## RE: [aima-talk] about A* search

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• Consistency of heuristics is a little more tricky to explain, since every consistent one is also admissible. If you re not from the U.S., I ll apologize in
Message 1 of 9 , Sep 27, 2005
Consistency of heuristics is a little more tricky to
explain, since every consistent one is also

If you're not from the U.S., I'll apologize in advance
for the following example....

Lets say you're trying to get from New York to L.A. by
car - forget the fact that it would now cost you a
small fortune to do so. A consistent heuristic is one
where the estimate to get from New York to L.A. must
be equal to or smaller than the actual cost to get
from New York to any other city **plus** the estimate
to get from that city to L.A. In other words, if you
drive from New York to Chicago, then estimate the
distance from Chicago to L.A. you're not supposed to
you use straight-line distance, it's easy to see this
is consistent.

Admissible heurstics must guarantee the estimate is no
larger than the actual cost turns out to be.
Consistent heuristics must also guarantee the "revised
estimate" (the sum of the actual distance traveled so
far plus the estimate of what you've got remaining)
never goes down as you explore the path.

You have to get kind of goofy to find things that are
admissible but not consistent - taking the
straight-line distance divided by the number of
letters in the city name for example. The estimate is
guaranteed to be low (since it's always less than the
straight-line distance), and thus is admissible. When
you start at New York your estimate would be 2400/7 =
342.86. If you drove 95 miles to Philadelphia, you're
estimate from Philadelphia to L.A. would be 2320 / 12
= 193.33. Adding that back to the 95 miles you drove
from New York we see that we now think we can get from
New York to L.A. by way of Philadelphia for an
estimated cost of 193.33 + 95 = 288.33, less than our
original estimate of 342.86, thus demonstrating that
the heuristic is not consistent.

Rob G.

--- savastinuk <minnie@...> wrote:

> This makes sense. : )
>
> Can you also explain consistent? Or, better yet,
> INconsistent?
> Still talking A*.
>
> thanks....
> Susan
>
>
> _____
>
> From: aima-talk@yahoogroups.com
> [mailto:aima-talk@yahoogroups.com] On Behalf
> Of The Geek
> Sent: Monday, September 26, 2005 6:03 PM
> To: aima-talk@yahoogroups.com
> Subject: Re: [aima-talk] about A* search
>
>
> I think my version is different from yours, but I
> assume you're talking about the A* search algorithm.
>
> The proof is in the book a page or so later, but
> look
> at it the other way for a second - if the path
> estimate were sometimes too high, then based on the
> inflated estimate you might ignore a path that would
> have turned out to have a "short cut" in it. But by
> guaranteeing that the actual cost will always be
> more
> than your estimate, you're guaranteed never to
> ignore
> a short cut.
>
> To put it another way, with an admissible heuristic
> any unexplored path is guaranteed to be worse than
> or
> equal to it's estimate - never better. Thus when
> you
> actually explore a path, you're guaranteed that it's
> cost will only get worse. So if you've found an
> actual path solution that's equal to or better than
> the best unexplored path estimates, the actual path
> you've found is guaranteed to be the best because
> the
> unexplored paths can only get more costly when
> they're
> explored.
>
> I hope that made sense.
>
> Rob G.
>
> --- lwudong <wudongs@...> wrote:
>
> > In page97, line 7:
> > The restriction is to choose an h function that
> > never overestimates
> > the cost to reach the goal. Such an h is called an
> > heuristic. Admissible heuristics are by nature
> > optimistic, because
> > they think the cost of solving the problem is less
> > than it actually is.
> >
> > Can anyone give me more explanation why it always
> > gets the optimial
> > result when it never overestimates the total cost.
> >
> >
> >
> >
> >
>
>
>
>
> __________________________________
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telligence&w4=Artificial+intelligence+introduction&c=4&s=150&.sig=LONI6S4JBL
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> Artificial
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> ig=n5dsIRz6BWbukAv5Ru4LcA> intelligence introduction
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• Dear Sir. When the path estimate is too high, this means that your h function has more less aware(h1) than time your path estimate has more accuracy(h2). when
Message 2 of 9 , Sep 27, 2005
Dear Sir.
When the path estimate is too high, this means that your h function has more less
aware(h1) than time your path estimate has more accuracy(h2). when h1 is less than h2 , it is natural that h1 develops nodes as number as h2 and perhaps more in your path.So it is possible for h1 that ignore a short cut path as compared with h2 .On the other hand heuristic fuctions have not guarantee for the best path but in more states act very good.

