Questions tagged [admissible-heuristic]
For questions related to admissible heuristics, which are heuristics that never overestimate the cost of reaching a goal.
14
questions
2
votes
1
answer
76
views
Is $\min(h_1(s),\ h_2(s))$ consistent?
If $h_1(s)$ is a consistent heuristic and $h_2(s)$ is a admissible heuristic, is $\min(h_1(s),\ h_2(s))$ consistent?
- 21
2
votes
1
answer
136
views
If $h_1(n)$ is admissible, why does A* tree search with $h_2(n) = 3h_1(n)$ return a path that is at most thrice as long as the optimal path?
Consider a heuristic function $h_2(n) = 3h_1(n)$. Where $h_1(n)$ is admissible.
Why are the following statements true?
$A^*$ tree search with $h_2(n)$ will return a path that is at most thrice as ...
- 21
2
votes
1
answer
970
views
Is A* with an admissible but inconsistent heuristic optimal?
I understand that, in tree search, an admissible heuristic implies that $A*$ is optimal. The intuitive way I think about this is as follows:
Let $P$ and $Q$ be two costs from any respective nodes $p$ ...
- 151
1
vote
1
answer
497
views
Which heuristics guarantee the optimality of A*?
The following is a statement and I am trying to figure out if it's true or false and why.
Given a non-admissible heuristic function, A* will always give a solution if one exists, but there is no ...
- 25
2
votes
1
answer
827
views
If $h_i$ are consistent and admissible, are their sum, maximum, minimum and average also consistent and admissible?
Consider the following question:
$n$ vehicles occupy squares $(1, 1)$ through $(n, 1)$ (i.e., the bottom row) of an $n \times n$ grid. The vehicles must be moved to the top row but in reverse order; ...
- 177
3
votes
1
answer
669
views
Is the summation of consistent heuristic functions also consistent?
Imagine that we have a set of heuristic functions $\{h_i\}_{i=1}^N$, where each $h_i$ is both admissible and consistent (monotonic). Is $\sum_{i=1}^N h_i$ still consistent or not?
Is there any proof ...
- 177
4
votes
2
answers
5k
views
If an heuristic is not admissible, can it be consistent?
I am solving a problem in which, according to the given values, the heuristic is not admissible. According to my calculation from other similar problems, it should be consistent, as well as keeping in ...
- 41
6
votes
1
answer
281
views
Can two admissable heuristics not dominate each other?
I am working on a project for my artificial intelligence class. I was wondering if I have 2 admissible heuristics, A and B, is it possible that A does not dominate B and B does not dominate A? I am ...
- 163
6
votes
1
answer
1k
views
How do we determine whether a heuristic function is better than another?
I am trying to solve a maze puzzle using the A* algorithm. I am trying to analyze the algorithm based on different applicable heuristic functions.
Currently, I explored the Manhattan and Euclidean ...
- 303
2
votes
1
answer
924
views
Understanding the proof that A* search is optimal
I don't understand the proof that $A^*$ is optimal.
The proof is by contradiction:
Assume $A^*$ returns $p$ but there exists a $p'$ that is cheaper. When $p$ is chosen from the frontier, assume $...
- 351
4
votes
1
answer
2k
views
Is the minimum and maximum of a set of admissible and consistent heuristics also consistent and admissible?
Let's suppose I have a set of heuristics $H$ = {$h_1, h_2, ..., h_N$}.
If all heuristics in $H$ are admissible, does that mean that a heuristic that takes the $\min(H)$ (or $\max(H)$ for that matter) ...
- 245
3
votes
1
answer
536
views
How do I find whether this heuristic is or not admissible and consistent?
I was given the following problem to solve.
Given a circular trail divided by $n> 2$ segments labeled $0 \dots n-1$. In the beginning, an agent is at the start of segment number $0$ (the edge ...
- 31
2
votes
1
answer
950
views
Why isn't Nilsson's Sequence Score an admissible heuristic function?
I understand what an admissible heuristic is, I just don't know how to tell whether one heuristic is admissible or not. So, in this case, I'd like to know why Nilsson's sequence score heuristic ...
- 343
12
votes
1
answer
20k
views
Why is A* optimal if the heuristic function is admissible?
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 ...
- 293