11 alternative search
- 1. Alternative Search Formulations and Applications Chapter 11.
- 2. 2 Outline Assignment Problems Constraint Propagation Constructive Methods Heuristic Repair Function Optimization
- 3. 3 Assignment Problems Assigning values to variables subject to constraints Examples – Eight-Queens problem – Crossword puzzles
- 4. 4 Eight-Queens Problem X X X X X X X X No queen can be placed so that it can capture any of the others, according to the rules of chess An obvious data structure is 8-by-8 array containing queen(1) or empty(0)
- 5. 5 Eight-Queens Problem (cont’d) We can solve constraint-satisfaction problems by graph-search methods – Constructive method – Repair approach – Function optimization
- 6. 6 Constructive Method – Begin with no assignments – Each operator adds a queen to the array in such a way that the resulting array satisfies constraints among its queens – Constraint propagation technique helps markedly in reducing the size of the search space
- 7. 7 Constraint Propagation (four-queens problem) – Each variable constrains all of the others, so all of the nodes have arcs to all other nodes – A directed constraint arc(i,j), variable labeling i is constrained by the value of the variable labeling j
- 8. 8 Constraint Propagation (cont’d) – Circle: Values eliminated by first making arc(q2,q3) consistent – Box: Values eliminated by next making arc(q3,q4) consistent
- 9. 9 Heuristic Repair – Starts with a proposed solution, which most probably does not satisfy the constraints – The operators change a data structure so that it violates fewer constraints
- 10. 10 Function Optimization Hill-climbing – Traversing by moving from one point to that “adjacent” point having the highest elevation – To solve local maxima problem Several separate hill-climbing, stating at different locations(choose the highest of these) Simulated annealing (choose by probability distribution)
- 11. 11 Solving the Two-Color Problem (Hill Climbing) 1. Set the current node, n, to a randomly selected node, n0. 2. Generate the successors of n. 3. If Vb<V(n), exit with n as the best node found so far. 4. Otherwise,set n to nb, and go to step 2.