Gabriele Röger

Axioms are a feature of the Planning Domain Definition Language PDDL that can be considered as a generalization of database query languages such as DATALOG. The PDDL standard restricts negative occurrences of predicates in axiom bodies to predicates that are directly set by actions and not derived by axioms. In the literature, authors often deviate from this limitation and only require that the set of axioms is stratifiable. We relate the axioms to fixed point logics to show that this aspect does not affect what queries can be expressed by the axioms.

Planning domains are an important notion, e.g. when it comes to restricting the input for generalized planning or learning approaches. However, domains as specified in PDDL cannot fully capture the intuitive understanding of a planning domain. We close this semantic gap and propose using PDDL axioms to characterize the (typically infinite) set of legal tasks of a domain. A minor extension makes it possible to express all properties that can be determined in polynomial time. We demonstrate the suitability of the approach on established domains from the International Planning Competition.

The merge-and-shrink framework is a powerful tool for computing abstraction heuristics for optimal classical planning. Merging is one of its name-giving transformations. It entails computing the product of two factors of a factored transition system. To decide which two factors to merge, the framework uses a merge strategy. While there exist many merge strategies, it is generally unclear what constitutes a strong merge strategy, and a previous analysis shows that there is still lots of room for improvement with existing merge strategies. In this paper, we devise a new scoring function for score-based merge strategies based on answering the question whether merging two factors has any benefits over computing saturated cost partitioning heuristics over the factors instead. Our experimental evaluation shows that our new merge strategy achieves state-of-the-art performance on IPC benchmarks.

Cost-optimal planning is at the heart of planning research, with many existing planners that produce provably optimal solutions. While some applications pose additional restric- tions, such as producing shortest (in the number of actions) among the cost-optimal plans, standard cost-optimal planning does not provide such a guarantee. We discuss two possible approaches to produce provably the shortest among the cost- optimal plans, one corresponding to an instantiation of cost- algebraic A∗ , the other based on a cost transformation. We formally prove that the new cost-transformation method in- deed produces the shortest among the cost-optimal plans and empirically compare the performance of the approaches in different configurations.

Debugging can be a painful task, especially when bugs only occur for large input files. We present Machetli, a tool to help with debugging in such situations. It takes a large input file and cuts away parts of it, while still provoking the bug. The resulting file is much smaller than the original, making the bug easier to find and fix. In our experience, Machetli was able to reduce planning tasks with thousands of actions to trivial tasks that could even be solved by hand. Machetli is an open-source project and it can be extended to other use cases such as debugging SAT solvers or LaTeX compilation bugs.

The aim of the AIPlan4EU project is to make state-of-the-art planning technology easily accessible for real-world applications and to integrate planning as a service on the European AI-on-demand platform. At the very heart of the project is the development of a unified planning framework that permits to programmatically specify planning tasks and to interact with different planning engines through a common interface. The demo presents the AIPlan4EU vision for the unified planning framework and the current state of the development.

In classical planning, cost partitioning is a powerful method which allows to combine multiple admissible heuristics while retaining an admissible bound. In this paper, we extend the theory of cost partitioning to probabilistic planning by generalizing from deterministic transition systems to stochastic shortest path problems (SSPs). We show that fundamental results related to cost partitioning still hold in our extended theory. We also investigate how to optimally partition costs for a large class of abstraction heuristics for SSPs. Lastly, we analyze occupation measure heuristics for SSPs as well as the theory of approximate linear programming for reward-oriented Markov decision processes. All of these fit our framework and can be seen as cost-partitioned heuristics.

Optimal cost partitioning of classical planning heuristics has been shown to lead to excellent heuristic values but is often prohibitively expensive to compute. We analyze the application of Lagrangian decomposition, a classical tool in mathematical programming, to cost partitioning of operator-counting heuristics. This allows us to view the computation as an iterative process that can be seeded with any cost partitioning and that improves over time. In the case of non-negative cost partitioning of abstraction heuristics the computation reduces to independent shortest path problems and does not require an LP solver.

