Efficient Temporal Piecewise-Linear Numeric Planning With Lazy Consistency Checking

Josef Bajada*, Maria Fox, Derek Long

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Temporal planning often involves numeric effects that are directly proportional to their action's duration. These include continuous effects, where a numeric variable is subjected to a rate of change while the action is being executed, and discrete duration-dependent effects, where the variable is updated instantaneously but the magnitude of such change is computed from the action's duration. When these effects are linear, state-of-the-art temporal planners often make use of linear programming to ensure that these numeric updates are consistent with the chosen start times and durations of the plan's actions. This is typically done for each evaluated state as a part of the search process. This exhaustive approach is not scalable to solve real-world problems that require long plans, because the size of the linear program becomes larger and slower to solve. In this article, we propose techniques that minimize this overhead by computing these checks more selectively and formulating linear programs that have a smaller footprint. The effectiveness of these techniques is demonstrated on domains that use a mix of discrete and continuous effects, which is typical of real-world planning problems. The resultant planner also outperforms most state-of-the-art temporal-numeric and hybrid planners, in terms of both coverage and scalability.

Original languageEnglish
Pages (from-to)506-517
Number of pages12
JournalIEEE Transactions on Artificial Intelligence
Issue number4
Publication statusPublished - 1 Aug 2022


  • Continuous effects
  • numeric planning
  • planning domain definition language (PDDL)
  • scheduling
  • temporal planning


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