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Artificial Intelligence Chapter 11 Alternative Search Formulations and Applications

This chapter explores alternative search formulations in artificial intelligence, focusing on concepts from the Biointelligence Lab at Seoul National University. It covers assignment problems, constraint propagation, constructive methods, heuristic repair, and function optimization. Key examples include the Eight-Queens problem, illustrating constraint satisfaction through graph search methods and constructive techniques. The chapter also discusses heuristic approaches such as hill climbing and simulated annealing, providing insights into optimizing problem-solving strategies in various contexts.

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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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