Stubborn sets are an optimality-preserving pruning technique for factored state-space search, for example in classical planning. Their applicability is limited by their computational overhead. We describe a new algorithm for computing stubborn sets that is based on the state variables of the state space, while previous algorithms are based on its actions. Typical factored state spaces tend to have far fewer state variables than actions, and therefore our new algorithm is much more efficient than the previous state of the art, making stubborn sets a viable technique in many cases where they previously were not.

Optimal cost partitioning of classical planning heuristics has been shown to lead to excellent heuristic values but is often prohibitively expensive to compute. Lagrangian decomposition and Lagrangian relaxation are classical tools in mathematical programming that apply to optimization problems with a special block structure. We analyze the application of Lagrangian decomposition to cost partitioning in the context of operator-counting heuristics and interpret Lagrangian multipliers as cost functions for the combined heuristics. This allows us to view the computation of an optimal cost partitioning as an iterative process that can be seeded with any cost partitioning and improves over time. We derive an any-time algorithm to compute an optimal non-negative cost partitioning of abstraction heuristics without involving an LP solver. In each iteration, the computation reduces to independent shortest path problems in all abstractions. Finally, we discuss the extension to general cost functions.

We transfer the notion of structural symmetries to lifted planning task representations, based on abstract structures which we define to model planning tasks. We show that symmetries are preserved by common grounding methods and we shed some light on the relation to previous symmetry concepts used in planning. Using a suitable graph representation of lifted tasks, our experimental analysis of common planning benchmarks reveals that symmetries occur in the lifted representation of many domains. Our work establishes the theoretical ground for exploiting symmetries beyond their previous scope, such as for faster grounding and mutex generation, as well as for state space transformations and reductions.

If a planning system outputs a solution for a given problem, it is simple to verify that the solution is valid. However, if a planner claims that a task is unsolvable, we currently have no choice but to trust the planner blindly. We propose a sound and complete class of certificates of unsolvability, which can be verified efficiently by an independent program. To highlight their practical use, we show how these certificates can be generated for a wide range of state-of-the-art planning techniques with only polynomial overhead for the planner.

While traditionally classical planning concentrated on finding plans for solvable tasks, detecting unsolvable instances has recently attracted increasing interest. To preclude wrong results, it is desirable that the planning system provides a certificate of unsolvability that can be independently verified. We propose a rule-based proof system for unsolvability where a proof establishes a knowledge base of verifiable basic statements and applies a set of derivation rules to infer the unsolvability of the task from these statements. We argue that this approach is more flexible than a recent proposal of inductive certificates of unsolvability and show how our proof system can be used for a wide range of planning techniques.

Relaxed reachability analysis is relevant to efficient grounding, invariant synthesis as well as the computation of relaxation-based heuristics. Planning domains are typically specified in a lifted representation, where the size of the tasks grows exponentially with the number of objects in the world. This growth also affects the analysis of relaxed reachability. We present a task reduction based on symmetries of the lifted representation that allows to perform the same analysis on smaller tasks.

While it is easy to verify that an action sequence is a solution for a classical planning task, there is no such verification capability if a task is reported unsolvable. We are therefore interested in certifi- cates that allow an independent verification of the absence of solutions. We identify promising con- cepts for certificates that can be generated by a wide range of planning approaches. We present a first proposal of unsolvability certificates and sketch ideas how the underlying concepts can be used as part of a more flexible unsolvability proof system.

The plans that planning systems generate for solvable planning tasks are routinely verified by independent validation tools. For unsolvable planning tasks, no such validation capabilities currently exist. We describe a family of certificates of unsolvability for classical planning tasks that can be efficiently verified and are sufficiently general for a wide range of planning approaches including heuristic search with delete relaxation, critical-path, pattern database and linear merge-and-shrink heuristics, symbolic search with binary decision diagrams, and the Trapper algorithm for detecting dead ends. We also augmented a classical planning system with the ability to emit certificates of unsolvability and implemented a planner-independent certificate validation tool. Experiments show that the overhead for producing such certificates is tolerable and that their validation is practically feasible.

