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Temporal Numeric Planning with Patterns
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Extends symbolic pattern planning (SPP/patty) to temporal numeric planning in PDDL2.1 by encoding plans as SMT formulas with rolled-up action variables and temporal constraints, and reports highest coverage on 9 of 10 temporal domains with required concurrency.
Problem
Temporal numeric planning in PDDL2.1 (durative actions, concurrency, numeric and Boolean state) where standard SMT encodings need large bounds when concurrency is required.
Approach
Generalizes the pattern (SPP) encoding from numeric to temporal planning: each action in a fixed pattern of durative starting/ending actions gets an integer variable counting consecutive rolled-up executions, with time and duration variables and temporal constraints (epsilon-separation, lasting conditions) encoded in SMT, so that fewer solver calls (bound) are needed.
Key results
- patty_t solves 157 of 200 problems versus 98 for the second-best planner.
- patty_t achieves the highest coverage in 9 of 10 domains (second-best has highest in 4).
- On the Painter domain patty_t (35% coverage) is below AnmlSMT (45%), the only domain where it is beaten.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the temporal pattern encoding in patty_t instead of the compared temporal planners | patty_t · 10 temporal domains with required concurrency | coverage: 157 out of the 200 considered problems, compared to the 98 of the second best | Helped |
| Use the temporal pattern encoding instead of the strongest competing planner | patty_t · 9 of 10 temporal domains | domain coverage leadership: 9 out of 10 domains; second-best planner had the highest coverage in 4 domains | Helped |
| Use patty_t instead of AnmlSMT | temporal planning · Cushing | coverage (%): 30.0 -> 100.0 | Helped |
| Use patty_t instead of AnmlSMT | temporal planning · Pour | coverage (%): 5.0 -> 95.0 | Helped |
| Use patty_t instead of AnmlSMT | temporal planning · Shake | coverage (%): 50.0 -> 100.0 | Helped |
| Use patty_t instead of AnmlSMT | temporal planning · Pack | coverage (%): 5.0 -> 60.0 | Helped |
| Use patty_t instead of AnmlSMT | temporal planning · Painter | coverage (%): 45.0 -> 35.0 | Hurt |
| Use patty_t instead of AnmlSMT | temporal planning · Pour | time (s): 285.96 -> 46.51 | Helped |
| Use patty_t instead of Optic | temporal planning · MatchAC | time (s): 0.01 -> 2.20 | Hurt |
| Use patty_t instead of Optic | temporal planning · Cushing | time (s): 3.12 -> 1.70 | Helped |
Surprising findings
- On the Painter domain the symbolic standard-encoding planner AnmlSMT has higher coverage than patty_t.
Limitations
- Only the Painter domain is lost to AnmlSMT; encoding is lossy on complete patterns requiring chaining for completeness
- Rolling only applies to durative actions meeting eligibility conditions; only Pour and Bottles contain rollable actions
- Completeness requires a complete pattern and may need repeated chaining, and plans may be found before pattern supersequence condition holds
Experimental setup
Datasets: Cushing Pour Shake Pack Bottles Majsp MatchAC MatchMS Oversub Painter
Benchmarks: Cushing Pour Shake Pack Bottles Majsp MatchAC MatchMS Oversub Painter
Metrics: coverage time bound
Baselines: AnmlSMT ITSat Optic LPG TemporalFastDownward
Builds on: Symbolic Pattern Planning PDDL2.1 action rolling (R encoding) relaxed-relaxed encoding
Closest papers by meaning
- Symbolic Numeric Planning with Patterns (AAAI 2024 · similarity 0.90)
- PDBs Go Numeric: Pattern-Database Heuristics for Simple Numeric Planning (AAAI 2025 · similarity 0.90)
- Managing Infinite Abstractions in Numeric Pattern Database Heuristics (AAAI 2026 · similarity 0.89)
- Dealing with Numeric and Metric Time Constraints in PDDL3 via Compilation to Numeric Planning (AAAI 2024 · similarity 0.89)
- Towards Practical Classical Planning Compilations of Numeric Planning (AAAI 2025 · similarity 0.87)
- Abstract Action Scheduling for Optimal Temporal Planning via OMT (AAAI 2024 · similarity 0.85)
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