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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
Empirical Evaluation of Search Algorithms for Satisficing Planning - - PowerPoint PPT Presentation
Empirical Evaluation of Search Algorithms for Satisficing Planning - - PowerPoint PPT Presentation
Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work Empirical Evaluation of Search Algorithms for Satisficing Planning Patrick von Reth Department of Mathematics and Computer Science Artificial
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
Misleading heuristics
Exploration of states not leading to a goal. Plateaus:
Many states are explored. No improvement of h(s).
Random Exploration: Explore random States from the open list. Local Exploration: Start a search on a limited subset of states.
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
Search enhancements
Deferred evaluation: States are inserted with the heuristic value of their parent. Evaluated when they are explored. Preferred Operators: Operators most probable part of a solution. Alternate open lists.
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
ǫ-GBFS
Extension of standard GBFS.
Probability ǫ select a state uniformly randomly from the open list. Probability 1 − ǫ use standard behaviour of GBFS.
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
Type-based exploration
States are inserted into buckets based on h(s), g(s), const(1), .... Buckets are selected uniformly randomly as well as the states in the buckets. Used alternating with a standard open list.
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
Enforced hill climbing
Standard GBFS until a better h(s′) value is found or the search fails. Run a new GBFS on state s′.
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
Monte-Carlo random walks
Random exploration:
Multiple random walks:
Random operators are applied. Only the end point is evaluated.
The path providing the best improvement is added to the global path.
Configurations:
Helpful actions Dead end avoidance Iterative deepening Acceptable progress
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
Local exploration
Start a standard GBFS. If the heuristic value was not improved over a period of steps, start a local search. Depth of local search is limited. Close list is shared. Local search ends if:
the configured depth is reached. a state s′ with h(s′) < h(s) is found. the local search fails, the local open list is empty.
Remaining states are merged. Alternate configuration: Local Random Walks
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
Diverse best-first search
Global open list:
Probabilistic selection of states, based on their h(s) and g(s) value. Smaller g(s) and h(s) are preferred.
Local open list:
Standard open list.
Only local searches. Local search is limited by the initial h(s) . Remaining states are merged into the global open list. Next local search is started.
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
Experiments
All experiments were run on the same benchmark sets as in the original papers. Results named base are those of a standard GBFS.
528
- riginal results
589
- ur results
589
- ur results of a second implementation
650 Coverage sum
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
ǫ-GBFS
528 base 589 base 589 base 588 0.00 584 0.00 578 0.05 607 0.05 618 0.05 581 0.10 599 0.10 616 0.10 585 0.20 596 0.20 621 0.20 584 0.30 599 0.30 608 0.30 574 0.50 581 0.50 602 0.50 546 0.75 522 0.75 581 0.75 500 650 Coverage sum
Results:
Scale similar.
Two implementations:
Bucket based Heap based
FIFO by ID.
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
ǫ-GBFS
10−2 10−1 100 101 102 103 104 10−2 10−1 100 101 102 103 104 104 104 RandomBucketOpenList time usage (seconds) RandomOpenList time usage (seconds) Action RandomBucketOpenList RandomOpenList Insert state O(1) O(log(n)) Remove random state O(m) O(log(n)) Remove min state O(1) O(log(n))
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
type-based-GBFS
1561 ff-base 1612 ff-base 1755 ff-typed 1785 ff-typed 1498 cea-base 1530 cea-base 1678 cea-typed 1719 cea-typed 1513 cg-base 1538 cg-base 1691 cg-typed 1694 cg-typed 1400 1800 Coverage sum
Results:
Results scale similar.
Implementation:
Reduced complexity O(1) instead of O(m) to the number of buckets.
Vector containing buckets. Map pointing to buckets.
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
type-based-GBFS: Multiple heuristics
1561 ff-base 1612 ff-base 1529 1 1735 1 1758 g 1725 g 1729 ff 1690 ff 1755 ff-g 1787 ff-g 1691 ff-cea-g 1661 ff-cg-cea-g 1723 ff-cg-g 1400 1800 Coverage sum
ff-cea-g, ff-cg-cea-g, ff-cg-g are additions on our side. Longer keys lead to more evaluations resulting in worse results. Even the const(1) performs better.
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
Monte-Carlo random walks
214 base 234 base 282 pure 230 pure 205 MDA 237 MHA 248 pure-no-accaptable-progress 250 Coverage sum
Results:
Number estimated from percentage results. Good MHA results.
Implementation:
Support for multiple configurations
Helpful actions Dead end avoidance Iterative deepening Acceptable progress
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
Local exploration
1561 ff-base 1612 ff-base 1657 ff-local 1700 ff-local 1513 cg-base 1540 cg-base 1602 cg-local 1600 cg-local 1498 cea-base 1528 cea-base 1603 cea-local 1607 cea-local 1400 1750 Coverage sum
Results:
The results scale similar to the original results.
Implementation:
Abstract wrapper Combinations of different search engines possible.
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
DBFS
1209 ff-base 1228 ff-base 1451 ff-diverse 1440 ff-diverse 1170 cg-base 1207 cg-base 1358 cg-diverse 1397 cg-diverse 1202 cea-base 1223 cea-base 1388 cea-diverse 1451 cea-diverse 1222 ff-diverse-lazy 1100 1500 Coverage sum
Results:
Good results. Bad results for deferred evaluation.
Implementation:
Three open lists:
DiverseOpenList ProbabilisticOpenList (global
- pen list)
Any open list (local open list)
ProbabilisticOpenList modified algorithm
Only iterate over existing values.
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
Comparison
Comparison of all algorithms. On IPC 2011 benchmarks. Standard (eager) search. Deferred (lazy) search where applicable.
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
Eager
192 base 224 DBFS 200 GBFS-LS 214 e-GBFS 213 type-based-GBFS 104 EHC 118 Monte-Carlo random walks 250 Coverage sum
All new algorithms improve results compared to standard GBFS. Random walks and EHC can not compete with the current algorithms. Simple randomisation leads to a similar improvement (ǫ-GBFS, type-based-GBFS).
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
Lazy
197 base 156 DBFS 193 GBFS-LS 207 e-GBFS 218 type-based-GBFS 250 Coverage sum
Deferred evaluation leads to worse results in most cases.
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work
Conclusion
All algorithms perform as good as announced. Simple randomisation can massively improve the results. For ǫ-GBFS improvements showed their potential.
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Background Algorithms Implementation & Experiments Comparison Conclusion & Future Work