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Unformatted text preview: 1 Artificial Intelligence CS4365  Spring 2009 a Local Search Reading: Section 4.3, R&N 2 So far, we have considered methods that systematically explore the full search space, possibly using principled pruning (A* etc.). The current best such algorithms (IDA* / SMA*) can handle search spaces of up to 10 100 states. But search spaces for some realworld problems might be much bigger — e.g. 10 30 , 000 states. A completely different kind of method is called for: Local Search Methods 3 Local Search Methods Applicable when we’re interested in the Goal State — not in how to get there. E.g. NQueens, VLSI layout, or map coloring. Basic idea: use a single current state don’t save paths followed generally move only to successors/neighbors of that state Generally require a complete state description . 4 Example 5 HillClimbing Search 6 7 Hill Climbing Pathologies 8 Example A wide variety of key CS problems can be translated into a propositional logical formalization e.g., (A ∨ B ∨ C) ∧ ( • • B ∧ C ∨ D) ∧ (A ∨ • • C ∨ D) and solved by finding a truth assignment to the propositional variables (A, B, C, ...) that makes it true, i.e., a model . If a formula has a model, we say that it is “satisfiable". Special kind of CSP. 9 Satisfiability Testing Bestknown method: DavisPutnam Procedure (1960) Backtrack search (DFS) through the space of truth assignments (with unitpropagation). 10 11 To date, DavisPutnam still the fastest sound and complete method. However, there are classes of formulas where the procedure scales badly. Consider an incomplete local search procedure. 12 Greedy Local Search  GSAT Begin with a random truth assignment (assume CNF). Flip the value assigned to the variable that yields the greatest number of satisfied clauses. (Note: Flip even if there is no improvement.) Repeat until a model is found, or have performed a specified maximum number of flips. If a model is still not found, repeat the entire process, starting from a different initial random assignment. 13 14 How well does it work? First intuition: It will get stuck in local minima, with a few unsatisfied clauses. Note we are not interested in almost satisfying assignments E.g ., a plan with one “magic" step is useless....
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This note was uploaded on 07/02/2009 for the course CS 4365 taught by Professor Vincent during the Spring '09 term at Universidad Torcuato Di Tella.
 Spring '09
 vincent
 Artificial Intelligence

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