From Non-Negative to General Operator Cost Partitioning

AAAI, pp. 3335-3341, 2015.

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We introduced potential heuristics as a fast alternative to optimal cost partitioning

Abstract:

Operator cost partitioning is a well-known technique to make admissible heuristics additive by distributing the operator costs among individual heuristics. Planning tasks are usually defined with non-negative operator costs and therefore it appears natural to demand the same for the distributed costs. We argue that this requirement is not...More

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Introduction
  • Heuristic search is commonly used to solve classical planning tasks. Optimal planning requires admissible heuristics, which estimate the cost to the goal without overestimation.
  • The authors demonstrate that when allowing negative operator costs, heuristics based on the recently proposed operator-counting constraints (Pommerening et al 2014b) can be interpreted as a form of optimal cost partitioning
  • This includes the state equation heuristic (Bonet and van den Briel 2014), which was previously thought (Bonet 2013) to fall outside the four main categories of heuristics for classical planning: abstractions, landmarks, delete-relaxations and critical paths (Helmert and Domshlak 2009).
Highlights
  • Heuristic search is commonly used to solve classical planning tasks
  • We show that the state equation heuristic computes a general optimal cost partitioning over atomic projection heuristics
  • We implemented the state equation heuristic and the potential heuristic that optimizes the heuristic value of the initial state in the Fast Downward planning system (Helmert 2006)
  • We showed that the traditional restriction to non-negative cost partitioning is not necessary and that heuristics can benefit from permitting operators with negative cost
  • We demonstrated that heuristics based on operatorcounting constraints compute an optimal general cost partitioning
  • We introduced potential heuristics as a fast alternative to optimal cost partitioning
Results
  • The authors implemented the state equation heuristic and the potential heuristic that optimizes the heuristic value of the initial state in the Fast Downward planning system (Helmert 2006).
  • Previous experiments (Pommerening et al 2014b) showed that the state equation heuristic outperforms the optimal non-negative cost partitioning of projections to goal variables.
  • To explain this difference the authors compare these two heuristics to the optimal cost partitioning over all projections to single variables using non-negative and general cost partitioning.
  • The heuristics hOGCoaPl1+ and hOACll1P+ compute the same value because non-goal variables cannot contribute to the heuristic with non-negative cost partitioning
Conclusion
  • The authors showed that the traditional restriction to non-negative cost partitioning is not necessary and that heuristics can benefit from permitting operators with negative cost.
  • The authors demonstrated that heuristics based on operatorcounting constraints compute an optimal general cost partitioning.
  • This allows for a much more compact representation of cost-partitioning LPs, and the authors saw that the state equation heuristic can be understood as such a compact form of expressing an optimal cost partitioning over projections.
  • The authors introduced potential heuristics as a fast alternative to optimal cost partitioning.
  • The authors think that the introduction of potential heuristics opens the door for many interesting research avenues and intend to pursue this topic further in the future
Summary
  • Introduction:

    Heuristic search is commonly used to solve classical planning tasks. Optimal planning requires admissible heuristics, which estimate the cost to the goal without overestimation.
  • The authors demonstrate that when allowing negative operator costs, heuristics based on the recently proposed operator-counting constraints (Pommerening et al 2014b) can be interpreted as a form of optimal cost partitioning
  • This includes the state equation heuristic (Bonet and van den Briel 2014), which was previously thought (Bonet 2013) to fall outside the four main categories of heuristics for classical planning: abstractions, landmarks, delete-relaxations and critical paths (Helmert and Domshlak 2009).
  • Results:

    The authors implemented the state equation heuristic and the potential heuristic that optimizes the heuristic value of the initial state in the Fast Downward planning system (Helmert 2006).
  • Previous experiments (Pommerening et al 2014b) showed that the state equation heuristic outperforms the optimal non-negative cost partitioning of projections to goal variables.
  • To explain this difference the authors compare these two heuristics to the optimal cost partitioning over all projections to single variables using non-negative and general cost partitioning.
  • The heuristics hOGCoaPl1+ and hOACll1P+ compute the same value because non-goal variables cannot contribute to the heuristic with non-negative cost partitioning
  • Conclusion:

    The authors showed that the traditional restriction to non-negative cost partitioning is not necessary and that heuristics can benefit from permitting operators with negative cost.
  • The authors demonstrated that heuristics based on operatorcounting constraints compute an optimal general cost partitioning.
  • This allows for a much more compact representation of cost-partitioning LPs, and the authors saw that the state equation heuristic can be understood as such a compact form of expressing an optimal cost partitioning over projections.
  • The authors introduced potential heuristics as a fast alternative to optimal cost partitioning.
  • The authors think that the introduction of potential heuristics opens the door for many interesting research avenues and intend to pursue this topic further in the future
Tables
  • Table1: Coverage for different variants of optimal cost partitioning
Download tables as Excel
Funding
  • This work was supported by the Swiss National Science Foundation (SNSF) as part of the project “Abstraction Heuristics for Planning and Combinatorial Search” (AHPACS)
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