Multiple-Goal Heuristic Search

This paper presents a new framework for anytime heuristic search where the task is to achieve as many goals as possible within the allocated resources. We show the inadequacy of traditional distance-estimation heuristics for tasks of this type and present alternative heuristics that are more appropriate for multiple-goal search. In particular, we introduce the marginal-utility heuristic, which estimates the cost and the benefit of exploring a subtree below a search node. We developed two methods for online learning of the marginal-utility heuristic. One is based on local similarity of the partial marginal utility of sibling nodes, and the other generalizes marginal-utility over the state feature space. We apply our adaptive and non-adaptive multiple-goal search algorithms to several problems, including focused crawling, and show their superiority over existing methods

Inductive and numerical methods in knowledge compilation

Many important application problems can be formalized as constrained non-linear optimization tasks. However, numerical methods for solving such problems are brittle and do not scale well. Furthermore, they do not provide much insight into the structure of the problem space. This paper describes a method for discovering efficient rules that can bypass the numerical methods and produce solutions directly. The rules also provide some insight into the problem structure. The method is illustrated in the domain of 2-dimensional structural design. To discover design rules in this domain, a numerical optimizer is run on example problems. The resulting optimal designs are then analyzed to detect geometric patterns . These patterns can then be applied to reformulate the search space and the objective function and construct a more direct and efficient problem-solving procedure. As a side-effect of this process, new geometric features are defined that can be used to help discover additional design rules for more complex problems

Efficient Learning and Inference for High-dimensional Lagrangian Systems

Learning the nature of a physical system is a problem that presents many challenges and opportunities owing to the unique structure associated with such systems. Many physical systems of practical interest in engineering are high-dimensional, which prohibits the application of standard learning methods to such problems. This first part of this work proposes therefore to solve learning problems associated with physical systems by identifying their low-dimensional Lagrangian structure. Algorithms are given to learn this structure in the case that it is obscured by a change of coordinates. The associated inference problem corresponds to solving a high-dimensional minimum-cost path problem, which can be solved by exploiting the symmetry of the problem. These techniques are demonstrated via an application to learning from high-dimensional human motion capture data. The second part of this work is concerned with the application of these methods to high-dimensional motion planning. Algorithms are given to learn and exploit the struc- ture of holonomic motion planning problems effectively via spectral analysis and iterative dynamic programming, admitting solutions to problems of unprecedented dimension com- pared to known methods for optimal motion planning. The quality of solutions found is also demonstrated to be much superior in practice to those obtained via sampling-based planning and smoothing, in both simulated problems and experiments with a robot arm. This work therefore provides strong validation of the idea that learning low-dimensional structure is the key to future advances in this field

Extensions and applications of the A* algorithm

In this thesis we investigate path finding problems, that is, planning routes from a start node to some goal nodes in a graph. Such problems arise in many fields of technology, for example, production planning, energy-aware message routing in large networks, resource allocation, and vehicle navigation systems. We concentrate mostly on planning a minimum cost path using the A* algorithm. We begin by proving new theorems comparing the performance of A* to other (generalized) path finding algorithms. In some cases, A* is an optimal method in a large class of algorithms. This means, roughly speaking, that A* explores a smaller region of the search space than the other algorithms in the given class. We develop a new method of improving a given (static) heuristic for A* dynamically, during search. A heuristic controls the search of A* so that unnecessary branches of the tree of nodes that A* visits are pruned. The new method also finds an optimal path to any node it visits for the first time so that every node will be visited only once. The latter is an important property considering the efficiency of the search. We examine the use of A* as a higher level method to allocate resources among several path finding algorithms. In some cases, the A* is an optimal resource allocation method, which means that the number of the nodes the path finding algorithms together visit is minimized. As applications of A*, we have developed new hierarchical algorithms for robot point-to-point path planning tasks, and new algorithms for power-aware routing of messages in large communication networks. The new algorithms are more robust than some older ones to which we compare. Moreover, one of the message routing algorithms produces higher average lifetimes of the network than those of the widely quoted max-min zPmin algorithm.reviewe

