Contents

- 1 Can a heuristic be admissible but not consistent?
- 2 Is admissible heuristic optimal?
- 3 What is the maximum of N admissible heuristics?
- 4 Why is a heuristic acceptable?
- 5 Which of the following is guaranteed to give an optimal solution?
- 6 When is a heuristic considered to be admissible?
- 7 Why is the heuristic at C1 inconsistent at C1?

## Can a heuristic be admissible but not consistent?

In the unusual event that an admissible heuristic is not consistent, a node will need repeated expansion every time a new best (so-far) cost is achieved for it.

## Is admissible heuristic optimal?

A heuristic is admissible if it never overestimates the true cost to reach the goal node from n. If a heuristic is consistent, then the heuristic value of n is never greater than the cost of its successor, n′, plus the successor’s heuristic value.

**What is an optimal heuristic?**

Heuristic designates a computational procedure that determines an optimal solution by iteratively trying to improve a candidate solution with regard to a given measure of quality.

**What happens if heuristic is not admissible?**

A non-admissible heuristic may overestimate the cost of reaching the goal. It may or may not result in an optimal solution. Thus, the total cost (= search cost + path cost) may actually be lower than an optimal solution using an admissible heuristic.

### What is the maximum of N admissible heuristics?

two

Answer: Yes, the max of two admissible heuristics is itself admissible, because each of the two heuristics is guaranteed to underestimate the distance from the given node to the goal, and so therefore must their max. domains) such that the constraint r(X, ¯ Y ) is satisfied.

### Why is a heuristic acceptable?

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.

**What makes A heuristic admissible?**

**What is meant by admissible heuristic?**

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.

## Which of the following is guaranteed to give an optimal solution?

XG boost is the guaranteed to give an optimal solution.

## 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.

**What does a * with admissible non consistent mean?**

And hey! That’s the definition of a consistent heuristic. What this means is that things can go wrong using A* with an inconsistent heuristic in exactly the same way that things can go wrong with Dijkstra’s algorithm using negative edge weights.

### 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).