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A heuristic function, also simply called a heuristic, is a function that ranks alternatives in search algorithms at each branching step based on available information to decide which branch to follow. For example, it may approximate the exact solution.
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 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 ...
A heuristic device is used when an entity X exists to enable understanding of, or knowledge concerning, some other entity Y. A good example is a model that, as it is never identical with what it models, is a heuristic device to enable understanding of what it models. Stories, metaphors, etc., can also be termed heuristic in this sense.
Comparison of an admissible but inconsistent and a consistent heuristic evaluation function. Consistent heuristics are called monotone because the estimated final cost of a partial solution, () = + is monotonically non-decreasing along any path, where () = = (,) is the cost of the best path from start node to .
The search algorithm uses the admissible heuristic to find an estimated optimal path to the goal state from the current node. For example, in A* search the evaluation function (where is the current node) is: = + where = the evaluation function.
A search algorithm is said to be admissible if it is guaranteed to return an optimal solution. If the heuristic function used by A* is admissible, then A* is admissible. An intuitive "proof" of this is as follows: Call a node closed if it has been visited and is not in the open set.
Beam search with width 3 (animation) In computer science, beam search is a heuristic search algorithm that explores a graph by expanding the most promising node in a limited set. Beam search is a modification of best-first search that reduces its memory requirements. Best-first search is a graph search which orders all partial solutions (states ...
Examples of the latter include the exhaustive methods such as depth-first search and breadth-first search, as well as various heuristic-based search tree pruning methods such as backtracking and branch and bound. Unlike general metaheuristics, which at best work only in a probabilistic sense, many of these tree-search methods are guaranteed to ...