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1. Informed search algorithms
Lecture 4

2. Introduction
• Heuristics are formalized as rules for choosing
those branches in a state space that are most
likely to lead to an acceptable problem solution.
• Much more efficient than un-informed searches.
• Heuristics are employed in two basic situations:
– A problem may not have an exact solution because of
inherent ambiguities in the problem statement or
available data
– A problem may have an exact solution, but the
computational cost of finding it may be prohibitive

3. Limitations
• Heuristics are fallible
• Only an informed guess of the next step to
be taken in solving a problem
• Based on limited information
• Often based on experience or intuition
• Heuristic algorithm has two parts
– The heuristic measurement
– An algorithm that uses it to search the state
space (best first search)

4. The “most wins” heuristic applied to the first children in tic-tac-toe.

5. Hill Climbing Search
• The simplest way to implement a heuristic search
• Like climbing the Mount Everest in thick fog with
amnesia
• Hill climbing strategies expand the current state in
the search and evaluate its children
• The best child is selected for further expansion;
neither its parent nor its siblings are retained
• Search halts when it reaches a state that is better
than any of its children

6. Hill-climbing search

7. Limitations of Hill Climbing Search
• Because it keeps no history, the algorithm
cannot recover from failure of its strategy
• Tendency to become stuck in local
maxima

8. Hill-climbing search Example

9. BEST FIRST SEARCH (BEST-FS)

10. Variants of BEST-FS
• Greedy BEST-FS
– Only the heuristic value is considered
– The path cost is not considered
• Beam Search
– Operates in a level-by-level manner
– Searches at most m children of the nodes
expanded at the previous level
– Selects the best m children according to some
heuristic evaluation

11. Heuristic search of a hypothetical state space.
Worked Example of Greedy Best-FS

12. A trace of the execution of Greedy Best_FS for the example

13. Greedy Best-FS

14. Greedy Best-FS
Worked Example 2

15. Greedy Best-FS is not optimal-
Example
h(n1)=200h(n1)=200 h(n3)=50h(n3)=50
100100
100100
1010
1010
1010

16. Implementing heuristic evaluation
functions (A* Search)
• Because heuristics are fallible, it is
possible that a search algorithm can be
misled down some path that fails to lead to
a goal
• If two states have approximately the same
heuristic value, examine the state that is
nearest to the root of the state graph.
• This state will have a greater chance of
being on the shortest path to the goal

17. • this makes our evaluation function, f, the
sum of two components
f(n)=g(n)+h(n)
• where g(n) measures the actual length of
the path from any state n to the start state.
• h(n) is an admissible heuristic estimate of
the distance from state n to a goal
A* Search

18. The heuristic f applied to states in the 8-puzzle.

19. State space generated in heuristic search of the 8-puzzle graph.

20. The successive stages of open and closed that generate this graph are: