All Questions
10 questions
0
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1
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110
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How do we know that $c(n,a,G) = h^{\ast}(n)$, in the proof that if a heuristic is consistent then it is admissible?
I found a proof that if a heuristic $h$ is consistent, then it is admissible, but I'm confused by one of the steps in the proof.
The proof is by induction on $k$, the number of actions from a node $n$ ...
1
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0
answers
137
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Is N the total number of nodes in the frontier plus the number of nodes in the explored list?
I'm studying fundamentals of AI from the classic Russell-Norvig book (3rd edition). I have a small doubt about the effective branching factor, which is defined as follows (section 3.6.1, p. 103):
One ...
- 111
3
votes
1
answer
3k
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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
1
vote
1
answer
2k
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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 ...
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2
votes
1
answer
4k
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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
7
votes
1
answer
396
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A* is similar to Dijkstra with reduced cost
According to this Wikipedia article
If the heuristic $h$ satisfies the additional condition $h(x) \leq d(x, y) + h(y)$ for every edge $(x, y)$ of the graph (where $d$ denotes the length of that edge),...
4
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3
answers
9k
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What heuristic to use when doing A* search with multiple targets? [closed]
Usually, using the Manhattan distance as a heuristic function is enough when we do an A* search with one target. However, it seems like for multiple goals, this is not the most useful way. Which ...
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0
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1
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11k
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How do you calculate the heuristic value in this specific case?
The A* algorithm uses the "evaluation function" $f(n) = g(n) + h(n)$, where
$g(n)$ = cost of the path from the start node to node $n$
$h(n)$ = estimated cost of the cheapest path from $n$ to the ...
- 371
13
votes
1
answer
31k
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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 ...
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6
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2
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3k
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How does A* search work given there are multiple goal states?
When I have read through the fundamentals of AI, I saw a situation (i.e., a search space) which is illustrated in the following picture.
These are the heuristic estimates:
...
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