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
search algorithms
heuristic
3.5.1 Best-First Search
(Greedy Best-First Search)
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).
• QueueingFn is sort-by-h
• Best-first search only as good as heuristic
Example – map of Romania
Driving from Arad to Bucharest
Example – Driving from Arad to Bucharest
heuristic 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
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 solution
ε: every action cost at least ε
m: maximum depth of search space
IDS
Best
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 n
h(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
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 solution
ε: every action cost at least ε
m: maximum depth of search space
IDS
Best
A*
: 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