# 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.

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### 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
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### 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) ...
• 265
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### 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 ...
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### 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 $p$ ...
• 161
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### 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
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### 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
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### 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; ...
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### 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 ...
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### 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 ...
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