M.Assarian
The Geek <guihergeek61@...> wrote:
I think my version is different from yours, but I
assume you're talking about the A* search algorithm.

The proof is in the book a page or so later, but  look
at it the other way for a second - if the path
estimate were sometimes too high, then based on the
inflated estimate you might ignore a path that would
have turned out to have a "short cut" in it.  But by
guaranteeing that the actual cost will always be more
than your estimate, you're guaranteed never to ignore
a short cut.

To put it another way, with an admissible heuristic
any unexplored path is guaranteed to be worse than or
equal to it's estimate - never better.  Thus when you
actually explore a path, you're guaranteed that it's
cost will only get worse.  So if you've found an
actual path solution that's equal to or better than
the best unexplored path estimates, the actual path
you've found is guaranteed to be the best because the
unexplored paths can only get more costly when they're
explored.

Rob G.

--- lwudong <wudongs@...> wrote:

> In page97, line 7:
> The restriction is to choose an h function that
> never overestimates
> the cost to reach the goal. Such an h is called an
> heuristic. Admissible heuristics are by nature
> optimistic, because
> they think the cost of solving the problem is less
> than it actually is.
>
> Can anyone give me more explanation why it always
> gets the optimial
> result when it never overestimates the total cost.
>
>
>
>
>

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• Rob, Thanks so much! This helps me with a homework problem that I was completely stumped on. I ll cite your letter, as our teacher asked us to do if we get
Message 3 of 9 , Sep 27, 2005
Rob,

Thanks so much! This helps me with a homework problem that I was completely stumped on. I'll cite your letter, as our teacher asked us to do if we get help with an answer.

regards,
Susan

From: aima-talk@yahoogroups.com [mailto:aima-talk@yahoogroups.com] On Behalf Of The Geek
Sent: Tuesday, September 27, 2005 1:46 PM
To: aima-talk@yahoogroups.com
Subject: RE: [aima-talk] about A* search

Consistency of heuristics is a little more tricky to
explain, since every consistent one is also

If you're not from the U.S., I'll apologize in advance
for the following example....

Lets say you're trying to get from New York to L.A. by
car - forget the fact that it would now cost you a
small fortune to do so.  A consistent heuristic is one
where the estimate to get from New York to L.A. must
be equal to or smaller than the actual cost to get
from New York to any other city **plus** the estimate
to get from that city to L.A.  In other words, if you
drive from New York to Chicago, then estimate the
distance from Chicago to L.A. you're not supposed to
you use straight-line distance, it's easy to see this
is consistent.

Admissible heurstics must guarantee the estimate is no
larger than the actual cost turns out to be.
Consistent heuristics must also guarantee the "revised
estimate" (the sum of the actual distance traveled so
far plus the estimate of what you've got remaining)
never goes down as you explore the path.

You have to get kind of goofy to find things that are
admissible but not consistent - taking the
straight-line distance divided by the number of
letters in the city name for example.  The estimate is
guaranteed to be low (since it's always less than the
straight-line distance), and thus is admissible.  When
you start at New York your estimate would be 2400/7 =
342.86.  If you drove 95 miles to Philadelphia, you're
estimate from Philadelphia to L.A. would be 2320 / 12
= 193.33.  Adding that back to the 95 miles you drove
from New York we see that we now think we can get from
New York to L.A. by way of Philadelphia for an
estimated cost of 193.33 + 95 = 288.33, less than our
original estimate of 342.86, thus demonstrating that
the heuristic is not consistent.

Rob G.

--- savastinuk <minnie@...> wrote:

> This makes sense. : )

> Can you also explain consistent? Or, better yet,
> INconsistent?
> Still talking A*.

