Strengthening Canonical Pattern Databases with Structural Symmetries

Symmetry-based state space pruning techniques have proved to greatly improve heuristic search based classical planners. Similarly, abstraction heuristics in general and pattern databases in particular are key ingredients of such planners. However, only little work has dealt with how the abstraction heuristics behave under symmetries. In this work, we investigate the symmetry properties of the popular canonical pattern databases heuristic. Exploiting structural symmetries, we strengthen the canonical pattern databases by adding symmetric pattern databases, making the resulting heuristic invariant under structural symmetry, thus making it especially attractive for symmetry-based pruning search methods. Further, we prove that this heuristic is at least as informative as using symmetric lookups over the original heuristic. An experimental evaluation confirms these theoretical results

Optimal Planning with State Constraints

In the classical planning model, state variables are assigned values in the initial state and remain unchanged unless explicitly affected by action effects. However, some properties of states are more naturally modelled not as direct effects of actions but instead as derived, in each state, from the primary variables via a set of rules. We refer to those rules as state constraints. The two types of state constraints that will be discussed here are numeric state constraints and logical rules that we will refer to as axioms. When using state constraints we make a distinction between primary variables, whose values are directly affected by action effects, and secondary variables, whose values are determined by state constraints. While primary variables have finite and discrete domains, as in classical planning, there is no such requirement for secondary variables. For example, using numeric state constraints allows us to have secondary variables whose values are real numbers. We show that state constraints are a construct that lets us combine classical planning methods with specialised solvers developed for other types of problems. For example, introducing numeric state constraints enables us to apply planning techniques in domains involving interconnected physical systems, such as power networks. To solve these types of problems optimally, we adapt commonly used methods from optimal classical planning, namely state-space search guided by admissible heuristics. In heuristics based on monotonic relaxation, the idea is that in a relaxed state each variable assumes a set of values instead of just a single value. With state constraints, the challenge becomes to evaluate the conditions, such as goals and action preconditions, that involve secondary variables. We employ consistency checking tools to evaluate whether these conditions are satisfied in the relaxed state. In our work with numerical constraints we use linear programming, while with axioms we use answer set programming and three value semantics. This allows us to build a relaxed planning graph and compute constraint-aware version of heuristics based on monotonic relaxation. We also adapt pattern database heuristics. We notice that an abstract state can be thought of as a state in the monotonic relaxation in which the variables in the pattern hold only one value, while the variables not in the pattern simultaneously hold all the values in their domains. This means that we can apply the same technique for evaluating conditions on secondary variables as we did for the monotonic relaxation and build pattern databases similarly as it is done in classical planning. To make better use of our heuristics, we modify the A* algorithm by combining two techniques that were previously used independently – partial expansion and preferred operators. Our modified algorithm, which we call PrefPEA, is most beneficial in cases where heuristic is expensive to compute, but accurate, and states have many successors

