VITALI SEPETNITSKY 22/05/2013 Research Current Status.
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Transcript of VITALI SEPETNITSKY 22/05/2013 Research Current Status.
VITALI SEPETNITSKY
22/05/2013
Research Current Status
Background
Classical WA* algorithm was takenDifferent reopening policies (currently, the
radical): Always Reopen (AR) No Reopen (NR)
It sounds reasonable that any solution found by the “AR” policy it at least “good”(*) (or even better) as any solution found by the “NR” policy
(*) Measured by cost of the found path and number of expanded states
Experiments
Korf’s 100 instances of 15-puzzle were takenKorf’s example weights were takenWA* with “AR” and “NR” policies was ran in
order to solve each instance (using the weights)
In the results we can see a lot of runs in which WA* with “NR” policy outperforms WA* with “AR” policy!
This contradicts our assumption!
More detailed analysis
A toy example
Strange!
Moreover, let’s look on this graph:
Sh=2
4
Bh=2
Ch=4
Dh=3
Eh=4
Gh=0
4
4
40 5
Kh=4
4
4
61
D3h=4
1
S1h=4
S2h=4
S3h=4
S4h=4
S5h=4
6
6
6
6
6
A toy example (1)
Sh=2
4
Bh=2
Ch=4
Dh=3
Eh=4
Gh=0
4
4
40 5
Kh=4
4
4
61
D3h=4
1
S1h=4
S2h=4
S3h=4
S4h=4
S5h=4
6
6
6
6
6
A toy example (2): Case 1
See Run
A toy example (3): Case 2
A toy example (4): Case 3
A toy example (5): Case 4
Some Results
9-puzzle15-puzzle
(2x3-puzzle yields the same results)
Distribution - the instances set
9-puzzle 15-puzzle
Distribution - different weights
9-puzzle 15-puzzle
Distribution – depth improvement
9-puzzle 15-puzzle
Distribution over 4-cases
Number of different runs(run = instance (#) + weight)
2x3-puzzle 9-puzzle 15-puzzle(Case 1)
NR-dep < AR-depNR-exp+gen < AR-exp+gen
97 413
(Case 2)
NR-dep < AR-depNR-exp+gen > AR-exp+gen
66 406
(Case 3)
NR-dep > AR-depNR-exp+gen < AR-exp+gen
187 568
(Case 4)
NR-dep > AR-depNR-exp+gen > AR-exp+gen
147 579
avg: 124.25sdev: 54.51
avg: 491.5sdev: 94.83