> thanks....
> Susan
>
>
>   _____
>
> From: aima-talk@yahoogroups.com
> [mailto:aima-talk@yahoogroups.com] On Behalf
> Of The Geek
> Sent: Monday, September 26, 2005 6:03 PM
> To: aima-talk@yahoogroups.com
> Subject: Re: [aima-talk] about A* search
>
>
> I think my version is different from yours, but I
> assume you're talking about the A* search algorithm.
>
> The proof is in the book a page or so later, but
> look
> at it the other way for a second - if the path
> estimate were sometimes too high, then based on the
> inflated estimate you might ignore a path that would
> have turned out to have a "short cut" in it.  But by
> guaranteeing that the actual cost will always be
> more
> than your estimate, you're guaranteed never to
> ignore
> a short cut.
>
> To put it another way, with an admissible heuristic
> any unexplored path is guaranteed to be worse than
> or
> equal to it's estimate - never better.  Thus when
> you
> actually explore a path, you're guaranteed that it's
> cost will only get worse.  So if you've found an
> actual path solution that's equal to or better than
> the best unexplored path estimates, the actual path
> you've found is guaranteed to be the best because
> the
> unexplored paths can only get more costly when
> they're
> explored.
>
> I hope that made sense.
>
> Rob G.
>
> --- lwudong <wudongs@...> wrote:
>
> > In page97, line 7:
> > The restriction is to choose an h function that
> > never overestimates
> > the cost to reach the goal. Such an h is called an
> > heuristic. Admissible heuristics are by nature
> > optimistic, because
> > they think the cost of solving the problem is less
> > than it actually is.
> >
> > Can anyone give me more explanation why it always
> > gets the optimial
> > result when it never overestimates the total cost.
> >
> >
> >
> >
> >
>
>
>
>
> __________________________________
> Yahoo! Mail - PC Magazine Editors' Choice 2005
> http://mail.yahoo.com
>
>
>
>
>
> Artificial
>
>
>
ficial+intelligence&w4=Artificial+intelligence+introduction&c=4&s=150&.sig=Z
> -KgstNm21fXWEV4ASPvHQ> intelligence software
> Artificial
>
>
>
rtificial+intelligence&w4=Artificial+intelligence+introduction&c=4&s=150&.si
> Artificial
>
>
>
telligence&w4=Artificial+intelligence+introduction&c=4&s=150&.sig=LONI6S4JBL
> JohI0gb7t-Ug> intelligence
> Artificial
>
>
>
Artificial+intelligence&w4=Artificial+intelligence+introduction&c=4&s=150&.s
> ig=n5dsIRz6BWbukAv5Ru4LcA> intelligence introduction
>
>
>   _____
>
>
>
>
> *      Visit your group "aima-talk
> <http://groups.yahoo.com/group/aima-talk> " on the
> web.
>
>
> *      To unsubscribe from this group, send an email to:
>  aima-talk-unsubscribe@yahoogroups.com
>
<mailto:aima-talk-unsubscribe@yahoogroups.com?subject=Unsubscribe>
>
>
>
> *      Your use of Yahoo! Groups is subject to the
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>
>   _____
>
>
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__________________________________
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• Does anyone have the implementation of A* search Of Romania Map or some other in prolog or any other reply urgently savastinuk wrote:
Message 4 of 9 , Oct 11, 2005
Does anyone have the implementation of A* search
Of Romania Map or some other
in prolog or any other

savastinuk <minnie@...> wrote:
Rob,

Thanks so much! This helps me with a homework problem that I was completely stumped on. I'll cite your letter, as our teacher asked us to do if we get help with an answer.

regards,
Susan

From: aima-talk@yahoogroups.com [mailto:aima-talk@yahoogroups.com] On Behalf Of The Geek
Sent: Tuesday, September 27, 2005 1:46 PM
To: aima-talk@yahoogroups.com
Subject: RE: [aima-talk] about A* search

Consistency of heuristics is a little more tricky to
explain, since every consistent one is also

If you're not from the U.S., I'll apologize in advance
for the following example....

Lets say you're trying to get from New York to L.A. by
car - forget the fact that it would now cost you a
small fortune to do so.  A consistent heuristic is one
where the estimate to get from New York to L.A. must
be equal to or smaller than the actual cost to get
from New York to any other city **plus** the estimate
to get from that city to L.A.  In other words, if you
drive from New York to Chicago, then estimate the
distance from Chicago to L.A. you're not supposed to
you use straight-line distance, it's easy to see this
is consistent.

Admissible heurstics must guarantee the estimate is no
larger than the actual cost turns out to be.
Consistent heuristics must also guarantee the "revised
estimate" (the sum of the actual distance traveled so
far plus the estimate of what you've got remaining)
never goes down as you explore the path.

You have to get kind of goofy to find things that are
admissible but not consistent - taking the
straight-line distance divided by the number of
letters in the city name for example.  The estimate is
guaranteed to be low (since it's always less than the
straight-line distance), and thus is admissible.  When
you start at New York your estimate would be 2400/7 =
342.86.  If you drove 95 miles to Philadelphia, you're
estimate from Philadelphia to L.A. would be 2320 / 12
= 193.33.  Adding that back to the 95 miles you drove
from New York we see that we now think we can get from
New York to L.A. by way of Philadelphia for an
estimated cost of 193.33 + 95 = 288.33, less than our
original estimate of 342.86, thus demonstrating that
the heuristic is not consistent.

