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23
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.
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.
Recent progress in heuristic search: A case study of the fourpeg Towers of Hanoi problem
 in: International Joint Conference on Artificial Intelligence (IJCAI07
"... We integrate a number of recent advances in heuristic search, and apply them to the fourpeg Towers of Hanoi problem. These include frontier search, diskbased search, multiple compressed disjoint additive pattern database heuristics, and breadthfirst heuristic search. The main new idea we introduc ..."
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Cited by 22 (9 self)
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We integrate a number of recent advances in heuristic search, and apply them to the fourpeg Towers of Hanoi problem. These include frontier search, diskbased search, multiple compressed disjoint additive pattern database heuristics, and breadthfirst heuristic search. The main new idea we introduce here is the use of pattern database heuristics to search for any of a number of explicit goal states, with no overhead compared to a heuristic for a single goal state. We perform the first complete breadthfirst searches of the 21 and 22disc fourpeg Towers of Hanoi problems, and extend the verification of a “presumed optimal solution ” to this problem from 24 to 30 discs, a problem that is 4096 times larger. Fourpeg Towers of Hanoi Problem The threepeg Towers of Hanoi problem is well known in
Solving the 24puzzle with instance dependent pattern databases
 In Proceedings of SARA05
, 2005
"... Abstract. A pattern database (PDB) is a heuristic function in a form of a lookup table which stores the cost of optimal solutions for instances of subproblems. These subproblems are generated by abstracting the entire search space into a smaller space called the pattern space. Traditionally, the ent ..."
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Cited by 12 (3 self)
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Abstract. A pattern database (PDB) is a heuristic function in a form of a lookup table which stores the cost of optimal solutions for instances of subproblems. These subproblems are generated by abstracting the entire search space into a smaller space called the pattern space. Traditionally, the entire pattern space is generated and each distinct pattern has an entry in the pattern database. Recently, [10] described a method for reducing pattern database memory requirements by storing only pattern database values for a specific instant of start and goal state thus enabling larger PDBs to be used and achieving speedup in the search. We enhance their method by dynamically growing the pattern database until memory is full, thereby allowing using any size of memory. We also show that memory could be saved by storing hierarchy of PDBs. Experimental results on the large 24 sliding tile puzzle show improvements of up to a factor of 40 over previous benchmark results [8]. 1
Partial pattern databases
"... Abstract. Perimeters and pattern databases are two similar memorybased techniques used in singleagent search problems. We present partial pattern databases, which unify the two approaches into a single memorybased heuristic table. Our approach allows the use of any abstraction level. We achieve a t ..."
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Cited by 9 (1 self)
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Abstract. Perimeters and pattern databases are two similar memorybased techniques used in singleagent search problems. We present partial pattern databases, which unify the two approaches into a single memorybased heuristic table. Our approach allows the use of any abstraction level. We achieve a threefold reduction in the average number of nodes generated on the 13pancake puzzle and a 27 % reduction on the 15puzzle. 1
Automated creation of pattern database search heuristics
 In Proc. MoChArt2006
"... Abstract. Pattern databases are dictionaries for heuristic estimates storing statetogoal distances in state space abstractions. Their effectiveness is sensitive to the selection of the underlying patterns. Especially for multiple and additive pattern databases, the manual selection of patterns tha ..."
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Cited by 8 (1 self)
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Abstract. Pattern databases are dictionaries for heuristic estimates storing statetogoal distances in state space abstractions. Their effectiveness is sensitive to the selection of the underlying patterns. Especially for multiple and additive pattern databases, the manual selection of patterns that leads to good exploration results is involved. For automating the selection process, greedy binpacking has been suggested. This paper proposes genetic algorithms to optimize its output. Patterns are encoded as binary strings and optimized using an objective function that predicts the heuristic search tree size based on the distribution of heuristic values in abstract space. To reduce the memory requirements we construct the pattern databases symbolically. Experiments in heuristic search planning indicate that the total search efforts can be reduced significantly. 1
Admissible Heuristics for Automated Planning
 Ph.D. Dissertation, Linköpings Universitet
"... The problem of domainindependent automated planning has been a topic of research in Artificial Intelligence since the very beginnings of the field. Due to the desire not to rely on vast quantities of problem specific knowledge, the most widely adopted approach to automated planning is search. The t ..."
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Cited by 5 (2 self)
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The problem of domainindependent automated planning has been a topic of research in Artificial Intelligence since the very beginnings of the field. Due to the desire not to rely on vast quantities of problem specific knowledge, the most widely adopted approach to automated planning is search. The topic of this thesis is the development of methods for achieving effective search control for domainindependent optimal planning through the construction of admissible heuristics. The particular planning problem considered is the so called “classical ” AI planning problem, which makes several restricting assumptions. Optimality with respect to two measures of plan cost are considered: in planning with additive cost, the cost of a plan is the sum of the costs of the actions that make up the plan, which are assumed independent, while in planning with time, the cost of a plan is the total execution time – makespan – of the plan. The makespan optimization objective can not, in general, be formulated as a sum of independent action costs and therefore necessitates a problem model slightly different from the classical one. A further small extension to the classical