Questions tagged [consistent-heuristic]

For questions related to consistent heuristics, which are heuristics whose estimate is always less than or equal to the estimated distance from any neighboring vertex to the goal, plus the cost of reaching that neighbor.

Filter by
Sorted by
Tagged with
0 votes
1 answer
354 views

Can A* be non-optimal if it uses an admissible but inconsistent heuristic with graph search?

The book "Artificial Intelligence: A Modern Approach" (4th edition, global version) says "With an admissible heuristic, A* is cost-optimal...". An admissible heuristic is one ...
numq's user avatar
  • 1
0 votes
0 answers
216 views

Is possible to perform an early goal test with A* using a consistent heuristic?

I have a doubt about A* goal test. As far as I know an early goal test is performed when a node (representing a certain state) is inserted in the frontier or, to conform with AIMA terminology, when is ...
InCrisis's user avatar
2 votes
1 answer
174 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?
hello's user avatar
  • 21
3 votes
1 answer
2k 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 $p$ ...
Harry Stuart's user avatar
1 vote
1 answer
464 views

What does a consistent heuristic become if an edge is removed in A*?

For the A* algorithm, a consistent heuristic is defined as follows: if, for every node $n$ and every successor $m$ of $n$ generated by any action $a$, $h(n) \leq c(n,m) + h(m)$. Suppose the edge $c(...
calveeen's user avatar
  • 1,251
2 votes
1 answer
1k 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; ...
Mostafa Ghadimi's user avatar
3 votes
1 answer
1k 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 ...
Mostafa Ghadimi's user avatar
4 votes
2 answers
8k 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 ...
Awa's user avatar
  • 41
2 votes
1 answer
979 views

In the graph search version of A*, can I stop the search the first time I encounter the goal node?

I am going through Russel and Norvig's Artificial Intelligence: A Modern Approach (3rd edition). I was reading the part regarding the A* algorithm A* graph search version is optimal when heuristic ...
Fenil's user avatar
  • 181
4 votes
1 answer
4k 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) ...
ihavenoidea's user avatar
3 votes
1 answer
927 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 ...
hpr16's user avatar
  • 31