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59
Landmarks, Critical Paths and Abstractions: What’s the Difference Anyway?
, 2009
"... Current heuristic estimators for classical domainindependent planning are usually based on one of four ideas: delete relaxations, critical paths, abstractions, and, most recently, landmarks. Previously, these different ideas for deriving heuristic functions were largely unconnected. We prove that a ..."
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Cited by 111 (28 self)
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Current heuristic estimators for classical domainindependent planning are usually based on one of four ideas: delete relaxations, critical paths, abstractions, and, most recently, landmarks. Previously, these different ideas for deriving heuristic functions were largely unconnected. We prove that admissible heuristics based on these ideas are in fact very closely related. Exploiting this relationship, we introduce a new admissible heuristic called the landmark cut heuristic, which compares favourably with the state of the art in terms of heuristic accuracy and overall performance.
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.
The More, the Merrier: Combining Heuristic Estimators for Satisficing Planning (Extended Version)
, 2010
"... 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 satisf ..."
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Cited by 25 (2 self)
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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 bestfirst 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.
Optimal additive composition of abstractionbased admissible heuristics
 In ICAPS (this volume
, 2008
"... We describe a procedure that takes a classical planning task, a forwardsearch state, and a set of abstractionbased admissible heuristics, and derives an optimal additive composition of these heuristics with respect to the given state. Most importantly, we show that this procedure is polynomialtim ..."
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Cited by 22 (9 self)
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We describe a procedure that takes a classical planning task, a forwardsearch state, and a set of abstractionbased admissible heuristics, and derives an optimal additive composition of these heuristics with respect to the given state. Most importantly, we show that this procedure is polynomialtime for arbitrary sets of all known to us abstractionbased heuristics such as PDBs, constrained PDBs, mergeandshrink abstractions, forkdecomposition structural patterns, and structural patterns based on tractable constraint optimization. 1.
New islands of tractability of costoptimal planning
 JAIR
, 2008
"... We study the complexity of costoptimal classical planning over propositional state variables and unaryeffect actions. We discover novel problem fragments for which such optimization is tractable, and identify certain conditions that differentiate between tractable and intractable problems. These r ..."
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Cited by 17 (3 self)
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We study the complexity of costoptimal classical planning over propositional state variables and unaryeffect actions. We discover novel problem fragments for which such optimization is tractable, and identify certain conditions that differentiate between tractable and intractable problems. These results are based on exploiting both structural and syntactic characteristics of planning problems. Specifically, following Brafman and Domshlak (2003), we relate the complexity of planning and the topology of the causal graph. The main results correspond to tractability of costoptimal planning for propositional problems with polytree causal graphs that either have O(1)bounded indegree, or are induced by actions having at most one prevail condition each. Almost all our tractability results are based on a constructive proof technique that connects between certain tools from planning and tractable constraint optimization, and we believe this technique is of interest on its own due to a clear evidence for its robustness.
To Max or not to Max: Online Learning for Speeding Up Optimal Planning
, 2010
"... It is well known that there cannot be a single “best ” heuristic for optimal planning in general. One way of overcoming this is by combining admissible heuristics (e.g. by using their maximum), which requires computing numerous heuristic estimates at each state. However, there is a tradeoff between ..."
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Cited by 17 (7 self)
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It is well known that there cannot be a single “best ” heuristic for optimal planning in general. One way of overcoming this is by combining admissible heuristics (e.g. by using their maximum), which requires computing numerous heuristic estimates at each state. However, there is a tradeoff between the time spent on computing these heuristic estimates for each state, and the time saved by reducing the number of expanded states. We present a novel method that reduces the cost of combining admissible heuristics for optimal search, while maintaining its benefits. Based on an idealized search space model, we formulate a decision rule for choosing the best heuristic to compute at each state. We then present an active online learning approach for that decision rule, and employ the learned model to decide which heuristic to compute at each state. We evaluate this technique empirically, and show that it substantially outperforms each of the individual heuristics that were used, as well as their regular maximum.
Implicit abstraction heuristics
"... Statespace search with explicit abstraction heuristics is at the state of the art of costoptimal planning. These heuristics are inherently limited, nonetheless, because the size of the abstract space must be bounded by some, even if a very large, constant. Targeting this shortcoming, we introduce t ..."
