## Pure Heuristic Search

Pure Heuristic Search

The simplest of heuristic search algorithms, the pure heuristic search, expands nodes in order of their heuristic values h(n). It maintains a closed list of those nodes that have already been expanded, and a open list of those nodes that have been generated but not yet been expanded. The algorithm begins with just the initial state on the open list. At each cycle, a node on the open list with the minimum h(n) value is expanded, generating all of its children and is placed on the closed list. The heuristic function is applied to the children, and they are placed on the open list in order of their heuristic values. The algorithm continues until a goal state is chosen for expansion.

In a graph with cycles, multiple paths will be found to the same node, and the first path found may not be the shortest. When a shorter path is found to an open node, the shorter path is saved and the longer one is discarded. When a shorter path to a closed node is found, the node is inaved to open and the shorter path is associated with it. The main drawback of pure heuristic search is that since it ignores the cost of the path so far to node n, it does not find optimal solutions.

Breadth-first search, uniform-cost search, and pure heuristic search are all special cases of a more general algorithm called best-first search. In each cycle of a best-first search, the node that is best according to some cost function is chosen for expansion. These best-first search algorithms differ only in their cost functions the depth of node n for breadth-first search, g(n) for uniform-cost search h(n) for pure heuristic search.

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