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 - GEN A1 - Kötzing, Timo A1 - Krejca, Martin Stefan T1 - First-Hitting times under additive drift T2 - Parallel Problem Solving from Nature – PPSN XV, PT II 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 nonnegative, that is, we remove unnecessary restrictions like a finite, discrete, or bounded search space. As corollaries, the same is true for our upper bounds in the case of variable and multiplicative drift. Y1 - 2018 SN - 978-3-319-99259-4 SN - 978-3-319-99258-7 U6 - https://doi.org/10.1007/978-3-319-99259-4_8 SN - 0302-9743 SN - 1611-3349 VL - 11102 SP - 92 EP - 104 PB - Springer CY - Cham ER - TY - GEN A1 - Kötzing, Timo A1 - Krejca, Martin Stefan T1 - First-Hitting times for finite state spaces T2 - Parallel Problem Solving from Nature – PPSN XV, PT II N2 - One of the most important aspects of a randomized algorithm is bounding its expected run time on various problems. Formally speaking, this means bounding the expected first-hitting time of a random process. The two arguably most popular tools to do so are the fitness level method and drift theory. The fitness level method considers arbitrary transition probabilities but only allows the process to move toward the goal. On the other hand, drift theory allows the process to move into any direction as long as it move closer to the goal in expectation; however, this tendency has to be monotone and, thus, the transition probabilities cannot be arbitrary. We provide a result that combines the benefit of these two approaches: our result gives a lower and an upper bound for the expected first-hitting time of a random process over {0,..., n} that is allowed to move forward and backward by 1 and can use arbitrary transition probabilities. In case that the transition probabilities are known, our bounds coincide and yield the exact value of the expected first-hitting time. Further, we also state the stationary distribution as well as the mixing time of a special case of our scenario. Y1 - 2018 SN - 978-3-319-99259-4 SN - 978-3-319-99258-7 U6 - https://doi.org/10.1007/978-3-319-99259-4_7 SN - 0302-9743 SN - 1611-3349 VL - 11102 SP - 79 EP - 91 PB - Springer CY - Cham ER - TY - THES A1 - Krejca, Martin Stefan T1 - Theoretical analyses of univariate estimation-of-distribution algorithms N2 - 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. N2 - Optimierung ist ein Hauptbestandteil technologischen Fortschritts und oftmals computergestützt. Da viele Optimierungsprobleme schwer sind, ist es jedoch unrealistisch, eine optimale Lösung in angemessener Zeit zu erwarten. Daher werden Heuristiken verwendet, also Programme, die versuchen hochwertige Lösungen schnell zu erzeugen. Eine konkrete Klasse sind Estimation-of-Distribution-Algorithmen (EDAs), die sich durch das Entwickeln probabilistischer Modelle über dem Problemraum auszeichnen. Ein solches Modell wird genutzt, um neue Lösungen zu erzeugen und damit das Modell zu verfeinern, um im nächsten Schritt mit erhöhter Wahrscheinlichkeit bessere Lösungen zu generieren. In dieser Arbeit untersuchen wir die Klasse univariater EDAs in der booleschen Domäne, also im Raum aller Bitstrings der Länge n. Das probabilistische Modell eines univariaten EDAs besteht dann aus einem n-dimensionalen Wahrscheinlichkeitsvektor, in dem jede Komponente die Wahrscheinlichkeit angibt, eine 1 an der entsprechenden Stelle zu erzeugen. Mein Beitrag folgt zwei Hauptrichtungen: Erst untersuchen wir allgemeine inhärente Eigenschaften univariater EDAs. Danach bestimmen wir die erwartete Laufzeit gewisser EDAs auf Benchmarks aus der Theorie. Im ersten Abschnitt charakterisieren wir, wann EDAs unbefangen bezüglich der Problemcodierung sind. Dann untersuchen wir sie in einem Szenario, in dem alle Lösungen gleich gut sind, und zeigen, dass sich ihr Modell schnell zu einem falschen entwickelt, falls es immer so angepasst wird, dass sich im Erwartungswert nichts ändert. Im zweiten Abschnitt zeigen wir, dass die Algorithmen