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Cited by 17 (8 self)
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Statespace search with explicit abstraction heuristics is at the state of the art of costoptimal planning. These heuristics are inherently limited, nonetheless, because the size of the abstract space must be bounded by some, even if a very large, constant. Targeting this shortcoming, we introduce the notion of (additive) implicit abstractions, in which the planning task is abstracted by instances of tractable fragments of optimal planning. We then introduce a concrete setting of this framework, called forkdecomposition, that is based on two novel fragments of tractable costoptimal planning. The induced admissible heuristics are then studied formally and empirically. This study testifies for the accuracy of the fork decomposition heuristics, yet our empirical evaluation also stresses the tradeoff between their accuracy and the runtime complexity of computing them. Indeed, some of the power of the explicit abstraction heuristics comes from precomputing the heuristic function offline and then determining h(s) for each evaluated state s by a very fast lookup in a “database. ” By contrast, while forkdecomposition heuristics can be calculated in polynomial time, computing them is far from being fast. To address this problem, we show that the timepernode complexity bottleneck of the forkdecomposition heuristics can be successfully overcome. We demonstrate that an equivalent of the explicit abstraction notion of a “database ” exists for the forkdecomposition abstractions as well, despite their exponentialsize abstract spaces. We then verify empirically that heuristic search with the “databased ” forkdecomposition heuristics favorably competes with the state of the art of costoptimal planning. 1.
Structural Patterns Heuristics via Fork Decomposition
, 2008
"... We consider a generalization of the PDB homomorphism abstractions to what is called “structural patterns”. The basic idea is in abstracting the problem in hand into provably tractable fragments of optimal planning, alleviating by that the constraint of PDBs to use projections of only low dimensional ..."
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Cited by 15 (8 self)
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We consider a generalization of the PDB homomorphism abstractions to what is called “structural patterns”. The basic idea is in abstracting the problem in hand into provably tractable fragments of optimal planning, alleviating by that the constraint of PDBs to use projections of only low dimensionality. We introduce a general framework for additive structural patterns based on decomposing the problem along its causal graph, suggest a concrete nonparametric instance of this framework called forkdecomposition, and formally show that the admissible heuristics induced by the latter abstractions provide stateoftheart worstcase informativeness guarantees on several standard domains.
Additivedisjunctive heuristics for optimal planning
 IN PROC. ICAPS 2008
, 2008
"... The development of informative, admissible heuristics for costoptimal planning remains a significant challenge in domainindependent planning research. Two techniques are commonly used to try to improve heuristic estimates. The first is disjunction: taking the maximum across several heuristic value ..."
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Cited by 14 (1 self)
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The development of informative, admissible heuristics for costoptimal planning remains a significant challenge in domainindependent planning research. Two techniques are commonly used to try to improve heuristic estimates. The first is disjunction: taking the maximum across several heuristic values. The second is the use of additive techniques, taking the sum of the heuristic values from a set of evaluators in such a way that admissibility is preserved. In this paper, we explore how the two can be combined in a novel manner, using disjunction within additive heuristics. We define a general structure, the Additive–Disjunctive Heuristic Graph (ADHG), that can be used to define an interesting class of heuristics based around these principles. As an example of how an ADHG can be employed, and as an empirical demonstration, we then present a heuristic based on the wellknown additive h m heuristic, showing an improvement in performance when additive–disjunctive techniques are used.
Accuracy of admissible heuristic functions in selected planning domains
 In AAAI. (Extended abstract in the ICAPS’07 workshops
, 2007
"... The efficiency of optimal planning algorithms based on heuristic search crucially depends on the accuracy of the heuristic function used to guide the search. Often, we are interested in domainindependent heuristics for planning. In order to assess the limitations of domainindependent heuristic pla ..."
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Cited by 13 (4 self)
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The efficiency of optimal planning algorithms based on heuristic search crucially depends on the accuracy of the heuristic function used to guide the search. Often, we are interested in domainindependent heuristics for planning. In order to assess the limitations of domainindependent heuristic planning, we analyze the (in)accuracy of common domainindependent planning heuristics in the IPC benchmark domains. For a selection of these domains, we analytically investigate the accuracy of the h + heuristic, the h m family of heuristics, and certain (additive) pattern database heuristics, compared to the perfect heuristic h ∗. Whereas h + and additive pattern database heuristics usually return cost estimates proportional to the true cost, nonadditive h m and nonadditive patterndatabase heuristics can yield results underestimating the true cost by arbitrarily large factors.