@article{FriedrichKoetzingKrejca2019,
  author    = {Friedrich, Tobias and K{\"o}tzing, Timo and Krejca, Martin Stefan},
  title     = {Unbiasedness of estimation-of-distribution algorithms},
  series = {Theoretical computer science},
  volume    = {785},
  journal   = {Theoretical computer science},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0304-3975},
  doi       = {10.1016/j.tcs.2018.11.001},
  pages     = {46 -- 59},
  year      = {2019},
  abstract  = {In the context of black-box optimization, black-box complexity is used for understanding the inherent difficulty of a given optimization problem. Central to our understanding of nature-inspired search heuristics in this context is the notion of unbiasedness. Specialized black-box complexities have been developed in order to better understand the limitations of these heuristics - especially of (population-based) evolutionary algorithms (EAs). In contrast to this, we focus on a model for algorithms explicitly maintaining a probability distribution over the search space: so-called estimation-of-distribution algorithms (EDAs). We consider the recently introduced n-Bernoulli-lambda-EDA framework, which subsumes, for example, the commonly known EDAs PBIL, UMDA, lambda-MMAS(IB), and cGA. We show that an n-Bernoulli-lambda-EDA is unbiased if and only if its probability distribution satisfies a certain invariance property under isometric automorphisms of [0, 1](n). By restricting how an n-Bernoulli-lambda-EDA can perform an update, in a way common to many examples, we derive conciser characterizations, which are easy to verify. We demonstrate this by showing that our examples above are all unbiased. (C) 2018 Elsevier B.V. All rights reserved.},
  language  = {en}
}
@article{FriedrichKrejcaRothenbergeretal.2019,
  author    = {Friedrich, Tobias and Krejca, Martin Stefan and Rothenberger, Ralf and Arndt, Tobias and Hafner, Danijar and Kellermeier, Thomas and Krogmann, Simon and Razmjou, Armin},
  title     = {Routing for on-street parking search using probabilistic data},
  series = {AI communications : AICOM ; the European journal on artificial intelligence},
  volume    = {32},
  journal   = {AI communications : AICOM ; the European journal on artificial intelligence},
  number    = {2},
  publisher = {IOS Press},
  address   = {Amsterdam},
  issn      = {0921-7126},
  doi       = {10.3233/AIC-180574},
  pages     = {113 -- 124},
  year      = {2019},
  abstract  = {A significant percentage of urban traffic is caused by the search for parking spots. One possible approach to improve this situation is to guide drivers along routes which are likely to have free parking spots. The task of finding such a route can be modeled as a probabilistic graph problem which is NP-complete. Thus, we propose heuristic approaches for solving this problem and evaluate them experimentally. For this, we use probabilities of finding a parking spot, which are based on publicly available empirical data from TomTom International B.V. Additionally, we propose a heuristic that relies exclusively on conventional road attributes. Our experiments show that this algorithm comes close to the baseline by a factor of 1.3 in our cost measure. Last, we complement our experiments with results from a field study, comparing the success rates of our algorithms against real human drivers.},
  language  = {en}
}
@article{FriedrichKoetzingKrejcaetal.2016,
  author    = {Friedrich, Tobias and K{\"o}tzing, Timo and Krejca, Martin Stefan and Sutton, Andrew M.},
  title     = {Robustness of Ant Colony Optimization to Noise},
  series = {Evolutionary computation},
  volume    = {24},
  journal   = {Evolutionary computation},
  publisher = {MIT Press},
  address   = {Cambridge},
  issn      = {1063-6560},
  doi       = {10.1162/EVCO_a_00178},
  pages     = {237 -- 254},
  year      = {2016},
  abstract  = {Recently, ant colony optimization (ACO) algorithms have proven to be efficient in uncertain environments, such as noisy or dynamically changing fitness functions. Most of these analyses have focused on combinatorial problems such as path finding. We rigorously analyze an ACO algorithm optimizing linear pseudo- Boolean functions under additive posterior noise. We study noise distributions whose tails decay exponentially fast, including the classical case of additive Gaussian noise. Without noise, the classical (mu + 1) EA outperforms any ACO algorithm, with smaller mu being better; however, in the case of large noise, the (mu + 1) EA fails, even for high values of mu (which are known to help against small noise). In this article, we show that ACO is able to deal with arbitrarily large noise in a graceful manner; that is, as long as the evaporation factor. is small enough, dependent on the variance s2 of the noise and the dimension n of the search space, optimization will be successful. We also briefly consider the case of prior noise and prove that ACO can also efficiently optimize linear functions under this noise model.},
  language  = {en}
}
@article{KoetzingKrejca2019,
  author    = {K{\"o}tzing, Timo and Krejca, Martin Stefan},
  title     = {First-hitting times under drift},
  series = {Theoretical computer science},
  volume    = {796},
  journal   = {Theoretical computer science},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0304-3975},
  doi       = {10.1016/j.tcs.2019.08.021},
  pages     = {51 -- 69},
  year      = {2019},
  abstract  = {For the last ten years, almost every theoretical result concerning the expected run time of a randomized search heuristic used drift theory, making it the arguably most important tool in this domain. Its success is due to its ease of use and its powerful result: drift theory allows the user to derive bounds on the expected first-hitting time of a random process by bounding expected local changes of the process - the drift. This is usually far easier than bounding the expected first-hitting time directly. Due to the widespread use of drift theory, it is of utmost importance to have the best drift theorems possible. We improve the fundamental additive, multiplicative, and variable drift theorems by stating them in a form as general as possible and providing examples of why the restrictions we keep are still necessary. Our additive drift theorem for upper bounds only requires the process to be lower-bounded, that is, we remove unnecessary restrictions like a finite, discrete, or bounded state space. As corollaries, the same is true for our upper bounds in the case of variable and multiplicative drift. By bounding the step size of the process, we derive new lower-bounding multiplicative and variable drift theorems. Last, we also state theorems that are applicable when the process has a drift of 0, by using a drift on the variance of the process.},
  language  = {en}
}
@article{DoerrKrejca2021,
  author    = {Doerr, Benjamin and Krejca, Martin Stefan},
  title     = {A simplified run time analysis of the univariate marginal distribution algorithm on LeadingOnes},
  series = {Theoretical computer science},
  volume    = {851},
  journal   = {Theoretical computer science},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0304-3975},
  doi       = {10.1016/j.tcs.2020.11.028},
  pages     = {121 -- 128},
  year      = {2021},
  abstract  = {With elementary means, we prove a stronger run time guarantee for the univariate marginal distribution algorithm (UMDA) optimizing the LEADINGONES benchmark function in the desirable regime with low genetic drift. If the population size is at least quasilinear, then, with high probability, the UMDA samples the optimum in a number of iterations that is linear in the problem size divided by the logarithm of the UMDA's selection rate. This improves over the previous guarantee, obtained by Dang and Lehre (2015) via the deep level-based population method, both in terms of the run time and by demonstrating further run time gains from small selection rates. Under similar assumptions, we prove a lower bound that matches our upper bound up to constant factors.},
  language  = {en}
}