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Towards Practical Classical Planning Compilations of Numeric Planning
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Revisits the bounded numeric-to-classical compilation of Gigante and Scala (2023) and proposes three practical encodings (ONE-HOT, BLAST, BLASTX), finding that an axiom-based binary encoding with LAMA is competitive on mildly numeric domains.
Problem
Numeric planning restricted to finite domains can be compiled into classical planning with conditional effects and plan-size preservation, but it was unclear whether such compilations are practically useful for classical planners.
Approach
Three compilations of simple numeric planning into classical planning: a one-hot encoding of numeric values, and two two's-complement binary encodings (BLAST with conditional effects only, and BLASTX that uses axioms to compute the full adder compactly), with BLASTX markedly improving scalability.
Key results
- BLASTX with LAMA-FIRST solves 208 of 280 instances in total versus 96 for NLM-like/native baselines' best (PATTY 92, ENHSP 117 reported in table; BLASTX 195 vs ONE-HOT 118), with 132 in strongly numeric and 122 vs 43 for ENHSP... (see table)
- On mildly numeric domains BLASTX solves 86 instances, the best among compared systems, exceeding ENHSP (74) and PATTY (59).
- SYMK with BLASTX solves 23 problems, versus 15 with BLAST, 0 with ONE-HOT, and 86 for ORBIT optimal NLM.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use BLASTX with axioms rather than BLAST without axioms (ablation) | LAMA-FIRST on numeric planning tasks · All domains | coverage: 195 -> 208 | Helped |
| Use BLASTX rather than ONE-HOT encoding (ablation) | LAMA-FIRST on numeric planning tasks · All domains | coverage: 118 -> 208 | Helped |
| Use BLASTX rather than native numeric planners | LAMA-FIRST on strongly numeric domains · ΣSN | coverage: 43 -> 122 | Helped |
| Use BLASTX rather than the strongest native numeric planner | LAMA-FIRST on mildly numeric domains · ΣMN | coverage: 74 -> 86 | Helped |
| Use BLASTX rather than native numeric planners | LAMA-FIRST on numeric planning tasks · All domains | coverage: 117 -> 208 | Helped |
| Use BLASTX rather than the strongest numeric planner | LAMA-FIRST on Pathways · Pathways | coverage: 14 -> 3 | Hurt |
| Use BLASTX rather than the strongest numeric planner | LAMA-FIRST on Settlers · Settlers | coverage: 15 -> 2 | Hurt |
| Use BLASTX rather than the strongest numeric planner | LAMA-FIRST on Sugar · Sugar | coverage: 15 -> 13 | Hurt |
| Use BLASTX rather than the strongest numeric planner | LAMA-FIRST on MPrime · MPrime | coverage: 20 -> 19 | Hurt |
| Use BLASTX rather than the strongest numeric planner | LAMA-FIRST on Delivery · Delivery | coverage: 20 -> 20 | No clear effect |
Surprising findings
- The logarithmic encoding, previously deemed overly complex, becomes practical when axioms are used to encode the full adder, outperforming ONE-HOT and BLAST.
- BLASTX with LAMA is competitive with or beats native numeric planners on mildly numeric domains, while performing poorly on strongly numeric ones.
Limitations
- Only simple numeric planning fragment (linear conditions, constant increments) is supported; tasks with undefined numeric variables are excluded.
- Coverage on strongly numeric domains is poor for compiled approaches.
- Optimal planning results with SYMK are indicative only since optimal plans depend on the choice of bit width.
Experimental setup
Datasets: IPC 2023 numeric (SNP) domains SETTLERS SNP formulation from Scala et al. 2020
Benchmarks: IPC 2023 SNP domains (280 instances, 14 domains)
Metrics: coverage expanded nodes runtime coverage over time
Baselines: PATTY ENHSP M(3h||3n) NLM-CUTPLAN SAT2 ONE-HOT BLAST SYMK
Builds on: Gigante and Scala 2023 logarithmic compilation LAMA simple numeric planning (Scala et al. 2020) SYMK
Closest papers by meaning
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