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RE: [aima-talk] about A* search

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  • savastinuk
    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 1 of 9 , Sep 27, 2005
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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 help with an answer.
       
      Your admissible but inconsistent trip example went right past where I live, near Philadelphia. : )
       
      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
      admissible.

      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
      get a smaller answer than your original estimate.  If
      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
      > > admissible
      > > 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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    • [3!|_/\|_
      Does anyone have the implementation of A* search Of Romania Map or some other in prolog or any other reply urgently savastinuk wrote:
      Message 2 of 9 , Oct 11, 2005
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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 <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.
         
        Your admissible but inconsistent trip example went right past where I live, near Philadelphia. : )
         
        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
        admissible.

        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
        get a smaller answer than your original estimate.  If
        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
        > > admissible
        > > 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
        >
        >
        >
        >
        >
        > SPONSORED LINKS
        > Artificial
        >
        <http://groups.yahoo.com/gads?t=ms&k=Artificial+intelligence+software&w1=Art
        >
        ificial+intelligence+software&w2=Artificial+intelligence+in+business&w3=Arti
        >
        ficial+intelligence&w4=Artificial+intelligence+introduction&c=4&s=150&.sig=Z
        > -KgstNm21fXWEV4ASPvHQ> intelligence software
        > Artificial
        >
        <http://groups.yahoo.com/gads?t=ms&k=Artificial+intelligence+in+business&w1=
        >
        Artificial+intelligence+software&w2=Artificial+intelligence+in+business&w3=A
        >
        rtificial+intelligence&w4=Artificial+intelligence+introduction&c=4&s=150&.si
        > g=477uHvbluHUGZv4M3Wsnag> intelligence in business
        > Artificial
        >
        <http://groups.yahoo.com/gads?t=ms&k=Artificial+intelligence&w1=Artificial+i
        >
        ntelligence+software&w2=Artificial+intelligence+in+business&w3=Artificial+in
        >
        telligence&w4=Artificial+intelligence+introduction&c=4&s=150&.sig=LONI6S4JBL
        > JohI0gb7t-Ug> intelligence      
        > Artificial
        >
        <http://groups.yahoo.com/gads?t=ms&k=Artificial+intelligence+introduction&w1
        >
        =Artificial+intelligence+software&w2=Artificial+intelligence+in+business&w3=
        >
        Artificial+intelligence&w4=Artificial+intelligence+introduction&c=4&s=150&.s
        > ig=n5dsIRz6BWbukAv5Ru4LcA> intelligence introduction
        >      
        >
        >   _____ 
        >
        > YAHOO! GROUPS LINKS
        >
        >
        >      
        > *      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
        > Yahoo! Terms of Service
        > <http://docs.yahoo.com/info/terms/> .
        >
        >
        >   _____ 
        >
        >
        >



                   
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      • Ivan Villanueva
        ... 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 3 of 9 , Oct 13, 2005
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          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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