3.5 informed (heuristic) searches this section show how an informed search strategy can find...
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3.5 Informed (Heuristic) Searches
This section show how an informed search strategy can find solution more efficiently than uninformed strategy.
• Best-first search, Hill climbing, Beam search, A*, IDA*, RBFS, SMA*• New terms
– Heuristics– Optimal solution– Informedness– Hill climbing problems– Admissibility
• New parameters– g(n) = estimated cost from initial state to state n– h(n) = estimated cost (distance) from state n to closest goal– h(n) is our heuristic
• Robot path planning, h(n) could be Euclidean distance• 8 puzzle, h(n) could be #tiles out of place
• Search algorithms which use h(n) to guide search are heuristic search algorithms
3.5.1 Best-First Search(Greedy Best-First Search)
• QueueingFn is sort-by-h• Best-first search only as good as heuristic
Best-first search is a search algorithm which explores a graph by expanding the most promising node chosen according to a specified rule.
A node is selected for expansion based on an evaluation function, f(n). Most best-first algorithm include as a component of f a heuristic function, h(n).
Example – map of RomaniaDriving from Arad to Bucharest
Example – Driving from Arad to Bucharestheuristic function f(n)=h(n), straight line distance hueristics
Example – Driving from Arad to Bucharest (cont’d)
Example – Driving from Arad to Bucharest (cont’d)
Comparison of Search TechniquesBFS DFS UCS IDS Best
Complete Y N Y Y N
Optimal N N Y N N
Heuristic N N N N Y
Time O(bd) O(bm) O(bd) O(bm)
Space O(bd) O(bm) O(bd) O(bm)
C*: the cost of the optimal solutionε: every action cost at least ε m: maximum depth of search space
3.5.2 A* Search• QueueingFn is sort-by-f– f(n) = g(n) + h(n)
g(n): path cost from the start node to node nh(n): estimated cost of the cheapest path from n to goal.
• Note that UCS and Best-first both improve search– UCS keeps solution cost low– Best-first helps find solution quickly
• A* combines these approaches
A * search example - Driving from Arad to Bucharest
Comparison of Search TechniquesBFS DFS UCS IDS Best A*
Complete Y N Y Y N Y
Optimal N N Y N N Y
Heuristic N N N N Y Y
Time O(bd) O(bm) O(bd) O(bm)
Space O(bd) O(bm) O(bd) O(bm)
C*: the cost of the optimal solutionε: every action cost at least ε m: maximum depth of search space
: Relative Error
3.5.3 Memory-bounded Heuristic Search
For A* search, the computation time is not a main drawback. Because it keeps all generated nodes in memory, it run out of space long before it runs out of time.
Method to reduce memory requirement:1. Iterative-deepening A* (IDA*)2. Recursive best-first search (RBFS)3. Memory-bounded A* (MA*)
RBFS
• Recursive Best First Search– Linear space variant of A*
• Perform A* search but discard subtrees when perform recursion
• Keep track of alternative (next best) subtree• Expand subtree until f value greater than
bound• Update f values before (from parent)
and after (from descendant) recursive call
RBFS Example - Driving from Arad to Bucharest
Example
3.7 Summary• Studied search methods that an agent can use to select actions in
environment that are deterministic, observable, static, and completely known.
• Before an agent start searching for solutions, a goal must be identified, and a well-defined problem must be formulated.
• A problem consists of 5 parts: the initial state a set of action a transition model describing the results of those actions a goal test function a path cost function
• A general Tree-Search algorithm considers all possible paths to find a solution, whereas a Graph-Search algorithm avoids consideration of redundant paths.
• Uninformed search methods have access only to the problem definition. Breadth-first search Uniform-cost search Depth-first search Iterative deepening search Bidirectional search
• Informed search methods may have access to a heuristic function h(n) that estimate the cost of a solution from n. Greedy best-first search A* search Recursive best-first search (RBFS) search
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