pengantar kecerdasan buatan 4 - informed search and exploration aima ch. 3.5 – 3.6
TRANSCRIPT
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Pengantar Kecerdasan Buatan4 - Informed Search and ExplorationAIMA Ch. 3.5 – 3.6
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OSCAR KARNALIM, S.T., M.T.
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Review : Tree Search
• A search strategy is defined by picking the order of node expansion
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Best-first Search
• Idea: use an evaluation function f(n) for each node• estimate of "desirability"• Expand most desirable unexpanded node
• Implementation:• Order the nodes in fringe in decreasing order of desirability
• Special cases:• Greedy best-first search• A* search
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Heuristic
• Heuristic are criteria, methods , or principle for deciding among several course of action promises to be the most effective in order to reach some goal
• h(n) = estimated cost of the cheapest path from node n to a goal node
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Greedy Best-first Search
• Evaluation function f(n) = h(n)
• Greedy best-first search expands the node that appears to be closest to goal
• e.g.in Bucharest Problem, hSLD(n) = straight-line distance from n to Bucharest
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Romania with Step Costs in KM
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Greedy Best-first Search Example
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Greedy Best-first Search Example (Cont)
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Greedy Best-first Search Example (Cont)
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Greedy Best-first Search Example (Cont)
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Properties of Greedy Best-first Search
Complete? No – can get stuck in loops, e.g., Iasi Neamt Iasi Neamt
Time? O(bm), but a good heuristic can give dramatic improvement
Space? O(bm) -- keeps all nodes in memory
Optimal? No
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A* Search
Idea: avoid expanding paths that are already expensive
Evaluation function f(n) = g(n) + h(n) g(n) = cost so far to reach n h(n) = estimated cost from n to goal f(n) = estimated total cost of path through n to goal
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A* Search Example
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A* Search Example (Cont)
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A* Search Example (Cont)
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A* Search Example (Cont)
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A* Search Example (Cont)
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A* Search Example (Cont)
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Admissible Heuristics
A heuristic h(n) is admissible if for every node n,
h(n) ≤ h*(n), where h*(n) is the true cost to reach the goal state from n.
An admissible heuristic never overestimates the cost to reach the goal, i.e., it is optimistic
Example: hSLD(n) (never overestimates the actual road distance)
Theorem: If h(n) is admissible, A* using TREE-SEARCH is optimal
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OSCAR KARNALIM, S.T., M.T.
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Consistent Heuristics A heuristic is consistent if for every node n, every successor n'
of n generated by any action a,
h(n) ≤ c(n,a,n') + h(n')
Theorem:
If h(n) is consistent,
A* using GRAPH-SEARCH is
optimal
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Properties of A*
• Complete? Yes
• Time? Exponential
• Space? Keeps all nodes in memory
• Optimal? Yes
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Iterative-deepening A* (IDA*)
• Adapt the idea of iterative deepening to the heuristic search context
• The main difference between IDA* and standard iterative deepening is that the cutoff used is the f -cost (g + h) rather than the depth
• The cutoff value is the smallest f -cost of any node that exceeded the cutoff on the previous iteration
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Properties of IDA*
• Complete? Yes
• Time? DFS
• Space? DFS
• Optimal? Yes
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Recursive best-first search (RBFS)
• Simple recursive algorithm that attempts to mimic the operation of standard best-first search, but using only linear space
• Its structure is similar to that of a recursive DFS, but rather than continuing indefinitely down the current path, it keeps track of the f-value of the best alternative path available from any ancestor of the current node
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Recursive best-first search (RBFS) (Cont)
• If the current node exceeds this limit, the recursion unwinds back to the alternative path
• As the recursion unwinds, RBFS replaces the f -value of each node along the path with the best f -value of its children
• In this way, RBFS remembers the f -value of the best leaf in the forgotten subtree and can therefore decide whether it's worth reexpanding the subtree at some later time
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RBFS search for the shortest route to Bucharest
• The path via Rimnicu Vilcea is followed until the current best leaf (Pitesti) has a value that is worse than the best alternative path (Fagaras)
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RBFS search for the shortest route to Bucharest (Cont)
• The recursion unwinds and the best leaf value of the forgotten subtree (417) is backed up to Rimnicu Vilcea; then Fagaras is expanded, revealing a best leaf value of 450
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RBFS search for the shortest route to Bucharest (Cont)
• The recursion unwinds and the best leaf value of the forgotten subtree (450) is backed up to Fagaras; then Rirnnicu Vilcea is expanded
• This time, because the best alternative path (through Timisoara) costs at least 447, the expansion continues to Bucharest
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Simplified Memory-bounded A* (SMA*)
• SMA* proceeds just like A*, expanding the best leaf until memory is full
• SMA* always drops the worst leaf node-the one with the highest f-value
• SMA* then backs up the value of the forgotten node to its parent
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Simplified Memory-bounded A* (SMA*) (Cont)
• In this way, the ancestor of a forgotten subtree knows the quality of the best path in that subtree
• With this information, SMA* regenerates the subtree only when all other paths have been shown to look worse than the path it has forgotten
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Relaxed Problem A problem with fewer restrictions on the actions is called a
relaxed problem
The cost of an optimal solution to a relaxed problem is an admissible heuristic for the original problem
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Admissible Heuristics in 8-PuzzleE.g., for the 8-puzzle:
h1(n) = number of misplaced tiles
h2(n) = total Manhattan distance
(i.e., no. of squares from desired location of each tile)
h1(S) = ? 8
h2(S) = ? 3+1+2+2+2+3+3+2 = 18
Cost = 1 for each move of blank tile
Alternatif PR-1: Diketahui bahwa kotak kosong bisabergerak ke: atas, bawah, kiri atau kanan.Gunakan salah satu heuristik di samping untukmencari kemungkinan langkah terbaik untukmencapai goal dengan A*.Batasi ruang pencarian pada kedalaman 3.
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Path Findinghttp://www.redblobgames.com/pathfinding/a-star/introduction.html
Real Cost Heuristics
Alternatif PR-2: Jelaskan bagaimana A* terbentuk dalam gambar di bawah ini