Pengantar Kecerdasan Buatan 4 - Informed Search and Exploration AIMA Ch. 3.5 – 3.6

Review : Tree Search A search strategy is defined by picking the order of node expansion OSCAR KARNALIM, S.T., M.T. 2

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. 3

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 OSCAR KARNALIM, S.T., M.T. 4

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, h SLD (n) = straight-line distance from n to Bucharest OSCAR KARNALIM, S.T., M.T. 5

Romania with Step Costs in KM OSCAR KARNALIM, S.T., M.T. 6

Greedy Best-first Search Example OSCAR KARNALIM, S.T., M.T. 7

Greedy Best-first Search Example (Cont) OSCAR KARNALIM, S.T., M.T. 8

Greedy Best-first Search Example (Cont) OSCAR KARNALIM, S.T., M.T. 9

Greedy Best-first Search Example (Cont) OSCAR KARNALIM, S.T., M.T. 10

Properties of Greedy Best-first Search  Complete? No – can get stuck in loops, e.g., Iasi  Neamt  Iasi  Neamt   Time? O(b m ), but a good heuristic can give dramatic improvement  Space? O(b m ) -- keeps all nodes in memory  Optimal? No OSCAR KARNALIM, S.T., M.T. 11

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 OSCAR KARNALIM, S.T., M.T. 12

A* Search Example OSCAR KARNALIM, S.T., M.T. 13

A* Search Example (Cont) OSCAR KARNALIM, S.T., M.T. 14

A* Search Example (Cont) OSCAR KARNALIM, S.T., M.T. 15

A* Search Example (Cont) OSCAR KARNALIM, S.T., M.T. 16

A* Search Example (Cont) OSCAR KARNALIM, S.T., M.T. 17

A* Search Example (Cont) OSCAR KARNALIM, S.T., M.T. 18

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: h SLD (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. 19

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. 20

Properties of A* Complete? Yes Time? Exponential Space? Keeps all nodes in memory Optimal? Yes OSCAR KARNALIM, S.T., M.T. 21

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. 22

Properties of IDA* Complete? Yes Time? DFS Space? DFS Optimal? Yes OSCAR KARNALIM, S.T., M.T. 23

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 OSCAR KARNALIM, S.T., M.T. 24

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 OSCAR KARNALIM, S.T., M.T. 25

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) OSCAR KARNALIM, S.T., M.T. 26

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 OSCAR KARNALIM, S.T., M.T. 27

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 OSCAR KARNALIM, S.T., M.T. 28

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 OSCAR KARNALIM, S.T., M.T. 29

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 OSCAR KARNALIM, S.T., M.T. 30

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 OSCAR KARNALIM, S.T., M.T. 31

Admissible Heuristics in 8-Puzzle E.g., for the 8-puzzle: h 1 (n) = number of misplaced tiles h 2 (n) = total Manhattan distance (i.e., no. of squares from desired location of each tile)  h 1 (S) = ? 8  h 2 (S) = ? = 18  Cost = 1 for each move of blank tile OSCAR KARNALIM, S.T., M.T. 32 Alternatif PR-1: Diketahui bahwa kotak kosong bisa bergerak ke: atas, bawah, kiri atau kanan. Gunakan salah satu heuristik di samping untuk mencari kemungkinan langkah terbaik untuk mencapai goal dengan A*. Batasi ruang pencarian pada kedalaman 3.

Path Finding OSCAR KARNALIM, S.T., M.T. 33 Real Cost Heuristics Alternatif PR-2: Jelaskan bagaimana A* terbentuk dalam gambar di bawah ini