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# chap3part3chap4 - CS2710,ISSP2610 Chapter3,Part3...

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1 CS 2710, ISSP 2610 Chapter 3, Part 3 Heuristic Search Chapter 4 Local Search and Optimization

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2 Beam Search Cheap, unpredictable search For problems with many solutions, it may be  worthwhile to discard unpromising paths Greedy best first search that keeps a fixed number  of nodes on the fringe
3 Beam Search def beamSearch(fringe,beamwidth):     while len(fringe) > 0:        cur = fringe[0]        fringe = fringe[1:]        if goalp(cur):  return cur        newnodes = makeNodes(cur, successors(cur))        for s in newnodes:           fringe = insertByH(s, fringe)        fringe = fringe[:beamwidth] return []

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4 Beam Search Optimal?  Complete? Hardly! Space? O(b)  (generates the successors) Often useful
Creating Heuristics 5

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6 Combining Heuristics If you have lots of heuristics and none dominates  the others and all are admissible… Use them all! H(n) = max(h1(n), …, hm(n))
Relaxed Heuristic Relaxed problem A problem with fewer restrictions on the actions The cost of an optimal solution to a relaxed problem  is an admissible heuristic for the original problem. 7

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8 Relaxed Problems Exact solutions to different (relaxed) problems H1  (# of misplaced tiles)  is perfectly accurate if a  tile could move to any square H2  (sum of Manhattan distances)  is perfectly  accurate if a tile could move 1 square in any  direction
9 Relaxed Problems If problem is defined formally as a set of constraints,  relaxed problems can be generated automatically Absolver (Prieditis, 1993) Discovered a better heuristic for 8 puzzle and the first useful  heuristic for Rubik’s cube

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Systematic Relaxation Precondition List A conjunction of predicates that must hold true before the action can be applied Add List A list of predicates that are to be added to the description of the world-state as a  result of applying the action Delete List A list of predicates that are no longer true once the action is applied and should,  therefore, be deleted from the state description Primitive Predicates ON(x, y) : tile x is on cell y CLEAR(y) : cell y is clear of tiles ADJ(y, z) : cell y is adjacent to cell z 10
Here is the full definition of s move for the n-puzzle Move(x, y, z): precondition list ON(x, y), CLEAR(z), ADJ(y, z) add list ON(x, z), CLEAR(y) delete list ON(x, y), CLEAR(z) 11

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chap3part3chap4 - CS2710,ISSP2610 Chapter3,Part3...

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