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