Conflict-driven learning in AI planning state-space search

Many combinatorial computation problems in computer science can be cast as a reachability problem in an implicitly described, potentially huge, graph: the state space. State-space search is a versatile and widespread method to solve such reachability problems, but it requires some form of guidance to prevent exploring that combinatorial space exhaustively. Conflict-driven learning is an indispensable search ingredient for solving constraint satisfaction problems (most prominently, Boolean satisfiability). It guides search towards solutions by identifying conflicts during the search, i.e., search branches not leading to any solution, learning from them knowledge to avoid similar conflicts in the remainder of the search. This thesis adapts the conflict-driven learning methodology to more general classes of reachability problems. Specifically, our work is placed in AI planning. We consider goal-reachability objectives in classical planning and in planning under uncertainty. The canonical form of "conflicts" in this context are dead-end states, i.e., states from which the desired goal property cannot be reached. We pioneer methods for learning sound and generalizable dead-end knowledge from conflicts encountered during forward state-space search. This embraces the following core contributions: When acting under uncertainty, the presence of dead-end states may make it impossible to satisfy the goal property with absolute certainty. The natural planning objective then is MaxProb, maximizing the probability of reaching the goal. However, algorithms for MaxProb probabilistic planning are severely underexplored. We close this gap by developing a large design space of probabilistic state-space search methods, contributing new search algorithms, admissible state-space reduction techniques, and goal-probability bounds suitable for heuristic state-space search. We systematically explore this design space through an extensive empirical evaluation. The key to our conflict-driven learning algorithm adaptation are unsolvability detectors, i.e., goal-reachability overapproximations. We design three complementary families of such unsolvability detectors, building upon known techniques: critical-path heuristics, linear-programming-based heuristics, and dead-end traps. We develop search methods to identify conflicts in deterministic and probabilistic state spaces, and we develop suitable refinement methods for the different unsolvability detectors so to recognize these states. Arranged in a depth-first search, our techniques approach the elegance of conflict-driven learning in constraint satisfaction, featuring the ability to learn to refute search subtrees, and intelligent backjumping to the root cause of a conflict. We provide a comprehensive experimental evaluation, demonstrating that the proposed techniques yield state-of-the-art performance for finding plans for solvable classical planning tasks, proving classical planning tasks unsolvable, and solving MaxProb in probabilistic planning, on benchmarks where dead-end states abound.Viele kombinatorisch komplexe Berechnungsprobleme in der Informatik lassen sich als Erreichbarkeitsprobleme in einem implizit dargestellten, potenziell riesigen, Graphen - dem Zustandsraum - verstehen. Die Zustandsraumsuche ist eine weit verbreitete Methode, um solche Erreichbarkeitsprobleme zu lösen. Die Effizienz dieser Methode hängt aber maßgeblich von der Verwendung strikter Suchkontrollmechanismen ab. Das konfliktgesteuerte Lernen ist eine essenzielle Suchkomponente für das Lösen von Constraint-Satisfaction-Problemen (wie dem Erfüllbarkeitsproblem der Aussagenlogik), welches von Konflikten, also Fehlern in der Suche, neue Kontrollregeln lernt, die ähnliche Konflikte zukünftig vermeiden. In dieser Arbeit erweitern wir die zugrundeliegende Methodik auf Zielerreichbarkeitsfragen, wie sie im klassischen und probabilistischen Planen, einem Teilbereich der Künstlichen Intelligenz, auftauchen. Die kanonische Form von „Konflikten“ in diesem Kontext sind sog. Sackgassen, Zustände, von denen aus die Zielbedingung nicht erreicht werden kann. Wir präsentieren Methoden, die es ermöglichen, während der Zustandsraumsuche von solchen Konflikten korrektes und verallgemeinerbares Wissen über Sackgassen zu erlernen. Unsere Arbeit umfasst folgende Beiträge: Wenn der Effekt des Handelns mit Unsicherheiten behaftet ist, dann kann die Existenz von Sackgassen dazu führen, dass die Zielbedingung nicht unter allen Umständen erfüllt werden kann. Die naheliegendste Planungsbedingung in diesem Fall ist MaxProb, das Maximieren der Wahrscheinlichkeit, dass die Zielbedingung erreicht wird. Planungsalgorithmen für MaxProb sind jedoch wenig erforscht. Um diese Lücke zu schließen, erstellen wir einen umfangreichen Bausatz für Suchmethoden in probabilistischen Zustandsräumen, und entwickeln dabei neue Suchalgorithmen, Zustandsraumreduktionsmethoden, und Abschätzungen der Zielerreichbarkeitswahrscheinlichkeit, wie sie für heuristische Suchalgorithmen gebraucht werden. Wir explorieren den resultierenden Gestaltungsraum systematisch in einer breit angelegten empirischen Studie. Die Grundlage unserer Adaption des konfliktgesteuerten Lernens bilden Unerreichbarkeitsdetektoren. Wir konzipieren drei Familien solcher Detektoren basierend auf bereits bekannten Techniken: Kritische-Pfad Heuristiken, Heuristiken basierend auf linearer Optimierung, und Sackgassen-Fallen. Wir entwickeln Suchmethoden, um Konflikte in deterministischen und probabilistischen Zustandsräumen zu erkennen, sowie Methoden, um die verschiedenen Unerreichbarkeitsdetektoren basierend auf den erkannten Konflikten zu verfeinern. Instanziiert als Tiefensuche weisen unsere Techniken ähnliche Eigenschaften auf wie das konfliktgesteuerte Lernen für Constraint-Satisfaction-Problemen. Wir evaluieren die entwickelten Methoden empirisch, und zeigen dabei, dass das konfliktgesteuerte Lernen unter gewissen Voraussetzungen zu signifikanten Suchreduktionen beim Finden von Plänen in lösbaren klassischen Planungsproblemen, Beweisen der Unlösbarkeit von klassischen Planungsproblemen, und Lösen von MaxProb im probabilistischen Planen, führen kann

