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Concept
Admissible heuristic
Summary
In computer science, specifically in algorithms related to pathfinding, a heuristic function is said to be admissible if it never overestimates the cost of reaching the goal, i.e. the cost it estimates to reach the goal is not higher than the lowest possible cost from the current point in the path.
It is related to the concept of consistent heuristics. While all consistent heuristics are admissible, not all admissible heuristics are consistent.
An admissible heuristic is used to estimate the cost of reaching the goal state in an informed search algorithm. In order for a heuristic
to be admissible to the search problem, the estimated cost must always be lower than or equal to the actual cost of reaching the goal state.
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.
= the cost from the start node to the current node
= estimated cost from current node to goal.
is calculated using the heuristic
function. With a non-admissible heuristic, the A* algorithm could
overlook the optimal solution to a search problem due to an
overestimation in .
is a node
is a heuristic
is cost indicated by to reach a goal from
is the optimal cost to reach a goal from
is admissible if,
An admissible heuristic can be derived from a relaxed
version of the problem, or by information from pattern databases that store exact solutions to subproblems of the problem, or by using inductive learning methods.
Two different examples of admissible heuristics apply to the fifteen puzzle problem:
Hamming distance
Manhattan distance
The Hamming distance is the total number of misplaced tiles. It is clear that this heuristic is admissible since the total number of moves to order the tiles correctly is at least the number of misplaced tiles (each tile not in place must be moved at least once). The cost (number of moves) to the goal (an ordered puzzle) is at least the Hamming distance of the puzzle.
Official source
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