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62
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 69 (23 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.
How good is almost perfect
 In ICAPSWorkshop on Heuristics for DomainIndependent Planning
, 2007
"... 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 wellknown results of Pohl, Gaschnig and Pearl, suggest that such heuristic ..."
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Cited by 44 (4 self)
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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 wellknown 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” planning domains such as GRIPPER. They suggest that in many applications, further improvements in runtime require changes to other parts of the search algorithm than the heuristic estimator.
Concise finitedomain representations for PDDL planning tasks
, 2009
"... We introduce an efficient method for translating planning tasks specified in the standard PDDL formalism into a concise grounded representation that uses finitedomain state variables instead of the straightforward propositional encoding. Translation is performed in four stages. Firstly, we transfo ..."
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Cited by 40 (13 self)
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We introduce an efficient method for translating planning tasks specified in the standard PDDL formalism into a concise grounded representation that uses finitedomain state variables instead of the straightforward propositional encoding. Translation is performed in four stages. Firstly, we transform the input task into an equivalent normal form expressed in a restricted fragment of PDDL. Secondly, we synthesize invariants of the planning task that identify groups of mutually exclusive propositions which can be represented by a single finitedomain variable. Thirdly, we perform an efficient relaxed reachability analysis using logic programming techniques to obtain a grounded representation of the input. Finally, we combine the results of the third and fourth stage to generate the final grounded finitedomain representation. The presented approach has originally been implemented as part of the Fast Downward planning system for the 4th International Planning Competition (IPC4). Since then, it has been used in a number of other contexts with considerable success, and the use of concise finitedomain representations has become a common feature of stateoftheart planners.
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 20 (8 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.
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 19 (11 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.
Scalable, Parallel BestFirst Search for Optimal Sequential Planning
, 2009
"... Largescale, parallel clusters composed of commodity processors are increasingly available, enabling the use of vast processing capabilities and distributed RAM to solve hard search problems. We investigate parallel algorithms for optimal sequential planning, with an emphasis on exploiting distribut ..."
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Cited by 15 (3 self)
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Largescale, parallel clusters composed of commodity processors are increasingly available, enabling the use of vast processing capabilities and distributed RAM to solve hard search problems. We investigate parallel algorithms for optimal sequential planning, with an emphasis on exploiting distributed memory computing clusters. In particular, we focus on an approach which distributes and schedules work among processors based on a hash function of the search state. We use this approach to parallelize the A * algorithm in the optimal sequential version of the Fast Downward planner. The scaling behavior of the algorithm is evaluated experimentally on clusters using up to 128 processors, a significant increase compared to previous work in parallelizing planners. We show that this approach scales well, allowing us to effectively utilize the large amount of distributed memory to optimally solve problems which require hundreds of gigabytes of RAM to solve. We also show that this approach scales well for a single, sharedmemory multicore machine.
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.
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 12 (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.
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 12 (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 11 (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.