We transfer the notion of structural symmetries to lifted planning task representations, based on a generalizing concept of abstract structures we use to model planning tasks. We show that symmetries are preserved by common grounding methods and shed some light on the relation to previous symmetry concepts. An analysis of common planning benchmarks reveals that symmetries occur in the lifted representation of many domains. Our concept prepares the ground for exploiting symmetries beyond their current scope, such as for faster grounding and mutex generation, as well as for state space transformations and state space reductions.

We propose techniques for efficiently determining optimal solutions to large logistics planning domain problems. We map a problem instance to a directed graph and show that no more than one vehicle per weakly connected component of the graph is needed for an optimal solution. We propose techniques for efficiently finding the vehicles which must be employed for an optimal solution. Also we develop a strong admissible heuristic based on the analysis of a directed graph, the cycles of which represent situations in the problem state in which a vehicle must visit a location more than once. To the best of our knowledge, ours is the first method that determines optimal solutions for large logistics instances (including the largest instances in the IPC 1998 and IPC 2000 problem sets).

We analyze how complex a heuristic function must be to directly guide a state-space search algorithm towards the goal. As a case study, we examine functions that evaluate states with a weighted sum of state features. We measure the complexity of a domain by the complexity of the required features. We analyze conditions under which the search algorithm runs in polynomial time and show complexity results for several classical planning domains.

We analyze how complex a heuristic function must be to directly guide a state-space search algorithm towards the goal. As a case study, we examine functions that evaluate states with a weighted sum of state features. We measure the complexity of a domain by the complexity of the required features. We analyze conditions under which the search algorithm runs in polynomial time and show complexity results for several classical planning domains.

Many heuristics for cost-optimal planning are based on linear programming. We cover several interesting heuristics of this type by a common framework that fixes the objective function of the linear program. Within the framework, constraints from different heuristics can be combined in one heuristic estimate which dominates the maximum of the component heuristics. Different heuristics of the framework can be compared on the basis of their constraints. We present theoretical results on the relation between existing heuristics and experimental results that demonstrate the potential of the proposed framework.

We suggest the use of linear temporal logic (LTL) for expressing declarative information about optimal solutions of search problems. We describe a general framework that associates LTLf formulas with search nodes in a heuristic search algorithm. Compared to previous approaches that integrate specific kinds of path information like landmarks into heuristic search, the approach is general, easy to prove correct and easy to integrate with other kinds of path information.

We prove that general merge-and-shrink representations are strictly more powerful than linear ones by showing that there exist problem families that can be represented compactly with general merge-and-shrink representations but not with linear ones. We also give a precise bound that quantifies the necessary blowup incurred by conversions from general merge-and-shrink representations to linear representations or BDDs/ADDs. Our theoretical results suggest an untapped potential for non-linear merging strategies and for the use of non-linear merge-and-shrink-like representations within symbolic search.

Operator cost partitioning is a well-known technique to make admissible heuristics additive by distributing the operator costs among individual heuristics. Planning tasks are usually defined with non-negative operator costs and therefore it appears natural to demand the same for the distributed costs. We argue that this requirement is not necessary and demonstrate the benefit of using general cost partitioning. We show that LP heuristics for operator-counting constraints are cost-partitioned heuristics and that the state equation heuristic computes a cost partitioning over atomic projections. We also introduce a new family of potential heuristics and show their relationship to general cost partitioning.

Many recent planning heuristics are based on LP optimization. However, planning experts mostly use LP solvers as a black box and it is often not obvious to them which LP techniques would be most suitable for their specific applications.

To foster the communication between the planning and the optimization community, this paper gives an easily accessible overview over these recent LP-based heuristics, namely the optimal cost partitioning heuristic for abstractions, the post-hoc optimization heuristic, a landmark heuristic, the state-equation heuristic, and a delete relaxation heuristic. All these heuristics fit the framework of so-called operator-counting constraints, which we also present.

The LM-Cut heuristic is currently the most successful heuristic in optimal STRIPS planning but it cannot be applied in the presence of conditional effects. Keyder, Hoffmann and Haslum recently showed that the obvious extensions to such effects ruin the nice theoretical properties of LM-Cut. We propose a new method based on context splitting that preserves these properties.

