Merge-and-Shrink Task Reformulation for Classical Planning

The performance of domain-independent planning systems heavily depends on how the planning task has been modeled. This makes task reformulation an important tool to get rid of unnecessary complexity and increase the robustness of planners with respect to the model chosen by the user. In this paper, we represent tasks as factored transition systems (FTS), and use the merge-and-shrink (M&S) framework for task reformulation for optimal and satisficing planning. We prove that the flexibility of the underlying representation makes the M&S reformulation methods more powerful than the counterparts based on the more popular finite-domain representation. We adapt delete-relaxation and M&S heuristics to work on the FTS representation and evaluate the impact of our reformulation

Merge-and-shrink abstractions for classical planning : theory, strategies, and implementation

Classical planning is the problem of finding a sequence of deterministic actions in a state space that lead from an initial state to a state satisfying some goal condition. The dominant approach to optimally solve planning tasks is heuristic search, in particular A* search combined with an admissible heuristic. While there exist many different admissible heuristics, we focus on abstraction heuristics in this thesis, and in particular, on the well-established merge-and-shrink heuristics. Our main theoretical contribution is to provide a comprehensive description of the merge-and-shrink framework in terms of transformations of transition systems. Unlike previous accounts, our description is fully compositional, i.e. can be understood by understanding each transformation in isolation. In particular, in addition to the name-giving merge and shrink transformations, we also describe pruning and label reduction as such transformations. The latter is based on generalized label reduction, a new theory that removes all of the restrictions of the previous definition of label reduction. We study the four types of transformations in terms of desirable formal properties and explain how these properties transfer to heuristics being admissible and consistent or even perfect. We also describe an optimized implementation of the merge-and-shrink framework that substantially improves the efficiency compared to previous implementations. Furthermore, we investigate the expressive power of merge-and-shrink abstractions by analyzing factored mappings, the data structure they use for representing functions. In particular, we show that there exist certain families of functions that can be compactly represented by so-called non-linear factored mappings but not by linear ones. On the practical side, we contribute several non-linear merge strategies to the merge-and-shrink toolbox. In particular, we adapt a merge strategy from model checking to planning, provide a framework to enhance existing merge strategies based on symmetries, devise a simple score-based merge strategy that minimizes the maximum size of transition systems of the merge-and-shrink computation, and describe another framework to enhance merge strategies based on an analysis of causal dependencies of the planning task. In a large experimental study, we show the evolution of the performance of merge-and-shrink heuristics on planning benchmarks. Starting with the state of the art before the contributions of this thesis, we subsequently evaluate all of our techniques and show that state-of-the-art non-linear merge-and-shrink heuristics improve significantly over the previous state of the art

Merge-and-Shrink Heuristics for Classical Planning: Efficient Implementation and Partial Abstractions

Merge-and-shrink heuristics are a successful class of abstraction heuristics used for optimal classical planning. With the recent addition of generalized label reduction, merge-and-shrink can be understood as an algorithm framework that repeatedly applies transformations to a factored representation of a given planning task to compute an abstraction. In this paper, we describe an efficient implementation of the framework and its transformations, comparing it to its previous implementation in Fast Downward. We further discuss partial merge-and-shrink abstractions that do not consider all aspects of the concrete state space. To compute such partial abstractions, we stop the merge-and-shrink computation early by imposing simple limits on the resource consumption of the algorithm. Our evaluation shows that the efficient implementation indeed improves over the previous one, and that partial merge-and-shrink abstractions further push the efficiency of merge-and-shrink planners

Additive Pattern Databases for Decoupled Search

Abstraction heuristics are the state of the art in optimal classical planning as heuristic search. Despite their success for explicit-state search, though, abstraction heuristics are not available for decoupled state-space search, an orthogonal reduction technique that can lead to exponential savings by decomposing planning tasks. In this paper, we show how to compute pattern database (PDB) heuristics for decoupled states. The main challenge lies in how to additively employ multiple patterns, which is crucial for strong search guidance of the heuristics. We show that in the general case, for arbitrary collections of PDBs, computing the heuristic for a decoupled state is exponential in the number of leaf components of decoupled search. We derive several variants of decoupled PDB heuristics that allow to additively combine PDBs avoiding this blow-up and evaluate them empirically

Automatic Configuration of Benchmark Sets for Classical Planning

The benchmarks from previous International Planning Competitions are commonly used to evaluate new planning algorithms. Since this set has grown organically over the years, it has several flaws: it contains duplicate tasks, unsolvable tasks, trivially solvable domains, and domains with modelling errors. Also, diverse domain sizes complicate aggregating results. Most importantly, however, the range of task difficulty is very small in many domains. We propose an automated method for creating benchmarks that solves these issues. To find a good scaling in difficulty, we automatically configure the parameters of benchmark domains. We show that the resulting benchmark set improves empirical comparisons by allowing to differentiate between planners more easily

Efficient Evaluation of Large Abstractions for Decoupled Search: Merge-and-Shrink and Symbolic Pattern Databases

Abstraction heuristics are a state-of-the-art technique to solve classical planning problems optimally. A common approach is to precompute many small abstractions and combine them admissibly using cost partitioning. Recent work has shown that this approach does not work out well when using such heuristics for decoupled state space search, where search nodes represent potentially large sets of states. This is due to the fact that admissibly combining the estimates of several heuristics without sacrificing accuracy is NP-hard for decoupled states. In this work we propose to use a single large abstraction instead. We focus on merge-and-shrink and symbolic pattern database heuristics, which are designed to produce such abstractions. For these heuristics, we prove that the evaluation of decoupled states is NP-hard in general, but we also identify conditions under which it is polynomial. We introduce algorithms for both the general and the polynomial case. Our experimental evaluation shows that single large abstraction heuristics lead to strong performance when the heuristic evaluation is polynomial

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

A Theory of Merge-and-Shrink for Stochastic Shortest Path Problems

The merge-and-shrink framework is a powerful tool to construct state space abstractions based on factored representations. One of its core applications in classical planning is the construction of admissible abstraction heuristics. In this paper, we develop a compositional theory of merge-and-shrink in the context of probabilistic planning, focusing on stochastic shortest path problems (SSPs). As the basis for this development, we contribute a novel factored state space model for SSPs. We show how general transformations, including abstractions, can be formulated on this model to derive admissible and/or perfect heuristics. To formalize the merge-and-shrink framework for SSPs, we transfer the fundamental merge-and-shrink transformations from the classical setting: shrinking, merging, and label reduction. We analyze the formal properties of these transformations in detail and show how the conditions under which shrinking and label reduction lead to perfect heuristics can be extended to the SSP setting