Pattern database (PDB) is one of the most popular automated heuristic generation techniques. A PDB maps states in a planning task to abstract states by considering a subset of variables and stores their optimal costs to the abstract goal in a look up table. As the result of the progress made on symbolic search over recent years, symbolic-PDB-based planners achieved impressive results in the International Planning Competition (IPC) 2018. Among them, Complementary 1 (CPC1) tied as the second best planners and the best non-portfolio planners in the cost optimal track, only 2 tasks behind the winner. It uses a combination of different pattern generation algorithms to construct PDBs that are complementary to existing ones. As shown in the post contest experiments, there is room for improvement. In this paper, we would like to present our work on refining the PDB construction mechanism of CPC1. By testing on IPC 2018 benchmarks, the results show that a significant improvement is made on our modified planner over the original version.

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 pattern database (PDB) is a pre-computed lookup table storing shortest distances from abstract states to abstract goal states. PDBs are key components in heuristic search as their entries are used to prune paths that cannot lead to an optimal solution. With the sliding-tile puzzle as an exemplary application domain, we present methods to improve the precision and size of PDBs by improving additive pattern databases to zero-aware additive pattern databases (ZPDBs), reducing the compression rate from previously 1.6 bit to 1 bit per entry, generating optimal additive pattern partitionings, and building effective collections of pattern databases. With these enhancements, we achieve an overall 8.59-fold performance gain on the 24-puzzle compared to the previously best set of 6-tile PDBs.

A popular way to create domain-independent heuristic functions is by using abstraction, where an abstract (coarse) version of the state space is derived from the original state space. An abstraction-based heuristic is usually implemented using a pattern database, a lookup table of (abstract state, heuristic value) pairs. Efficient representation and compression of pattern databases has been the topic of substantial ongoing research. In this paper, we present a novel domain-independent algorithm for this purpose using acyclic r-partite random hypergraphs. The theoretical and experimental results show that our proposed algorithm provides a consistent representation that works well across planning problem domains and provides a good trade-off between space usage and lookup time. Thus, it is suitable to be a standard efficient representation for pattern databases and a benchmark method for other pattern database representation/compression methods.

Heuristic search planning effectively finds solutions for large planning problems, but since the estimates are either not admissible or too weak, optimal solutions are found in rare cases only. In contrast, heuristic pattern databases are known to significantly improve lower bound estimates for optimally solving challenging single-agent problems like the 24-Puzzle or Rubik's Cube. This paper studies the effect of pattern databases in the context of deterministic planning. Given a fixed state description based on instantiated predicates, we provide a general abstraction scheme to automatically create admissible domain-independent memory-based heuristics for planning problems, where abstractions are found in factorizing the planning space. We evaluate the impact of pattern database heuristics in A* and hill climbing algorithms for a collection of benchmark domains.

Abstraction heuristics are a leading approach for deriving admissible estimates in cost-optimal planning. However, a drawback with respect to other families of heuristics is that they require a preprocessing phase for choosing the abstraction, computing the abstract distances, and/or suitable cost-partitionings. Typically, this is performed in advance by a fixed amount of time, even though some instances could be solved much faster with little or no preprocessing. We interleave the computation of abstraction heuristics with search, avoiding a long precomputation phase and allowing information from the search to be used for guiding the abstraction selection. To evaluate our ideas, we implement them on a planner that uses a single symbolic PDB. Our results show that delaying the preprocessing is not harmful in general even when an important amount of preprocessing is required to obtain good performance.

A pattern database (PDB) is a pre-computed lookup table storing shortest distances from abstract states to abstract goal states. PDBs are key components in heuristic search as their entries are used to prune paths that cannot lead to an optimal solution. With the sliding-tile puzzle as an exemplary application domain, we present methods to improve the precision and size of PDBs by improving additive pattern databases to zero-aware additive pattern databases (ZPDBs), reducing the compression rate from previously 1.6 bit to 1 bit per entry, generating optimal additive pattern partitionings, and building effective collections of pattern databases. With these enhancements, we achieve an overall 8.59-fold performance gain on the 24-puzzle compared to the previously best set of 6-tile PDBs.

Procedural generation of initial states of state-space search problems have applications in human and machine learning as well as in the evaluation of planning systems. In this paper we deal with the task of generating hard and solvable initial states of Sokoban puzzles. We propose hardness metrics based on pattern database heuristics and the use of novelty to improve the exploration of search methods in the task of generating initial states. We then present a system called Beta that uses our hardness metrics and novelty to generate initial states. Experiments show that Beta is able to generate initial states that are harder to solve by a specialized solver than those designed by human experts.

There has been an astounding improvement in domain-independent planning for solvable instances over the last decades and planners have become increasingly efficient at constructing plans. However, this advancement has not been matched by a similar improvement for identifying unsolvable instances. In this paper, we specialise pattern databases for dead-end detection and, thus, for detecting unsolvable instances. We propose two methods of constructing pattern collections and show that spending any more time constructing the pattern collection is likely to be unproductive. In other words, very few other pattern collections within the given space bounds are able to detect more dead-ends. We show this by carrying out a novel statistical analysis: a large computer cluster has been used to approximate the limit of pattern collections with respect to dead-end detection for many unsolvable instances, and this information is used in the analysis of the proposed methods. Consequently, further improvement must come from combining pattern databases with other techniques, such as mutexes. Furthermore, we explain why one of the proposed methods tends to find significantly more unsolvable variable projections, which is desirable since they imply that the instance is unsolvable. Finally, we compare the best proposed method with the winner and the runner up of the first unsolvability international planning competition, and show that the method is competitive.

Cost partitioning is a general and principled approach for constructing additive admissible heuristics for state-space search. Cost partitioning approaches for optimal classical planning include optimal cost partitioning, uniform cost partitioning, zero-one cost partitioning, saturated cost partitioning, post-hoc optimization and the canonical heuristic for pattern databases. We compare these algorithms theoretically, showing that saturated cost partitioning dominates greedy zero-one cost partitioning. As a side effect of our analysis, we obtain a new cost partitioning algorithm dominating uniform cost partitioning. We also evaluate these algorithms experimentally on pattern databases, Cartesian abstractions and landmark heuristics, showing that saturated cost partitioning is usually the method of choice on the IPC benchmark suite.