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Automatic Selection of Pattern Collections for Domain Independent Planning MASTER THESIS PRESENTATION
MSC THESIS SASCHA SCHERRER, UNIVERSITY BASEL
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Overview
• Introduction & Overview
• Background
• iPDB Heuristic
• PhO Heuristic
• Conclusion & Future Work
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Background: Planning
• Planning task
• Variables
• States assign values to variables
• Initial state 𝑠0 and goal state(s) 𝑠∗
• Operators have preconditions and effects
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Background: Planning
• Heuristic search in state space
• Heuristic • Estimates cost to nearest goal
•Admissible: never overestimates
• A* used as search algorithm
• IPC Benchmark & Coverage
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Background: 15-Puzzle
1 2 3 4
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13 14 15
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5 6 2
12 13 14 4
9 10 11 15
𝑠0 𝑠∗
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Background: Pattern Databases
• Pattern is a subset of variables 𝑃 ⊆ 𝑉
• Simplified problem ignoring all variables not in the pattern 𝑃
• PDB contains cost of optimal plans for all states in the simplified problem
• Evaluating ℎ𝑃(𝑠)
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Background: 15-Puzzle Abstraction
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15
1 3 8 7
5 6 2
12 13 14 4
9 10 11 15
Pattern 𝑃 = {𝑇1, 𝑇2, 𝑇3, 𝑇4}
𝑠0 𝑠∗
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ℎ𝑃 𝑠0 = 5
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Background: Using multiple PDB heuristics
• Selection of a pattern collection
• Combination of heuristic values •Maximum of both heuristics
• Sum of both heuristics if pattern are additive
• Two patterns are additive if there is no operator that affects both
• Canonical heuristic •Add where possible, maximum over sums
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iPDB Heuristic
• Haslum et al. 2007
• Hill climbing algorithm in space of pattern collections
• Candidate patterns
• Samples
• Evaluated using the canonical heuristic
• Improvement
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iPDB Heuristic: Hill Climbing
1. Add pattern for each goal variable to collection
2. Compute candidates
3. Repeat: 1. Evaluate candidates
2. Add best candidate to collection
3. Compute new candidates
4. Check stopping criterion
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iPDB: Changes
• Time limit
• Improvement limit
• Ignoring candidates
• Changed sampling
• Increasing neighbourhood
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iPDB: Improvement & Total Time
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iPDB: Increasing the Neighbourhood
• Uses time limit of 900 seconds
• Add 𝑛 new variables when creating candidates
• Variables must influence each other
• Memory issues
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iPDB: Evaluation
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• iPDB 2var and 3var include a time limit
Coverage
iPDB base iPDB time iPDB 2var iPDB 3var
664 684 706 698
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PhO: Posthoc Optimization
• Pommerening et al. 2013
• Systematic pattern generation
• Evaluation: solves linear program (LP) •One variable per operator
•One constraint per PDB
•Depends on state
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PhO: Changes
• Partial systematic sizes
• Dynamic systematic sizes
• Limiting number & total size of PDBs
• Limiting evaluation time
• Pruning unused constraints
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PhO: Pruning Unused Constraints
• Samples
• Evaluate heuristic on samples
• Count how often each constraint was “useful”
• Remove constraints that were never “useful”
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PhO: Evaluation
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Coverage
PhO base PhO prune
590 598
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Conclusion & Future Work
• Viability of abstraction heuristics
• Further investigate • Better limit for iPDB
• Better pruning of constraints for PhO
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iPDB 2var PhO prune LM-cut
Coverage 706 598 763
Avg. coverage percentage
54,38% 45,19% 53,07%
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Additional Data: iPDB
base dyn. time 2var 3var ign. FF
finished 1134 1360 1360 1361 1345 1308 1388
coverage 664 675 684 706 698 705 703
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Additional Data: PhO
base (k=2) eval. PhO prune
coverage 590 591 598
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