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Pure Heuristic Search

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1. 1. Pure Heuristic Search
2. 2. 2 Pure Heuristic Search  The simplest of heuristic search algorithms, the pure heuristic search, expands nodes in order of their heuristic values h(n). It maintains a closed list of those nodes that have already been expanded, and a open list of those nodes that have been generated but not yet been expanded.  The algorithm begins with just the initial state on the open list. At each cycle, a node on the open list with the minimum h(n) value is expanded, generating all of its children and is placed on the closed list. The heuristic function is applied to the children, and they are placed on the open list in order of their heuristic values. The algorithm continues until a goal state is chosen for expansion.
3. 3. 3 Heuristic searching  might not always find the best solution  but is guaranteed to find a good solution in reasonable time.  By sacrificing completeness it increases efficiency.  Useful in solving tough problems which  could not be solved any other way.  solutions take an infinite time or very long time to compute.
4. 4. 4 Heuristic searching  One example is the 15-puzzle  For each piece, figure out how many moves away it is from its goal position, if no other piece were in the way  The total of these gives a measure of distance from goal  This is a heuristic measure - The classic example of heuristic search methods is the “Missionaries and cannibals” problem.
5. 5. 5 Heuristics  A heuristic is a rule of thumb for deciding which choice might be best  There is no general theory for finding heuristics, because every problem is different  Choice of heuristics depends on knowledge of the problem space
6. 6. 6 Example 1: Maze  A maze can be represented as a state space  Each state represents “where you are” in the maze  The start state represents your starting position  The goal state represents the exit from the maze  Operators (for a rectangular maze) are: move north, move south, move east, and move west  Each operator takes you to a new state (maze location)  Operators may not always apply, because of walls in the maze
7. 7. Example of a Maze 7 G
8. 8. 8 Example 2: The 15-puzzle  The start state is some (almost) random configuration of the tiles  The goal state is as shown  Operators are  Move empty space up  Move empty space down  Move empty space right  Move empty space left  Operators apply if not against edge 3 10 13 7 9 14 6 1 4 15 2 11 8 5 12 Start state: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Goal state:
9. 9. Example 3 The Midterm Exam 9
10. 10. 10 Example 4: Missionaries and cannibals  “Missionaries and cannibals” problem (in various guises)  The missionaries and cannibals wish to cross a river  They have a canoe that can hold two people  It is unsafe to have cannibals outnumber missionaries M M M C C C Initial state M M M C C C Goal state
11. 11. 11 States  A state can be represented by the number of missionaries and cannibals on each side of the river  Initial state: 3m,3c,canoe / 0m,0c  Goal state: 0m,0c / 3m,3c,canoe  We assume that crossing the river is a simple procedure that always works (so we don’t have to represent the canoe being in the middle of the river)  However, this is redundant; we only need to represent how many missionaries/cannibals are on one side of the river  Initial state: 3m,3c,canoe  Goal state: 0m,0c
12. 12. 12 Operations  An operation takes us from one state to another  Operations can be:  Canoe takes ? missionary across river  Canoe takes ? cannibal across river  Canoe takes ? missionaries across river  Canoe takes ? cannibals across river  Canoe takes ? missionary and ? cannibal across river  We don’t have to specify “west to east” or “east to west” because only one of these will be possible at any given time
13. 13. States 13
14. 14.  M- missionary  C- cannibal  - canoe 1. MMM CCC MC 2. MM CC M C 3. MM C MC M CC 4. MM C (etc.) 14
15. 15. 15 Conclusion  The best searches combine a basic blind search technique with heuristic knowledge about the problem space
16. 16. 16 The End