3. Pathfinding is a subject of high research
interest
Applications inVideo Games and AI
3
4. Many Problems with PathfindingToday
http://www.ai-blog.net/archives/000152.html
In this Project…
An Empirical Study
UsingA-Star
But first a look at Pathfinding Methods…
4
10. Three Commonly Known Algorithms…
Dijkstra’s Algorithm
Expand outward in all directions until goal found
GuaranteedOptimal Path, but slow
Best-First Search
Expand in direction of goal, until goal is found
Not GuaranteedOptimal Path, but fast
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11. A-Star
Hybrid of first two
Expand in direction of goal node
GuaranteedOptimal Path, and is also fast
11
15. Research Goals
1. Does Neighborhood Region affect Runtime?
2. Does Heuristic Function affect Runtime?
3. Does Neighborhood Region affect Nodes Evaluated?
4. Does Heuristic Function affect Nodes Evaluated?
5. Does Neighborhood Region affect Path Length?
6. Does Heuristic Function to Path Length ?
7. Does Path Length affect Runtime ?
8. Does Nodes Evaluated affect Runtime ?
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17. Tests Used
TwoWay ANOVA
▪ 99% Confidence for Goals #1 and #2
▪ 75% Confidence for Goals #3 and #4
▪ 95% Confidence for Goals #5 and #6
Goodness of Fit quantified by R-Squared
▪ Using ExcelTrendlines
▪ For Goals #7 and #8
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18. Research Goals
1. Neighborhood Region strongly affects Runtime
F = 6.99 | F_Crit = 5.11
2. Heuristic Function has no significance on Runtime
F = 0.01 | F_Crit = 5.11
3. Neighborhood Region slightly affects Nodes Evaluated
F = 1.596 | F_Crit = 1.143
4. Heuristic Function has no significance on Nodes Evaluated
F = 1.596 | F_Crit = 1.143
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19. Research Goals
5. Neighborhood Region affects Path Length
F = 3.432 | F_Crit = 3.204
6. Heuristic Function does not affect Path Length
F = ~zero | F_Crit = 3.204
7. Path Length does not model Runtime very well
R-Squared = 0.388
8. Nodes Evaluated models Runtime fairly well
R-Squared = 0.898
Model: Runtime = 18.89*e0.111[Nodes Evaluated]
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20. Goodness of Fit Charts
Path Length vs Runtime
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21. Goodness of Fit Charts
Nodes Evaluated vs. Runtime
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23. Array-based A-Star
Time spent looping through arrays
ExternalValidity
Tested using Personal Computer
Not the best runtimes
Runtimes scaled higher than usual
May still be generalizable
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24. Want to minimize Nodes Evaluated
Avoid searching Swamps (dead-ends)
Use an appropriate Neighborhood Region
4-Way is best, but impractical
8-Way is the way to go
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