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 Techniques

BFS 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 Techniques

BFS 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