Contents

- 1 How do you prove a heuristic is consistent?
- 2 How do you know if monotone is heuristic?
- 3 When is a heuristic considered to be admissible?
- 4 When is a heuristic used in a consistent way?
- 5 Is the heuristic never overestimates the cost of reaching the goal?
- 6 Why is the heuristic at C1 inconsistent at C1?

## How do you prove a heuristic is consistent?

To check whether a heuristic is consistent, ensure that for all paths, h(N) h(L) path(N ! L), where N and L stand in for the actual nodes. In this problem, h(G) is always 0, so making sure that the direct paths to the goal (A ! G and B !

## How do you know if monotone is heuristic?

In the study of path-finding problems in artificial intelligence, a heuristic function is said to be consistent, or monotone, if its estimate is always less than or equal to the estimated distance from any neighbouring vertex to the goal, plus the cost of reaching that neighbour.

## When is a heuristic considered to be admissible?

Admissible Heuristic: A heuristic is admissible if the estimated cost is never more than the actual cost from the current node to the goal node. To understand this, we can imagine a diagram as depicted below.

## When is a heuristic used in a consistent way?

A heuristic is consistent if the cost from the current node to a successor node, plus the estimated cost from the successor node to the goal is less than or equal to the estimated cost from the current node to the goal.

## Is the heuristic never overestimates the cost of reaching the goal?

A consistent heuristic is also admissible, i.e. it never overestimates the cost of reaching the goal (the converse, however, is not always true). This is proved by induction on , the length of the best path from node to goal. By assumption, denotes the cost of the shortest path from n to the goal. Therefore, admissible. (

## Why is the heuristic at C1 inconsistent at C1?

This heuristic is inconsistent at c1 because it is giving a lower (i.e. less informative) lower bound on the cost to get to the goal than its parent node is. The cost estimate of getting to the goal through the parent node is at least 10 (because the cost of the path to p is 5 and the heuristic estimate at p is also 5).