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 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)

Comparison of Search Techniques BFSDFSUCSIDSBest CompleteYNYYN OptimalNNYNN HeuristicNNNNY TimeO(b d )O(b m )O(b d )O(b m ) SpaceO(b d )O(bm)O(bd)O(b m ) C*: the cost of the optimal solution ε: 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 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 BFSDFSUCSIDSBestA* CompleteYNYYNY OptimalNNYNNY HeuristicNNNNYY TimeO(b d )O(b m )O(b d )O(b m ) SpaceO(b d )O(bm)O(bd)O(b m ) C*: the cost of the optimal solution ε: 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