theory
KW  - runtime analysis
Y1  - 2020
U6  - https://doi.org/10.1016/j.tcs.2020.01.011
SN  - 0304-3975
SN  - 1879-2294
VL  - 816
SP  - 144
EP  - 168
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  -