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137
Planning with Pattern Databases
 PROCEEDINGS OF THE 6TH EUROPEAN CONFERENCE ON PLANNING (ECP01)
, 2001
"... Heuristic search planning eectively #12;nds 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 signi#12;cantly improve lowerbound estimates for opt ..."
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Cited by 132 (17 self)
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Heuristic search planning eectively #12;nds 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 signi#12;cantly improve lowerbound estimates for optimally solving challenging singleagent problems like the 24Puzzle or Rubik's Cube.
This paper studies the eect of pattern databases in the context of deterministic planning. Given afixed state description based on instantiated predicates, we provide a general abstraction scheme to automatically create admissible domainindependent memorybased 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.
Domainindependent construction of pattern database heuristics for costoptimal planning
, 2007
"... Heuristic search is a leading approach to domainindependent planning. For costoptimal planning, however, existing admissible heuristics are generally too weak to effectively guide the search. Pattern database heuristics (PDBs), which are based on abstractions of the search space, are currently one ..."
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Cited by 62 (17 self)
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Heuristic search is a leading approach to domainindependent planning. For costoptimal planning, however, existing admissible heuristics are generally too weak to effectively guide the search. Pattern database heuristics (PDBs), which are based on abstractions of the search space, are currently one of the most promising approaches to developing better admissible heuristics. The informedness of PDB heuristics depends crucially on the selection of appropriate abstractions (patterns). Although PDBs have been applied to many search problems, including planning, there are not many insights into how to select good patterns, even manually. What constitutes a good pattern depends on the problem domain, making the task even more difficult for domainindependent planning, where the process needs to be completely automatic and general. We present a novel way of constructing good patterns automatically from the specification of planning problem instances. We demonstrate that this allows a domainindependent planner to solve planning problems optimally in some very challenging domains, including a STRIPS formulation of the Sokoban puzzle.
New admissible heuristics for domainindependent planning
 In Proc
, 2005
"... Admissible heuristics are critical for effective domainindependent planning when optimal solutions must be guaranteed. Two useful heuristics are the h m heuristics, which generalize the reachability heuristic underlying the planning graph, and pattern database heuristics. These heuristics, however, ..."
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Cited by 60 (11 self)
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Admissible heuristics are critical for effective domainindependent planning when optimal solutions must be guaranteed. Two useful heuristics are the h m heuristics, which generalize the reachability heuristic underlying the planning graph, and pattern database heuristics. These heuristics, however, have serious limitations: reachability heuristics capture only the cost of critical paths in a relaxed problem, ignoring the cost of other relevant paths, while PDB heuristics, additive or not, cannot accommodate too many variables in patterns, and methods for automatically selecting patterns that produce good estimates are not known. We introduce two refinements of these heuristics: First, the additive h m heuristic which yields an admissible sum of h m heuristics using a partitioning of the set of actions. Second, the constrained PDB heuristic which uses constraints from the original problem to strengthen the lower bounds obtained from abstractions. The new heuristics depend on the way the actions or problem variables are partitioned. We advance methods for automatically deriving additive h m and PDB heuristics from STRIPS encodings. Evaluation shows improvement over existing heuristics in several domains, although, not surprisingly, no heuristic dominates all the others over all domains.
The generalized A* architecture
 Journal of Artificial Intelligence Research
, 2007
"... We consider the problem of computing a lightest derivation of a global structure using a set of weighted rules. A large variety of inference problems in AI can be formulated in this framework. We generalize A * search and heuristics derived from abstractions to a broad class of lightest derivation p ..."
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Cited by 48 (6 self)
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We consider the problem of computing a lightest derivation of a global structure using a set of weighted rules. A large variety of inference problems in AI can be formulated in this framework. We generalize A * search and heuristics derived from abstractions to a broad class of lightest derivation problems. We also describe a new algorithm that searches for lightest derivations using a hierarchy of abstractions. Our generalization of A * gives a new algorithm for searching AND/OR graphs in a bottomup fashion. We discuss how the algorithms described here provide a general architecture for addressing the pipeline problem — the problem of passing information back and forth between various stages of processing in a perceptual system. We consider examples in computer vision and natural language processing. We apply the hierarchical search algorithm to the problem of estimating the boundaries of convex objects in grayscale images and compare it to other search methods. A second set of experiments demonstrate the use of a new compositional model for finding salient curves in images. 1.
