For questions related to admissible heuristics, which are heuristics that never overestimate the cost of reaching a goal.

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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 $p$ ...
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### 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 ...
114 views

### Checking consistency and admissibility of heuristic functions

Consider the following question: n vehicles occupy squares (1, 1) through (n, 1) (i.e., the bottom row) of an n × n grid. The vehicles must be moved to the top row but in reverse order; so the ...
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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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### 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 ...
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### 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 ...