Rob G.

--- savastinuk <minnie@...> wrote:

> This makes sense. : )

> Can you also explain consistent? Or, better yet,
> INconsistent?
> Still talking A*.

> thanks....
> Susan
>
>
>   _____
>
> From: aima-talk@yahoogroups.com
> [mailto:aima-talk@yahoogroups.com] On Behalf
> Of The Geek
> Sent: Monday, September 26, 2005 6:03 PM
> To: aima-talk@yahoogroups.com
> Subject: Re: [aima-talk] about A* search
>
>
> I think my version is different from yours, but I
> assume you're talking about the A* search algorithm.
>
> The proof is in the book a page or so later, but
> look
> at it the other way for a second - if the path
> estimate were sometimes too high, then based on the
> inflated estimate you might ignore a path that would
> have turned out to have a "short cut" in it.  But by
> guaranteeing that the actual cost will always be
> more
> than your estimate, you're guaranteed never to
> ignore
> a short cut.
>
> To put it another way, with an admissible heuristic
> any unexplored path is guaranteed to be worse than
> or
> equal to it's estimate - never better.  Thus when
> you
> actually explore a path, you're guaranteed that it's
> cost will only get worse.  So if you've found an
> actual path solution that's equal to or better than
> the best unexplored path estimates, the actual path
> you've found is guaranteed to be the best because
> the
> unexplored paths can only get more costly when
> they're
> explored.
>
> I hope that made sense.
>
> Rob G.
>
> --- lwudong <wudongs@...> wrote:
>
> > In page97, line 7:
> > The restriction is to choose an h function that
> > never overestimates
> > the cost to reach the goal. Such an h is called an
> > heuristic. Admissible heuristics are by nature
> > optimistic, because
> > they think the cost of solving the problem is less
> > than it actually is.
> >
> > Can anyone give me more explanation why it always
> > gets the optimial
> > result when it never overestimates the total cost.
> >
> >
> >
> >
> >
>
>
>
>
> __________________________________
> Yahoo! Mail - PC Magazine Editors' Choice 2005
> http://mail.yahoo.com
>
>
>
>
>
> Artificial
>
>
>
ficial+intelligence&w4=Artificial+intelligence+introduction&c=4&s=150&.sig=Z
> -KgstNm21fXWEV4ASPvHQ> intelligence software
> Artificial
>
>
>
rtificial+intelligence&w4=Artificial+intelligence+introduction&c=4&s=150&.si
> Artificial
>
>
>
telligence&w4=Artificial+intelligence+introduction&c=4&s=150&.sig=LONI6S4JBL
> JohI0gb7t-Ug> intelligence
> Artificial
>
>
>
Artificial+intelligence&w4=Artificial+intelligence+introduction&c=4&s=150&.s
> ig=n5dsIRz6BWbukAv5Ru4LcA> intelligence introduction
>
>
>   _____
>
>
>
>
> *      Visit your group "aima-talk
> <http://groups.yahoo.com/group/aima-talk> " on the
> web.
>
>
> *      To unsubscribe from this group, send an email to:
>  aima-talk-unsubscribe@yahoogroups.com
>
<mailto:aima-talk-unsubscribe@yahoogroups.com?subject=Unsubscribe>
>
>
>
> *      Your use of Yahoo! Groups is subject to the
> <http://docs.yahoo.com/info/terms/> .
>
>
>   _____
>
>
>

__________________________________
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• ... If by any other you mean any other language, yes there are A* implementations in Lisp, Python and Java on the Aima webpage, and on my homepage in java
Message 5 of 9 , Oct 13, 2005
On Tue, Oct 11, 2005 at 01:44:06AM -0700, [3!|_/|_ wrote:
> Does anyone have the implementation of A* search
> Of Romania Map or some other
> in prolog or any other

If by "any other" you mean any other language, yes there are A* implementations
in Lisp, Python and Java on the Aima webpage, and on my homepage in java at:
www.artificialidea.com/index.php?page=my_programs

Regards,
Iván.
--
Ivan F. Villanueva B.
The dream of intelligent machines: www.artificialidea.com
Encrypted mail preferred.
GPG Key Id: 3FDBF85F 2004-10-18 Ivan-Fernando Villanueva Barrio
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