Results 1  10
of
61
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 ..."
Abstract

Cited by 111 (28 self)
 Add to MetaCart
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.
Flexible abstraction heuristics for optimal sequential planning
 In Proc. ICAPS 2007
, 2007
"... We describe an approach to deriving consistent heuristics for automated planning, based on explicit search in abstract state spaces. The key to managing complexity is interleaving composition of abstractions over different sets of state variables with abstraction of the partial composites. The appro ..."
Abstract

Cited by 95 (26 self)
 Add to MetaCart
We describe an approach to deriving consistent heuristics for automated planning, based on explicit search in abstract state spaces. The key to managing complexity is interleaving composition of abstractions over different sets of state variables with abstraction of the partial composites. The approach is very general and can be instantiated in many different ways by following different abstraction strategies. In particular, the technique subsumes planning with pattern databases as a special case. Moreover, with suitable abstraction strategies it is possible to derive perfect heuristics in a number of classical benchmark domains, thus allowing their optimal solution in polynomial time. To evaluate the practical usefulness of the approach, we perform empirical experiments with one particular abstraction strategy. Our results show that the approach is competitive with the state of the art.
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 ..."
Abstract

Cited by 65 (4 self)
 Add to MetaCart
(Show Context)
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 ..."
Abstract

Cited by 62 (13 self)
 Add to MetaCart
(Show Context)
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.
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 ..."
Abstract

Cited by 25 (15 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 22 (9 self)
 Add to MetaCart
(Show Context)
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.
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 ..."
Abstract

Cited by 17 (7 self)
 Add to MetaCart
(Show Context)
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 ..."
Abstract

Cited by 17 (8 self)
 Add to MetaCart
(Show Context)
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 ..."
Abstract

Cited by 15 (8 self)
 Add to MetaCart
(Show Context)
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 ..."
Abstract

Cited by 14 (1 self)
 Add to MetaCart
(Show Context)
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.