Many heuristics for cost-optimal planning are based on linear programming. We cover several interesting heuristics of this type by a common framework that fixes the objective function of the linear program. Within the framework, constraints from different heuristics can be combined in one heuristic estimate which dominates the maximum of the component heuristics. Different heuristics of the framework can be compared on the basis of their constraints. With this new method of analysis, we show dominance of the recent LP-based state-equation heuristic over optimal cost partitioning on single-variable abstractions. We also show that the previously suggested extension of the state-equation heuristic to exploit safe variables cannot lead to an improved heuristic estimate. We experimentally evaluate the potential of the proposed framework on an extensive suite of benchmark tasks.

The LM-Cut heuristic is currently the most successful heuristic in optimal STRIPS planning but it cannot be applied in the presence of conditional effects. Keyder, Hoffmann and Haslum recently showed that the obvious extensions to such effects ruin the nice theoretical properties of LM-Cut. We propose a new method based on context splitting that preserves these properties.

The iPDB procedure by Haslum et al. is the state-of-the-art method for computing additive abstraction heuristics for domain-independent planning. It performs a hill-climbing search in the space of pattern collections, combining information from multiple patterns in the so-called canonical heuristic.

We show how stronger heuristic estimates can be obtained through linear programming. An experimental evaluation demonstrates the strength of the new technique on the IPC benchmark suite.

Optimal solutions for multi-agent pathfinding problems are often too expensive to compute. For this reason, suboptimal approaches have been widely studied in the literature. Specifically, in recent years a number of efficient suboptimal algorithms that are complete for certain subclasses have been proposed at highly-rated robotics and AI conferences, all mentioning that it is an open problem which subclasses of non-optimal multi-agent pathfinding are tractable. However, it turns out that this problem has already been completely solved in another research community in the 1980s by a constructive proof that provides a polynomial algorithm that is complete for the entire class of problems. In this paper, we would like to bring this earlier related work to the attention of the robotics and AI communities.

Action programming languages like Golog allow to define complex behaviors for agents on the basis of action representations in terms of expressive (first-order) logical formalisms, making them suitable for realistic scenarios of agents with only partial world knowledge. Often these scenarios include sub-tasks that require sequential planning. While in principle it is possible to express and execute such planning sub-tasks directly in Golog, the system can performance-wise not compete with state-of-the-art planners. In this paper, we report on our efforts to integrate efficient planning and expressive action programming in the Platas project. The theoretical foundation is laid by a mapping between the planning language Pddl and the Situation Calculus, which is underlying Golog, together with a study of how these formalisms relate in terms of expressivity. The practical benefit is demonstrated by an evaluation of embedding a Pddl planner into Golog, showing a drastic increase in performance while retaining the full expressiveness of Golog.

BJOLP, The Big Joint Optimal Landmarks Planner uses landmarks to derive an admissible heuristic, which is then used to guide a search for a cost-optimal plan. In this paper we review landmarks and describe how they can be used to derive an admissible heuristic. We conclude with presenting the BJOLP planner.

Fast Downward Stone Soup is a sequential portfolio planner that uses various heuristics and search algorithms that have been implemented in the Fast Downward planning system.

We present a simple general method for concocting "planner soups", sequential portfolios of planning algorithms, and describe the actual recipes used for Fast Downward Stone Soup in the sequential optimization and sequential satisficing tracks of IPC 2011.

The FD-Autotune submissions for the IPC-2011 sequential tracks consist of three instantiations of the latest, highly parametric version of the Fast Downward Planning Framework. These instantiations have been automatically configured for performance on a wide range of planning domains, using the well-known ParamILS configurator. Two of the instantiations were entered into the sequential satisficing track and one into the sequential optimising track. We describe how the extremely large configuration space of Fast Downward was restricted to a subspace that, although still very large, can be managed by state-of-the-art automated configuration procedures, and how ParamILS was then used to obtain performance-optimised configurations.

