# Best-first search

### From Wikipedia, the free encyclopedia

**Best-first search** is a class of search algorithms, which explores a graph by expanding the most promising node chosen according to a specified rule.

Judea Pearl described the best-first search as estimating the promise of node *n* by a "heuristic evaluation function which, in general, may depend on the description of *n*, the description of the goal, the information gathered by the search up to that point, and most importantly, on any extra knowledge about the problem domain."^{[1]}^{[2]}

Some authors have used "best-first search" to refer specifically to a search with a heuristic that attempts to predict how close the end of a path is to a solution (or, goal), so that paths which are judged to be closer to a solution (or, goal) are extended first. This specific type of search is called *greedy best-first search*^{[2]} or *pure heuristic search*.^{[3]}

Efficient selection of the current best candidate for extension is typically implemented using a priority queue.

The A* search algorithm is an example of a best-first search algorithm, as is B*. Best-first algorithms are often used for path finding in combinatorial search. Neither A* nor B* is a greedy best-first search, as they incorporate the distance from the start in addition to estimated distances to the goal.

## Greedy BeFS

Using a greedy algorithm, expand the first successor of the parent. After a successor is generated:^{[4]}

- If the successor's heuristic is better than its parent, the successor is set at the front of the queue (with the parent reinserted directly behind it), and the loop restarts.
- Else, the successor is inserted into the queue (in a location determined by its heuristic value). The procedure will evaluate the remaining successors (if any) of the parent.

Below is a pseudocode example of this algorithm, where **queue** represents a priority queue which orders nodes based on their heuristic distances from the goal. This implementation keeps track of visited nodes, and can therefore be used for undirected graphs. It can be modified to retrieve the path.

procedureGBS(start, target)is: mark start as visited add start to queuewhilequeueisnotemptydo: current_node ← vertex of queue with min distance to target remove current_node from queueforeachneighbor n of current_nodedo:ifnnotinvisitedthen:ifnistarget:returnnelse: mark n as visited add n to queuereturnfailure

## See also

## References

- ↑ Pearl, J.
*Heuristics: Intelligent Search Strategies for Computer Problem Solving*. Addison-Wesley, 1984. p. 48. - ↑
^{a}^{b}Russell, Stuart J.; Norvig, Peter. (2021).*Artificial Intelligence: A Modern Approach*(4th ed.). Hoboken: Pearson. pp. 73–74. ISBN 9780134610993. LCCN 20190474. - ↑ Korf, Richard E. (1999). "Artificial intelligence search algorithms". In Atallah, Mikhail J. (ed.).
*Handbook of Algorithms and Theory of Computation*. CRC Press. ISBN 0849326494. - ↑ https://www.cs.cmu.edu/afs/cs/project/jair/pub/volume28/coles07a-html/node11.html#modifiedbestfs Greedy Best-First Search when EHC Fails, Carnegie Mellon