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Research Current Status

Research Current Status. Vitali Sepetnitsky 22/05/2013. Background. Classical WA* algorithm was taken Different reopening policies (currently, the radical): Always Reopen (AR) No Reopen (NR)

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Research Current Status

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  1. Research Current Status Vitali Sepetnitsky 22/05/2013

  2. Background • Classical WA* algorithm was taken • Different 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

  3. Experiments Korf’s 100 instances of 15-puzzle were taken Korf’s example weights were taken WA* 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 outperformsWA* with “AR” policy! This contradicts our assumption!

  4. More detailed analysis • By running the same test on: • 15-puzzle • 9-puzzle • 3x2-puzzle • The phenomenon described above can appear with any instance – there are no specific instances • The phenomenon appears mostly in around 4-5 • As the weight grows, the improvement of “NR” over “AR” grows too

  5. A toy example • Strange! • Moreover, let’slook on this graph:

  6. A toy example (1) • We will show 4 different cases by simply changing the weight of WA*

  7. A toy example (2): Case 1 • “NR”produces a better solution cost • “NR”generates and expands LESS states Solving using “AR” : Solving using “NR” : Path found : [S,C,D,G] Path found : [S,B,K,G] Path cost : 45 Path cost : 12 Generated : 28 Generated : 25 Expanded : 12 Expanded : 11 See Run

  8. A toy example (3): Case 2 • “NR”produces a better solution cost • “NR”generates and expands MORE states Solving using “AR” : Solving using “NR” : Path found : [S,C,D,G] Path found : [S,B,K,G] Path cost : 45 Path cost : 12 Generated : 22 Generated : 25 Expanded : 6 Expanded : 11

  9. A toy example (4): Case 3 • “AR”produces a better solution cost • “AR”generates and expands LESS states Solving using “AR” : Solving using “NR” : Path found : [S,C,D,G] Path found : [S,B,D,G] Path cost : 45 Path cost : 48 Generated : 22 Generated : 23 Expanded : 6 Expanded : 10

  10. A toy example (5): Case 4 • “AR”produces a better solution cost • “AR”generates and expands MORE states Solving using “AR” : Solving using “NR” : Path found : [S,C,D,G] Path found : [S,B,D,G] Path cost : 45 Path cost : 48 Generated : 22 Generated : 18 Expanded : 6 Expanded : 5

  11. Some Results 9-puzzle 15-puzzle (2x3-puzzle yields the same results)

  12. Distribution - the instances set 9-puzzle15-puzzle

  13. Distribution - different weights 9-puzzle15-puzzle

  14. Distribution – depth improvement 9-puzzle15-puzzle

  15. Distribution over 4-cases

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