The FD-Autotune learning planning system is based on the idea of domain-specific configuration of the latest, highly parametric version of the Fast Downward Planning Framework by means of a generic automated algorithm configuration procedure. We describe how the extremely large configuration space of Fast Downward was restricted to a subspace that, although still very large, can be managed by state-of-the-art automated configuration procedures. FD-Autotune uses the well-known ParamILS configurator and was realised using the recently developed HAL experimentation environment.

Fast Downward Stone Soup is a sequential portfolio planner that uses various heuristics and search algorithms that have been implemented in the Fast Downward planning system.

We present a simple general method for concocting "planner soups", sequential portfolios of planning algorithms, and describe the actual recipes used for Fast Downward Stone Soup in the sequential optimization and sequential satisficing tracks of IPC 2011.

This paper is, first and foremost, a planner description. Fast Downward Stone Soup was entered into the sequential (non-learning) tracks of IPC 2011. Due to time constraints, we did not enter it into the learning competition at IPC 2011. However, we believe that the approach might still be of interest to the planning and learning community, as it represents a baseline against which other, more sophisticated portfolio learners can be usefully compared.

In this work, we present the FD-Autotune learning planning system, which is based on the idea of domain-specific configuration of the latest, highly parametric version of the Fast Downward Planning Framework by means of a generic automated algorithm configuration procedure. We describe how the extremely large configuration space of Fast Downward was restricted to a subspace that, although still very large, can be managed by a state-of-the-art automated configuration procedure. Additionally, we give preliminary results obtained from applying our approach to the nine domains of the IPC-2011 learning track, using the well-known ParamILS configurator and the recently developed HAL experimentation environment.

The pancake problem is a famous search problem where the objective is to sort a sequence of objects (pancakes) through a minimal number of prefix reversals (flips). The best approaches for the problem are based on heuristic search with abstraction (pattern database) heuristics. We present a new class of abstractions for the pancake problem called relative-order abstractions. Relative-order abstractions have three advantages over the object-location abstractions considered in previous work. First, they are size-independent, i.e., do not need to be tailored to a particular instance size of the pancake problem. Second, they are more compact in that they can represent a larger number of pancakes within abstractions of bounded size. Finally, they can exploit symmetries in the problem specification to allow multiple heuristic lookups, significantly improving search performance over a single lookup. Our experiments show that compared to object-location abstractions, our new techniques lead to an improvement of one order of magnitude in runtime and up to three orders of magnitude in the number of generated states.

We empirically examine several ways of exploiting the information of multiple heuristics in a satisficing best-first search algorithm, comparing their performance in terms of coverage, plan quality, speed, and search guidance. Our results indicate that using multiple heuristics for satisficing search is indeed useful. Among the combination methods we consider, the best results are obtained by the alternation method of the "Fast Diagonally Downward" planner.

Planning systems for real-world applications need the ability to handle concurrency and numeric fluents. Nevertheless, the predominant approach to cope with concurrency followed by the most successful participants in the latest International Planning Competitions (IPC) is still to find a sequential plan that is rescheduled in a post-processing step. We present Temporal Fast Downward (TFD), a planning system for temporal problems that is capable of finding low-makespan plans by performing a heuristic search in a temporal search space. We show how the context-enhanced additive heuristic can be successfully used for temporal planning and how it can be extended to numeric fluents. TFD often produces plans of high quality and, evaluated according to the rating scheme of the last IPC, outperforms all state-of-the-art temporal planning systems.

The problem of effectively combining multiple heuristic estimators has been studied extensively in the context of optimal planning, but not in the context of satisficing planning. To narrow this gap, we empirically examine several ways of exploiting the information of multiple heuristics in a satisficing best-first search algorithm, comparing their performance in terms of coverage, plan quality and runtime. Our empirical results indicate that using multiple heuristics for satisficing search is indeed useful and that the best results are not obtained by the most obvious combination methods.

