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Artificial Intelligence CSC 361

Artificial Intelligence CSC 361. Tutorial# 4_Exercise#4. Constraint Satisfaction Problems. What is a CSP? Finite set of variables V 1 , V 2 , …, V n Nonempty domain of possible values for each variable D V1 , D V2 , … D Vn Finite set of constraints C 1 , C 2 , …, C m

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Artificial Intelligence CSC 361

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  1. Artificial IntelligenceCSC 361 Tutorial#4_Exercise#4

  2. Constraint Satisfaction Problems • What is a CSP? • Finite set of variables V1, V2, …, Vn • Nonempty domain of possible values for each variable DV1, DV2, … DVn • Finite set of constraints C1, C2, …, Cm • Each constraint Ci limits the values that variables can take, • e.g., V1 ≠ V2 • A state is defined as an assignment of values to some or all variables. • Consistent assignment • assignment does not violate the constraints. • A solution to a CSP is a complete assignment that satisfies all constraints.

  3. Backtracking search • Similar to Depth-first search • Chooses values for one variable at a time and backtracks when a variable has no legal values left to assign.

  4. Improving CSP efficiency • Previous improvements on uninformed search  introduce heuristics • For CSPS, general-purpose methods can give large gains in speed, e.g., • Which variable should be assigned next? • In what order should its values be tried? • Can we detect inevitable failure early?

  5. Minimum remaining values (MRV) • Choose variable with the fewest legal moves. • e.g., will immediately detect failure if X has no legal values.

  6. Least constraining value for value-ordering • Given a variable choose the least constraining value. • leaves the maximum flexibility for subsequent variable assignments.

  7. Forward checking • Can we detect inevitable failure early? • And avoid it later? • Forward checking idea: keep track of remaining legal values for unassigned variables. • Terminate search when any variable has no legal values.

  8. Exercise#4

  9. Q2 Q3 Q4 Q5 Q6 Q1 1 2 3 4 5 6 Solve 6-queens Problem using Foreword Checking

  10. Q2 Q3 Q4 Q5 Q6 Q1 1 2 3 4 5 6 Forward Checking • Solve 6-queens …

  11. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 4 5 6

  12. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 4 5 6

  13. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 4 5 6

  14. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 4 5 6

  15. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 Column 6 has domain wipeout Backtrack to next “choice” 1 2 3 4 5 6

  16. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 Column 5 has domain wipeout Backtrack to next “choice” 1 2 3 4 5 6

  17. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 4 5 6

  18. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 4 5 6

  19. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 Column 6 has domain wipeout Backtrack to next “choice” 1 2 3 4 5 6

  20. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 4 5 6

  21. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 Column 5 has domain wipeout Backtrack to next “choice” 1 2 3 4 5 6

  22. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 4 5 6

  23. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 4 5 6

  24. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 4 5 6

  25. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 Column 6 has domain wipeout Backtrack to next “choice” 1 2 3 4 5 6

  26. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 4 5 6

  27. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 Column 5 has domain wipeout Backtrack to next “choice” 1 2 3 4 5 6

  28. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 Column 5 has domain wipeout Backtrack to next “choice” 1 2 3 4 5 6

  29. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 4 5 6

  30. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 4 5 6

  31. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 4 5 6

  32. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 4 5 6

  33. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 Column 6 has domain wipeout Backtrack to next “choice” 1 2 3 4 5 6

  34. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 4 5 6

  35. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 4 5 6

  36. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 4 5 6

  37. Forward Checking • Solve 6-queens … 2 3 4 5 6 1 1 2 3 First Solution! 4 5 6

  38. Questions..

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