TY  - JOUR
A1  - Kötzing, Timo
A1  - Krejca, Martin Stefan
T1  - First-hitting times under drift
JF  - Theoretical computer science
N2  - 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.
KW  - First-hitting time
KW  - Random process
KW  - Drift
Y1  - 2019
U6  - https://doi.org/10.1016/j.tcs.2019.08.021
SN  - 0304-3975
SN  - 1879-2294
VL  - 796
SP  - 51
EP  - 69
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Friedrich, Tobias
A1  - Kötzing, Timo
A1  - Krejca, Martin Stefan
T1  - Unbiasedness of estimation-of-distribution algorithms
JF  - Theoretical computer science
N2  - 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.
KW  - Estimation-of-distribution algorithm
KW  - Unbiasedness
KW  - Theory
Y1  - 2019
U6  - https://doi.org/10.1016/j.tcs.2018.11.001
SN  - 0304-3975
SN  - 1879-2294
VL  - 785
SP  - 46
EP  - 59
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Friedrich, Tobias
A1  - Krejca, Martin Stefan
A1  - Rothenberger, Ralf
A1  - Arndt, Tobias
A1  - Hafner, Danijar
A1  - Kellermeier, Thomas
A1  - Krogmann, Simon
A1  - Razmjou, Armin
T1  - Routing for on-street parking search using probabilistic data
JF  - AI communications : AICOM ; the European journal on artificial intelligence
N2  - 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.
KW  - Parking search
KW  - probabilistic routing
KW  - constrained optimization
KW  - field study
Y1  - 2019
U6  - https://doi.org/10.3233/AIC-180574
SN  - 0921-7126
SN  - 1875-8452
VL  - 32
IS  - 2
SP  - 113
EP  - 124
PB  - IOS Press
CY  - Amsterdam
ER  -