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Artificial Intelligence Chapter 11 Alternative Search Formulations and Applications

Artificial Intelligence Chapter 11 Alternative Search Formulations and Applications. Biointelligence Lab School of Computer Sci. & Eng. Seoul National University. Outline. Assignment Problems Constraint Propagation Constructive Methods Heuristic Repair Function Optimization.

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Artificial Intelligence Chapter 11 Alternative Search Formulations and Applications

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  1. Artificial IntelligenceChapter 11Alternative Search Formulations and Applications Biointelligence Lab School of Computer Sci. & Eng. Seoul National University

  2. Outline • Assignment Problems • Constraint Propagation • Constructive Methods • Heuristic Repair • Function Optimization (c) 2000-2002 SNU CSE Biointelligence Lab

  3. Assignment Problems • Assigning values to variables subject to constraints • Examples • Eight-Queens problem • Crossword puzzles (c) 2000-2002 SNU CSE Biointelligence Lab

  4. Eight-Queens Problem 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) (c) 2000-2002 SNU CSE Biointelligence Lab

  5. Eight-Queens Problem (Cont’d) • We can solve constraint-satisfaction problems by graph-search methods • Constructive method • Repair approach • Function optimization (c) 2000-2002 SNU CSE Biointelligence Lab

  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 (c) 2000-2002 SNU CSE Biointelligence Lab

  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 (c) 2000-2002 SNU CSE Biointelligence Lab

  8. Constraint Propagation (Cont’d) Constraint Graph with q1 = 1 Constraint Graph with q1 = 2 (c) 2000-2002 SNU CSE Biointelligence Lab

  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 Repair Steps for the Eight-Queens Problem (c) 2000-2002 SNU CSE Biointelligence Lab

  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) (c) 2000-2002 SNU CSE Biointelligence Lab

  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. (c) 2000-2002 SNU CSE Biointelligence Lab

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