Navigation with uncertain spatio-temporal resources

Supporting people with intelligent navigation instructions enables users to efficiently achieve trip-related objectives (e.g., minimum travel time or fuel consumption) and preserves them from making unnecessary detours. This, in turn, enables them to save time, money and, additionally, minimize $CO_2$ emissions. For these reasons, manufacturers integrate navigation systems into almost all modern automobiles. Nevertheless, most of them support only simple routing instructions, i.e., how to drive from location A to B. Albeit, people are regularly faced with more complex decisions, e.g. navigating to a cheap gas station on the route while incorporating dynamic gas price changes. Another example-scenario is after reaching the destination, an available facility to park needs to be found. So far, people cruise almost randomly around the goal area in the search for a parking space. As a consequence, persons valuable time is consumed and unnecessary traffic arises. Besides private persons, transportation companies have to make complex mobility decisions. For instance, taxi drivers have to find out where to move next whenever the taxi is idle. There are plenty possibilities for where the taxi driver could go. In case the last drop-off was in a sparsely populated region, waiting for a call from the taxi office will likely result in a longer drive to the next customer. In turn, customer satisfaction decreases with a longer waiting time and implies a potential loss of customers. Recently, the number of data sources that potentially improve these mobility decisions increased. For instance, on-street parking sensors track the current state of the spaces (e.g. Melbourne), mobile applications collect taxi requests from customers and gas stations publish the current prices all in real-time. This thesis investigates the question of how to design algorithms such that they exploit this volatile data. Standard routing algorithms assume a static world. But the availability of passengers, gas prices and the availability of parking spots change over time in a non-deterministic manner. Hence, we model multiple real-world applications as Markov decision processes (MDP), i.e., a framework for sequential decision making under uncertainty. Depending on the task, we propose to solve the MDP with dynamic programming, replanning and hindsight planning or reinforcement learning. Ultimately, we combine all applications in a single problem domain. Subsequently, we propose a reinforcement learning approach that solves all applications in this domain without modification. Furthermore, it decouples the routing task from solving the application itself. Hence, it is transferable to previously unseen street networks without further training.Durch intelligente Navigationssysteme werden Verkehrsteilnehmer davor bewahrt, Umwege zu fahren. Dadurch sparen sie Zeit, Geld und verringern den $CO_2$-Ausstoß. Aus diesem Grund verbauen Hersteller Navigationssysteme in fast allen Neuwägen. Bis heute unterstützen die meisten Systeme nur einfache Routenplanung, die den kürzesten oder schnellsten Pfad von A nach B berechnen. Dennoch müssen Fahrer regelmäßig Entscheidungen darüber hinaus treffen. Beispielsweise soll eine möglichst günstige Tankstelle auf dem Weg zum eigentlichen Ziel besucht werden. Allerdings kann diese ihre Preise, während der Fahrer oder die Fahrerin auf dem Weg dort hin ist, dynamisch ändern. Anschließend muss, sobald das eigentliche Ziel erreicht ist, ein Parkplatz gefunden werden. Bisher fahren Parkplatzsuchende zufällig durch das Zielgebiet in der Hoffnung möglichst schnell einen freien Parkplatz zu finden. Die Suche verursacht zusätzlichen Verkehr und der Fahrer oder die Fahrerin verbringt mehr Zeit auf der Straße. Neben Privatpersonen müssen auch Transportunternehmen komplexe Entscheidungen über Bewegungen treffen. Zum Beispiel muss ein Taxifahrer, wenn er gerade keinen Fahrgast hat, entscheiden, wo er sich als nächstes positioniert. Zwar könnte er am letzten Zielort warten, bis er einen Anruf der Taxizentrale bekommt. Falls jedoch der letzte Zielort in einem entlegenen Gebiet ist, muss der nächste Fahrgast wahrscheinlich lange warten, bis der Fahrer oder die Fahrerin bei ihm ankommt. Damit sinkt die Kundenzufriedenheit, was wiederum einen potentiellen Verlust der Kunden bedeutet. Seit Kurzem gibt es immer mehr Datenquellen, die Entscheidungen für diese Probleme verbessern. Beispielsweise wird durch Parkplatzsensoren die Verfügbarkeit der Parkplätze verfolgt, mobile Anwendungen sammeln Anfragen über Fahrgäste und Tankstellen veröffentlichen ihren aktuellen Preis in Echtzeit. In dieser Arbeit wird der Forschungsfrage nachgegangen, wie Algorithmen gestaltet werden können, sodass diese veränderlichen Informationen verwendet werden können. Standard-Routing-Algorithmen gehen von einer statischen Welt aus. Aber die Verfügbarkeit von Fahrgästen, die Tankstellenpreise und die Parkplatzzustände ändern sich nicht deterministisch. Aus diesem Grund modellieren wir eine Reihe von Anwendungen als Markov-Entscheidungsproblem (MDP). Applikationsabhängig schlagen wir vor, das MDP mit dynamischer Programmierung, Replanning bzw. Hindsight Planning oder Reinforcement Learning zu lösen. Abschließend fassen wir alle Anwendungen in einer Domäne zusammen. Dadurch können wir einen Reinforcement Learning Ansatz definieren, der alle Anwendungen in dieser Domäne ohne Änderung lösen kann. Dieser Ansatz ermöglicht es, die Routenplanung von der eigentlichen Problemstellung zu lösen. Dadurch ist die gelernte Funktionsapproximation auch auf bisher unbekannte Straßennetze ohne weiteres Training anwendbar