What is the difference between admissible and consistent heuristics?

Can you explain the difference between admissible and consistent heuristics?

Sure! An admissible heuristic never overestimates the cost to reach the goal, while a consistent heuristic satisfies the triangle inequality.

Can you give me an example of each?

Of course! An example of an admissible heuristic is the straight-line distance in a pathfinding problem. A consistent heuristic could be the same straight-line distance, but it must also ensure that the estimated cost from any node to the goal is less than or equal to the cost from the node to a neighbor plus the cost from that neighbor to the goal.

Why is it important for heuristics to be admissible or consistent?

It's important because admissible heuristics guarantee that the optimal solution will be found, while consistent heuristics ensure that the search algorithm is efficient and doesn't revisit nodes unnecessarily.

Can a heuristic be admissible but not consistent?

Yes, a heuristic can be admissible but not consistent. This means it won't overestimate the cost to the goal, but it might not satisfy the triangle inequality.