Taming Numbers and Durations in the Model Checking Integrated Planning System

The Model Checking Integrated Planning System (MIPS) is a temporal least commitment heuristic search planner based on a flexible object-oriented workbench architecture. Its design clearly separates explicit and symbolic directed exploration algorithms from the set of on-line and off-line computed estimates and associated data structures. MIPS has shown distinguished performance in the last two international planning competitions. In the last event the description language was extended from pure propositional planning to include numerical state variables, action durations, and plan quality objective functions. Plans were no longer sequences of actions but time-stamped schedules. As a participant of the fully automated track of the competition, MIPS has proven to be a general system; in each track and every benchmark domain it efficiently computed plans of remarkable quality. This article introduces and analyzes the most important algorithmic novelties that were necessary to tackle the new layers of expressiveness in the benchmark problems and to achieve a high level of performance. The extensions include critical path analysis of sequentially generated plans to generate corresponding optimal parallel plans. The linear time algorithm to compute the parallel plan bypasses known NP hardness results for partial ordering by scheduling plans with respect to the set of actions and the imposed precedence relations. The efficiency of this algorithm also allows us to improve the exploration guidance: for each encountered planning state the corresponding approximate sequential plan is scheduled. One major strength of MIPS is its static analysis phase that grounds and simplifies parameterized predicates, functions and operators, that infers knowledge to minimize the state description length, and that detects domain object symmetries. The latter aspect is analyzed in detail. MIPS has been developed to serve as a complete and optimal state space planner, with admissible estimates, exploration engines and branching cuts. In the competition version, however, certain performance compromises had to be made, including floating point arithmetic, weighted heuristic search exploration according to an inadmissible estimate and parameterized optimization

Symbolic Search in Planning and General Game Playing

Search is an important topic in many areas of AI. Search problems often result in an immense number of states. This work addresses this by using a special datastructure, BDDs, which can represent large sets of states efficiently, often saving space compared to explicit representations. The first part is concerned with an analysis of the complexity of BDDs for some search problems, resulting in lower or upper bounds on BDD sizes for these. The second part is concerned with action planning, an area where the programmer does not know in advance what the search problem will look like. This part presents symbolic algorithms for finding optimal solutions for two different settings, classical and net-benefit planning, as well as several improvements to these algorithms. The resulting planner was able to win the International Planning Competition IPC 2008. The third part is concerned with general game playing, which is similar to planning in that the programmer does not know in advance what game will be played. This work proposes algorithms for instantiating the input and solving games symbolically. For playing, a hybrid player based on UCT and the solver is presented

ICAPS 2012. Proceedings of the third Workshop on the International Planning Competition

22nd International Conference on Automated Planning and Scheduling. June 25-29, 2012, Atibaia, Sao Paulo (Brazil). Proceedings of the 3rd the International Planning CompetitionThe Academic Advising Planning Domain / Joshua T. Guerin, Josiah P. Hanna, Libby Ferland, Nicholas Mattei, and Judy Goldsmith. -- Leveraging Classical Planners through Translations / Ronen I. Brafman, Guy Shani, and Ran Taig. -- Advances in BDD Search: Filtering, Partitioning, and Bidirectionally Blind / Stefan Edelkamp, Peter Kissmann, and Álvaro Torralba. -- A Multi-Agent Extension of PDDL3.1 / Daniel L. Kovacs. -- Mining IPC-2011 Results / Isabel Cenamor, Tomás de la Rosa, and Fernando Fernández. -- How Good is the Performance of the Best Portfolio in IPC-2011? / Sergio Nuñez, Daniel Borrajo, and Carlos Linares López. -- “Type Problem in Domain Description!” or, Outsiders’ Suggestions for PDDL Improvement / Robert P. Goldman and Peter KellerEn prens