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Local Search: walksat, ant colonies, and genetic algorithms Tonight Course evaluations Local search Final exam Issue How to search really large spaces 10^30,000 + states systematic search hopeless! Local search iterative repair, hill climbing, gradient descent, … guess a start state repeat until satisfied: make small change move to a local neighbor Examples Learning weights in a neural network Space: set of weights Neighborhood: small delta Learning CPT’s in a Bayesian network EM algorithm These are optimization problems… what about local search for decision problems? N-Queens N-Queens Demo GSAT Guess a random truth assignment while (#unsat clauses 0){ flip a variable that minimizes number of unsatisfied clauses } Room for improvement Less dramatic performance on structured problems (e.g. planning) Too greedy – can become stuck in local minima Solution: allow some “uphill” moves – many different strategies possible… Simulated annealing Tabu lists Alternate GSAT + random flips Random Walk Guess a random truth assignment while (#unsat clauses 0){ pick an unsat clause flip any variable in the clause } Suppose clauses are of length 2; what is probably a flip is “correct”? Solves 2-SAT in O(n^2) time! Greediness + Randomness If clause length 2, then pure random walk is very unlikely to converge Suppose we random walk greedily? Walksat Guess a random truth assignment while (#unsat clauses 0){ pick an unsat clause with probability p { flip a variable that minimizes number of newly-unsatisfied clauses } otherwise { flip any variable in clause } Walksat results Best known method for many problems graph coloring (certain) planning problems hard random problems For many (all?) other domains, can mix random walk backtrack search run backtrack DPLL until time out restart with new random seed for choosing branching variables Stochastic Backtrack Search Quasigroup Completion Demo Parallel local search Techniques considered so far only look at one point on the search space
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