Integrating agent programming languages and efficient action planning is a promising approach because it combines the expressive power of languages such as Golog with the possibility of searching for plans efficiently. In order to integrate a Golog interpreter with a planner, one has to understand, however, which part of the expressiveness of Golog can be captured by the planning language. Using Nebel's compilation framework, we identify a maximal fragment of basic action theories, the formalism Golog is based on, that is expressively equivalent to the ADL subset of PDDL. As we will show, almost all features that permit to specify incomplete information in basic action theories cannot be compiled to ADL.

The Golog family of action languages has proven to be a useful means for the high-level control of autonomous agents, such as mobile robots. In particular, the IndiGolog variant, where programs are executed in an online manner, is applicable in realistic scenarios where agents possess only incomplete knowledge about the state of the world, have to use sensors to gather necessary information at runtime and need to react to spontaneous, exogenous events that happen unpredictably due to a dynamic environment. Often, the specification of such an agent’s program also involves that certain subgoals have to be solved by means of planning. IndiGolog supports this in principle by providing a variety of lookahead mechanisms, but when it comes to pure, sequential planning, these usually cannot compete with modern state-of-the-art planning systems, most of which being based on the Planning Domain Definition Language PDDL. Previous theoretical results provide insights on the semantical compatibility between Golog and PDDL and how they compare in terms of expressiveness. In this paper, we complement these results with an empirical evaluation that shows that equipping IndiGolog with a PDDL planner (FF in our case) pays off in terms of the runtime performance of the overall system. For that matter, we study a number of example application domains and compare the needed computation times for varying problem sizes and difficulties.

Heuristic search using algorithms such as A* and IDA* is the prevalent method for obtaining optimal sequential solutions for classical planning tasks. Theoretical analyses of these classical search algorithms, such as the well-known results of Pohl, Gaschnig and Pearl, suggest that such heuristic search algorithms can obtain better than exponential scaling behaviour, provided that the heuristics are accurate enough.

Here, we show that for a number of common planning benchmark domains, including ones that admit optimal solution in polynomial time, general search algorithms such as A* must necessarily explore an exponential number of search nodes even under the optimistic assumption of almost perfect heuristic estimators, whose heuristic error is bounded by a small additive constant.

Our results shed some light on the comparatively bad performance of optimal heuristic search approaches in "simple" domains such as GRIPPER. They suggest that in many domains, further improvements in run-time require changes to other parts of the planning algorithm than the heuristic estimator.

Heuristic search using algorithms such as A* and IDA* is the prevalent method for obtaining optimal sequential solutions for classical planning tasks. Theoretical analyses of these classical search algorithms, such as the well-known results of Pohl, Gaschnig and Pearl, suggest that such heuristic search algorithms can obtain better than exponential scaling behaviour, provided that the heuristics are accurate enough.

Here, we show that for a number of common planning benchmark domains, including ones that admit optimal solution in polynomial time, general search algorithms such as A* must necessarily explore an exponential number of search nodes even under the optimistic assumption of almost perfect heuristic estimators, whose heuristic error is bounded by a small additive constant.

Our results shed some light on the comparatively bad performance of optimal heuristic search approaches in "simple" domains such as GRIPPER. They suggest that in many domains, further improvements in run-time require changes to other parts of the planning algorithm than the heuristic estimator.

The main focus in the area of action languages, such as GOLOG, was put on expressive power, while the development in the area of action planning was focused on efficient plan generation. An integration of GOLOG and planning languages would provide great advantages. A user could constrain a systems behavior on a high level using GOLOG, while the actual low-level actions are planned by an efficient planning system. First endeavors have been made by Eyerich et al. by identifying a subset of the situation calculus (which is the basis of GOLOG) with the same expressiveness as the ADL fragment of PDDL. However, it was not proven that the identified restrictions define a maximum subset. The most severe restriction appears to be that functions are limited to constants. We will show that this restriction is indeed necessary in most cases.

For many classical planning domains, the computational complexity of non-optimal and optimal planning is known. However, little is known about the area in between the two extremes of finding some plan and finding optimal plans. In this contribution, we provide a complete classification of the propositional domains from the first four International Planning Competitions with respect to the approximation classes PO, PTAS, APX, poly-APX, and NPO.