cGA und MMAS-fp eine verrauschte Variante des klassischen Benchmarks OneMax effizient optimieren, bei der eine Gaussverteilung mit Varianz σ² hinzuaddiert wird. Wir beweisen, dass die Algorithmen das wahre Optimum in polynomieller Zeit bezüglich σ² und n erzeugen. Für den MMAS-fp verallgemeinern wir dieses Ergebnis auf lineare Funktionen. Weiterhin beweisen wir eine Laufzeit von Ω(n log(n)) für den Algorithmus UMDA auf OneMax (ohne Rauschen). Zuletzt führen wir einen neuen Algorithmus ein, der die Benchmarks OneMax und LeadingOnes in O(n log(n)) optimiert, was zuvor für noch keine Heuristik gezeigt wurde. T2 - Theoretische Analysen univariater Estimation-of-Distribution-Algorithmen KW - theory KW - estimation-of-distribution algorithms KW - univariate KW - pseudo-Boolean optimization KW - run time analysis KW - Theorie KW - Estimation-of-Distribution-Algorithmen KW - univariat KW - pseudoboolesche Optimierung KW - Laufzeitanalyse Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-434870 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 - TY - GEN A1 - Blaesius, Thomas A1 - Eube, Jan A1 - Feldtkeller, Thomas A1 - Friedrich, Tobias A1 - Krejca, Martin Stefan A1 - Lagodzinski, Gregor J. A. A1 - Rothenberger, Ralf A1 - Severin, Julius A1 - Sommer, Fabian A1 - Trautmann, Justin T1 - Memory-restricted Routing With Tiled Map Data T2 - 2018 IEEE International Conference on Systems, Man, and Cybernetics (SMC) N2 - Modern routing algorithms reduce query time by depending heavily on preprocessed data. The recently developed Navigation Data Standard (NDS) enforces a separation between algorithms and map data, rendering preprocessing inapplicable. Furthermore, map data is partitioned into tiles with respect to their geographic coordinates. With the limited memory found in portable devices, the number of tiles loaded becomes the major factor for run time. We study routing under these restrictions and present new algorithms as well as empirical evaluations. Our results show that, on average, the most efficient algorithm presented uses more than 20 times fewer tile loads than a normal A*. Y1 - 2018 SN - 978-1-5386-6650-0 U6 - https://doi.org/10.1109/SMC.2018.00567 SN - 1062-922X SP - 3347 EP - 3354 PB - IEEE CY - New York ER - TY - BOOK A1 - Adriano, Christian A1 - Bleifuß, Tobias A1 - Cheng, Lung-Pan A1 - Diba, Kiarash A1 - Fricke, Andreas A1 - Grapentin, Andreas A1 - Jiang, Lan A1 - Kovacs, Robert A1 - Krejca, Martin Stefan A1 - Mandal, Sankalita A1 - Marwecki, Sebastian A1 - Matthies, Christoph A1 - Mattis, Toni A1 - Niephaus, Fabio A1 - Pirl, Lukas A1 - Quinzan, Francesco A1 - Ramson, Stefan A1 - Rezaei, Mina A1 - Risch, Julian A1 - Rothenberger, Ralf A1 - Roumen, Thijs A1 - Stojanovic, Vladeta A1 - Wolf, Johannes ED - Meinel, Christoph ED - Plattner, Hasso ED - Döllner, Jürgen Roland Friedrich ED - Weske, Mathias ED - Polze, Andreas ED - Hirschfeld, Robert ED - Naumann, Felix ED - Giese, Holger ED - Baudisch, Patrick ED - Friedrich, Tobias ED - Böttinger, Erwin ED - Lippert, Christoph T1 - Technical report BT - Fall Retreat 2018 N2 - Design and Implementation of service-oriented architectures imposes a huge number of research questions from the fields of software engineering, system analysis and modeling, adaptability, and application integration. Component orientation and web services are two approaches for design and realization of complex web-based system. Both approaches allow for dynamic application adaptation as well as integration of enterprise application. Commonly used technologies, such as J2EE and .NET, form de facto standards for the realization of complex distributed systems. Evolution of component systems has lead to web services and service-based architectures. This has been manifested in a multitude of industry standards and initiatives such as XML, WSDL UDDI, SOAP, etc. All these achievements lead to a new and promising paradigm in IT systems engineering which proposes to design complex software solutions as collaboration