D-heuristic-search

D-heuristic-search - (Where we try to choose smartly)...

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1 Heuristic (Informed) Search 1 (Where we try to choose smartly) R&N: Chap. 4, Sect. 4.1–3 Search Algorithm #2 SEARCH#2 1. INSERT(initial-node,FRINGE) Recall that the ordering of FRINGE defines the search strategy 2 2. Repeat: a. If empty(FRINGE) then return failure b. N Å REMOVE(FRINGE) c. s Å STATE( N ) d. If GOAL?( s ) then return path or goal state e. For every state s’ in SUCCESSORS( s ) i. Create a node N’ as a successor of N ii. INSERT( N’ ,FRINGE) Best-First Search ± It exploits state description to estimate how “good” each search node is ± An evaluation function f maps each node N of the search tree to a real number 3 f(N) 0 [Traditionally, f(N) is an estimated cost; so, the smaller f(N), the more promising N] ± Best-first search sorts the FRINGE in increasing f [Arbitrary order is assumed among nodes with equal f] Best-First Search ± It exploits state description to estimate how “good” each search node is ± An evaluation function f maps each node N of the search tree to a real number 4 f(N) 0 ± Best-first search sorts the FRINGE in increasing f [Arbitrary order is assumed among nodes with equal f] “Best” does not refer to the quality of the generated path Best-first search does not generate optimal paths in general ± Typically, f(N) estimates: either the cost of a solution path through N Then f(N) = g(N) + h(N), where g(N) is the cost of the path from the initial node to N h(N) is an estimate of the cost of a path from N to a goal node How to construct f? 5 or the cost of a path from N to a goal node Then f(N) = h(N) Æ Greedy best-search ± But there are no limitations on f. Any function of your choice is acceptable. But will it help the search algorithm? ± Typically, f(N) estimates: either the cost of a solution path through N Then f(N) = g(N) + h(N) , where g(N) is the cost of the path from the initial node to N h(N) is an estimate of the cost of a path from N to a goal node How to construct f? 6 or the cost of a path from N to a goal node Then f(N) = h(N) ± But there are no limitations on f. Any function of your choice is acceptable. But will it help the search algorithm? Heuristic function
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2 ± The heuristic function h(N) 0 estimates the cost to go from STATE(N) to a goal state Its value is independent of the current search tree ; it depends only on STATE(N) and the goal test GOAL? Heuristic Function 7 ± Example: h 1 (N) = number of misplaced numbered tiles = 6 [Why is it an estimate of the distance to the goal?] 1 4 7 5 2 6 3 8 STATE(N) 6 4 7 1 5 2 8 3 Goal state Other Examples 1 4 7 5 2 6 3 8 STATE(N) 6 4 7 1 5 2 8 3 Goal state 8 ± h 1 (N) = number of misplaced numbered tiles = 6 ± h 2 (N) = sum of the (Manhattan) distance of every numbered tile to its goal position = 2 + 3 + 0 + 1 + 3 + 0 + 3 + 1 = 13 ± h 3 (N) = sum of permutation inversions = n 5 + n 8 + n 4 + n 2 + n 1 + n 7 + n 3 + n 6 = 4 + 6 + 3 + 1 + 0 + 2 + 0 + 0 = 16 8-Puzzle 5 3 4 3 4 3 f(N) = h(N) = number of misplaced numbered tiles 9 4 5 3 4 2 1 2 0 4 3 The white tile is the empty tile 1+5 3+3 3+4 2+3 8-Puzzle f(N) = g(N) + h(N) with h(N) = number of misplaced numbered tiles 10 0+4
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D-heuristic-search - (Where we try to choose smartly)...

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