@article{KoetzingLagodzinskiLengleretal.2020, author = {K{\"o}tzing, Timo and Lagodzinski, Gregor J. A. and Lengler, Johannes and Melnichenko, Anna}, title = {Destructiveness of lexicographic parsimony pressure and alleviation by a concatenation crossover in genetic programming}, series = {Theoretical computer science}, volume = {816}, journal = {Theoretical computer science}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0304-3975}, doi = {10.1016/j.tcs.2019.11.036}, pages = {96 -- 113}, year = {2020}, abstract = {For theoretical analyses there are two specifics distinguishing GP from many other areas of evolutionary computation: the variable size representations, in particular yielding a possible bloat (i.e. the growth of individuals with redundant parts); and also the role and the realization of crossover, which is particularly central in GP due to the tree-based representation. Whereas some theoretical work on GP has studied the effects of bloat, crossover had surprisingly little share in this work.
We analyze a simple crossover operator in combination with randomized local search, where a preference for small solutions minimizes bloat (lexicographic parsimony pressure); we denote the resulting algorithm Concatenation Crossover GP. We consider three variants of the well-studied MAJORITY test function, adding large plateaus in different ways to the fitness landscape and thus giving a test bed for analyzing the interplay of variation operators and bloat control mechanisms in a setting with local optima. We show that the Concatenation Crossover GP can efficiently optimize these test functions, while local search cannot be efficient for all three variants independent of employing bloat control. (C) 2019 Elsevier B.V. All rights reserved.}, language = {en} } @article{KrejcaWitt2020, author = {Krejca, Martin S. and Witt, Carsten}, title = {Lower bounds on the run time of the Univariate Marginal Distribution Algorithm on OneMax}, series = {Theoretical computer science : the journal of the EATCS}, volume = {832}, journal = {Theoretical computer science : the journal of the EATCS}, publisher = {Elsevier}, address = {Amsterdam [u.a.]}, issn = {0304-3975}, doi = {10.1016/j.tcs.2018.06.004}, pages = {143 -- 165}, year = {2020}, abstract = {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.}, language = {en} } @article{DoerrKrejca2020, author = {Doerr, Benjamin and Krejca, Martin S.}, title = {Significance-based estimation-of-distribution algorithms}, series = {IEEE transactions on evolutionary computation}, volume = {24}, journal = {IEEE transactions on evolutionary computation}, number = {6}, publisher = {Institute of Electrical and Electronics Engineers}, address = {New York, NY}, issn = {1089-778X}, doi = {10.1109/TEVC.2019.2956633}, pages = {1025 -- 1034}, year = {2020}, abstract = {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.}, language = {en} } @phdthesis{Krejca2019, author = {Krejca, Martin Stefan}, title = {Theoretical analyses of univariate estimation-of-distribution algorithms}, doi = {10.25932/publishup-43487}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-434870}, school = {Universit{\"a}t Potsdam}, pages = {xii, 243}, year = {2019}, abstract = {Optimization is a core part of technological advancement and is usually heavily aided by computers. However, since many optimization problems are hard, it is unrealistic to expect an optimal solution within reasonable time. Hence, heuristics are employed, that is, computer programs that try to produce solutions of high quality quickly. One special class are estimation-of-distribution algorithms (EDAs), which are characterized by maintaining a probabilistic model over the problem domain, which they evolve over time. In an iterative fashion, an EDA uses its model in order to generate a set of solutions, which it then uses to refine the model such that the probability of producing good solutions is increased. In this thesis, we theoretically analyze the class of univariate EDAs over the Boolean domain, that is, over the space of all length-n bit strings. In this setting, the probabilistic model of a univariate EDA consists of an n-dimensional probability vector where each component denotes the probability to sample a 1 for that position in order to generate a bit string. My contribution follows two main directions: first, we analyze general inherent properties of univariate EDAs. Second, we determine the expected run times of specific EDAs on benchmark functions from theory. In the first part, we characterize when EDAs are unbiased with respect to the problem encoding. We then consider a setting where all solutions look equally good to an EDA, and we show that the probabilistic model of an EDA quickly evolves into an incorrect model if it is always updated such that it does not change in expectation. In the second part, we first show that the algorithms cGA and MMAS-fp are able to efficiently optimize a noisy version of the classical benchmark function OneMax. We perturb the function by adding Gaussian noise with a variance of σ², and we prove that the algorithms are able to generate the true optimum in a time polynomial in σ² and the problem size n. For the MMAS-fp, we generalize this result to linear functions. Further, we prove a run time of Ω(n log(n)) for the algorithm UMDA on (unnoisy) OneMax. Last, we introduce a new algorithm that is able to optimize the benchmark functions OneMax and LeadingOnes both in O(n log(n)), which is a novelty for heuristics in the domain we consider.}, language = {en} }