of contractually defined software services. Service-Oriented Systems Engineering represents a symbiosis of best practices in object-orientation, component-based development, distributed computing, and business process management. It provides integration of business and IT concerns. The annual Ph.D. Retreat of the Research School provides each member the opportunity to present his/her current state of their research and to give an outline of a prospective Ph.D. thesis. Due to the interdisciplinary structure of the research school, this technical report covers a wide range of topics. These include but are not limited to: Human Computer Interaction and Computer Vision as Service; Service-oriented Geovisualization Systems; Algorithm Engineering for Service-oriented Systems; Modeling and Verification of Self-adaptive Service-oriented Systems; Tools and Methods for Software Engineering in Service-oriented Systems; Security Engineering of Service-based IT Systems; Service-oriented Information Systems; Evolutionary Transition of Enterprise Applications to Service Orientation; Operating System Abstractions for Service-oriented Computing; and Services Specification, Composition, and Enactment. N2 - Der Entwurf und die Realisierung dienstbasierender Architekturen wirft eine Vielzahl von Forschungsfragestellungen aus den Gebieten der Softwaretechnik, der Systemmodellierung und -analyse, sowie der Adaptierbarkeit und Integration von Applikationen auf. Komponentenorientierung und WebServices sind zwei Ansätze für den effizienten Entwurf und die Realisierung komplexer Web-basierender Systeme. Sie ermöglichen die Reaktion auf wechselnde Anforderungen ebenso, wie die Integration großer komplexer Softwaresysteme. Heute übliche Technologien, wie J2EE und .NET, sind de facto Standards für die Entwicklung großer verteilter Systeme. Die Evolution solcher Komponentensysteme führt über WebServices zu dienstbasierenden Architekturen. Dies manifestiert sich in einer Vielzahl von Industriestandards und Initiativen wie XML, WSDL, UDDI, SOAP. All diese Schritte führen letztlich zu einem neuen, vielversprechenden Paradigma für IT Systeme, nach dem komplexe Softwarelösungen durch die Integration vertraglich vereinbarter Software-Dienste aufgebaut werden sollen. "Service-Oriented Systems Engineering" repräsentiert die Symbiose bewährter Praktiken aus den Gebieten der Objektorientierung, der Komponentenprogrammierung, des verteilten Rechnen sowie der Geschäftsprozesse und berücksichtigt auch die Integration von Geschäftsanliegen und Informationstechnologien. Die Klausurtagung des Forschungskollegs "Service-oriented Systems Engineering" findet einmal jährlich statt und bietet allen Kollegiaten die Möglichkeit den Stand ihrer aktuellen Forschung darzulegen. Bedingt durch die Querschnittstruktur des Kollegs deckt dieser Bericht ein weites Spektrum aktueller Forschungsthemen ab. Dazu zählen unter anderem Human Computer Interaction and Computer Vision as Service; Service-oriented Geovisualization Systems; Algorithm Engineering for Service-oriented Systems; Modeling and Verification of Self-adaptive Service-oriented Systems; Tools and Methods for Software Engineering in Service-oriented Systems; Security Engineering of Service-based IT Systems; Service-oriented Information Systems; Evolutionary Transition of Enterprise Applications to Service Orientation; Operating System Abstractions for Service-oriented Computing; sowie Services Specification, Composition, and Enactment. T3 - Technische Berichte des Hasso-Plattner-Instituts für Digital Engineering an der Universität Potsdam - 129 KW - Hasso Plattner Institute KW - research school KW - Ph.D. retreat KW - service-oriented systems engineering KW - Hasso-Plattner-Institut KW - Forschungskolleg KW - Klausurtagung KW - Service-oriented Systems Engineering Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-427535 SN - 978-3-86956-465-4 SN - 1613-5652 SN - 2191-1665 IS - 129 PB - Universitätsverlag Potsdam CY - Potsdam ER -