Admissible Heuristic

In the realm of Artificial Intelligence and Machine Learning, particularly within the scope of search algorithms and pathfinding problems, an admissible heuristic is a heuristic function used to estimate the cost of the cheapest path from a given point in the search space to the goal. The defining characteristic of an admissible heuristic is that it never overestimates this cost.

This means the estimated cost to reach the goal from any node on the graph is always less than or equal to the actual lowest cost to reach the goal from that node. The concept of admissibility is crucial for ensuring the optimality of search algorithms like A* (A-star), where the use of an admissible heuristic guarantees that the first complete path found to the goal is the shortest possible path.

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A classic example of an admissible heuristic is the straight-line distance in a road network problem, where the goal is to find the shortest path between two points. When using a map with locations represented as nodes and the distances between them as edges, the straight-line (Euclidean) distance from any node to the goal is an admissible heuristic.

This is because the actual shortest path between these two points can never be shorter than the straight-line distance, considering the roads must follow the geography's constraints. In the context of the A* search algorithm, this heuristic helps prioritize nodes that are closer to the goal, leading to more efficient pathfinding by exploring fewer nodes.

Another example is in the sliding tile puzzles (like the 8-puzzle or 15-puzzle), where an admissible heuristic is the number of misplaced tiles (or Manhattan distance for each tile to its goal position), ensuring that the search algorithm finds the optimal solution by considering the minimum moves necessary to achieve the goal state.

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