Compressing pattern databases
 In Proceedings of the Nineteenth National Conference on Artificial Intelligence (AAAI04
, 2004
"... A pattern database (PDB) is a heuristic function implemented as a lookup table that stores the lengths of optimal solutions for subproblem instances. Standard PDBs have a distinct entry in the table for each subproblem instance. In this paper we investigate compressing PDBs by merging several entrie ..."
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Cited by 47 (24 self)
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A pattern database (PDB) is a heuristic function implemented as a lookup table that stores the lengths of optimal solutions for subproblem instances. Standard PDBs have a distinct entry in the table for each subproblem instance. In this paper we investigate compressing PDBs by merging several entries into one, thereby allowing the use of PDBs that exceed available memory in their uncompressed form. We introduce a number of methods for determining which entries to merge and discuss their relative merits. These vary from domainindependent approaches that allow any set of entries in the PDB to be merged, to more intelligent methods that take into account the structure of the problem. The choice of the best compression method is based on domaindependent attributes. We present experimental results on a number of combinatorial problems, including the fourpeg Towers of Hanoi problem, the slidingtile puzzles, and the TopSpin puzzle. For the Towers of Hanoi, we show that the search time can be reduced by up to three orders of magnitude by using compressed PDBs compared to uncompressed PDBs of the same size. More modest improvements were observed for the other domains.
Maximizing over multiple pattern databases speeds up heuristic search
 Artificial Intelligence
, 2006
"... A pattern database (PDB) is a heuristic function stored as a lookup table. This paper considers how best to use a fixed amount (m units) of memory for storing pattern databases. In particular, we examine whether using n pattern databases of size m/n instead of one pattern database of size m improves ..."
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Cited by 26 (13 self)
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A pattern database (PDB) is a heuristic function stored as a lookup table. This paper considers how best to use a fixed amount (m units) of memory for storing pattern databases. In particular, we examine whether using n pattern databases of size m/n instead of one pattern database of size m improves search performance. In all the state spaces considered, the use of multiple smaller pattern databases reduces the number of nodes generated by IDA*. The paper provides an explanation for this phenomenon based on the distribution of heuristic values that occur during search. 1 Introduction and
Hierarchical heuristic search revisited
 In Abstraction, Reformulation and Approximation
, 2005
"... Abstract. Pattern databases enable difficult search problems to be solved very quickly, but are large and timeconsuming to build. They are therefore best suited to situations where many problem instances are to be solved, and less than ideal when only a few instances are to be solved. This paper ex ..."
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Cited by 26 (9 self)
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Abstract. Pattern databases enable difficult search problems to be solved very quickly, but are large and timeconsuming to build. They are therefore best suited to situations where many problem instances are to be solved, and less than ideal when only a few instances are to be solved. This paper examines a technique hierarchical heuristic searchespecially designed for the latter situation. The key idea is to compute, on demand, only those pattern database entries needed to solve a given problem instance. Our experiments show that Hierarchical IDA * can solve individual problems very quickly, up to two orders of magnitude faster than the time required to build an entire highperformance pattern database. 1
A general theory of additive state space abstractions
 JAIR
"... Informally, a set of abstractions of a state space S is additive if the distance between any two states in S is always greater than or equal to the sum of the corresponding distances in the abstract spaces. The first known additive abstractions, called disjoint pattern databases, were experimentally ..."
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Cited by 25 (15 self)
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Informally, a set of abstractions of a state space S is additive if the distance between any two states in S is always greater than or equal to the sum of the corresponding distances in the abstract spaces. The first known additive abstractions, called disjoint pattern databases, were experimentally demonstrated to produce state of the art performance on certain state spaces. However, previous applications were restricted to state spaces with special properties, which precludes disjoint pattern databases from being defined for several commonly used testbeds, such as Rubik’s Cube, TopSpin and the Pancake puzzle. In this paper we give a general definition of additive abstractions that can be applied to any state space and prove that heuristics based on additive abstractions are consistent as well as admissible. We use this new definition to create additive abstractions for these testbeds and show experimentally that well chosen additive abstractions can reduce search time substantially for the (18,4)TopSpin puzzle and by three orders of magnitude over state of the art methods for the 17Pancake puzzle. We also derive a way of testing if the heuristic value returned by additive abstractions is provably too low and show that the use of this test can reduce search time for the 15puzzle and TopSpin by roughly a factor of two. 1.