pengantar kecerdasan buatan 4 - informed search and exploration aima ch. 3.5 – 3.6

Pengantar Kecerdasan Buatan4 - Informed Search and ExplorationAIMA Ch. 3.5 – 3.6

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

OSCAR KARNALIM, S.T., M.T.

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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

OSCAR KARNALIM, S.T., M.T.

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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

OSCAR KARNALIM, S.T., M.T.

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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

OSCAR KARNALIM, S.T., M.T.

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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

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

OSCAR KARNALIM, S.T., M.T.

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Properties of A*

• Complete? Yes

• Time? Exponential

• Space? Keeps all nodes in memory

• Optimal? Yes

OSCAR KARNALIM, S.T., M.T.

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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

OSCAR KARNALIM, S.T., M.T.

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Properties of IDA*

• Complete? Yes

• Time? DFS

• Space? DFS

• Optimal? Yes

OSCAR KARNALIM, S.T., M.T.

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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