Complexity of Interval Relaxed Numeric Planning

Aldinger, Johannes; Mattmüller, Robert; Göbelbecker, Moritz

doi:10.1007/978-3-319-24489-1_2

Cited by 11 publications

(11 citation statements)

References 6 publications

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“…We now turn our attention to the relationship between h 1 hbd (the relaxation underlying bothĥ max hbd andĥ add hbd ) and the interval-based relaxation of Π (Scala et al, 2016b;Aldinger, Mattmüller, & Göbelbecker, 2015), denoted Π + . It is easy to see that problems that are solvable in h hbd are also solvable in Π + : The set of achievers that is used in the solution to the h 1 hbd equation can be used to solve Π + in an obvious way: achievers can be applied to extend state intervals up to the point where all the conditions they can possibly achieve become satisfied.…”

Section: Over-approximation Guarantees and Relation With Ibrmentioning

confidence: 99%

“…One of the powerful ideas behind previous and current approaches is to devise heuristics from a computationally effective relaxation or abstraction of the targeted problem. In particular, the solution of the relaxed problem can be used as a means to estimate the actual distance or cost to the problem goal Pioneered by Hoffman ( 2003), the interval-based relaxation (Aldinger et al, 2015;Gregory, Long, Fox, & Beck, 2012) has been the principle most used to extract such a heuristic information in the numeric extension to classical planning. These heuristics come in different flavours, including as metric extensions of the relaxed planning graph (Koehler, 1998;Hoffmann, 2003;Gerevini, Saetti, & Serina, 2008;Coles et al, 2012Coles et al, , 2013.…”

Section: Numeric Planning Via Heuristic Searchmentioning

confidence: 99%

“…It follows that any condition previously satisfied will also be satisfied in the successor state. Aldinger et al (2015) showed that termination and safe pruning can be ensured when the dependency relation between numeric variables in the planning task is acyclic. For such tasks, the set of reachable states are the fixed point intervals computed by executing applicable actions as many times as necessary, in the order defined by the dependency relation between numeric variables.…”

Section: Numeric Planning Via Heuristic Searchmentioning

confidence: 99%

“…As a difference w.r.t. previous work in this context(Aldinger et al, 2015;Hoffmann, 2003), the reachability analysis in(Scala et al, 2016b) does not require the transitive closure of the action effects dependency relation.…”

mentioning

confidence: 99%

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Subgoaling Techniques for Satisficing and Optimal Numeric Planning

Scala¹,

Haslum²,

Thiébaux³

et al. 2020

jair

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This paper studies novel subgoaling relaxations for automated planning with propositional and numeric state variables. Subgoaling relaxations address one source of complexity of the planning problem: the requirement to satisfy conditions simultaneously. The core idea is to relax this requirement by recursively decomposing conditions into atomic subgoals that are considered in isolation. Such relaxations are typically used for pruning, or as the basis for computing admissible or inadmissible heuristic estimates to guide optimal or satis_cing heuristic search planners. In the last decade or so, the subgoaling principle has underpinned the design of an abundance of relaxation-based heuristics whose formulations have greatly extended the reach of classical planning. This paper extends subgoaling relaxations to support numeric state variables and numeric conditions. We provide both theoretical and practical results, with the aim of reaching a good trade-o_ between accuracy and computation costs within a heuristic state-space search planner. Our experimental results validate the theoretical assumptions, and indicate that subgoaling substantially improves on the state of the art in optimal and satisficing numeric planning via forward state-space search.

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Section: Over-approximation Guarantees and Relation With Ibrmentioning

confidence: 99%

Section: Numeric Planning Via Heuristic Searchmentioning

confidence: 99%

Section: Numeric Planning Via Heuristic Searchmentioning

confidence: 99%

mentioning

confidence: 99%

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Subgoaling Techniques for Satisficing and Optimal Numeric Planning

Scala¹,

Haslum²,

Thiébaux³

et al. 2020

jair

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show abstract

“…] representing the range of possible values of the variable. Numeric expressions are defined recursively (Aldinger, Mattmüller, and Göbelbecker 2015) and action effects augment the range of the intervals. States satisfy numeric conditions if…”

Section: Delete and Interval Relaxationsmentioning

confidence: 99%

Linear and Integer Programming-Based Heuristics for Cost-Optimal Numeric Planning

Piacentini

Castro

Ciré

et al. 2018

AAAI

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Linear programming has been successfully used to compute admissible heuristics for cost-optimal classical planning. Although one of the strengths of linear programming is the ability to express and reason about numeric variables and constraints, their use in numeric planning is limited. In this work, we extend linear programming-based heuristics for classical planning to support numeric state variables. In particular, we propose a model for the interval relaxation, coupled with landmarks and state equation constraints. We consider both linear programming models and their harder-to-solve, yet more informative, integer programming versions. Our experimental analysis shows that considering an NP-Hard heuristic often pays off and that A* search using our integer programming heuristics establishes a new state of the art in cost-optimal numeric planning.

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