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Re: [aima-talk] about A* search

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  • The Geek
    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
    Message 1 of 9 , Sep 26, 2005
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      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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    • savastinuk
      This makes sense. : ) Can you also explain consistent? Or, better yet, INconsistent? Still talking A*. thanks.... Susan _____ From: aima-talk@yahoogroups.com
      Message 2 of 9 , Sep 27, 2005
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        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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      • The Geek
        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 3 of 9 , Sep 27, 2005
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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 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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          > http://mail.yahoo.com
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        • mohammad assarian
          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 4 of 9 , Sep 27, 2005
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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 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.

            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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          • 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 5 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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              > http://mail.yahoo.com
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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 6 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.
                > >
                > >
                > >
                > >
                > >
                >
                >
                >
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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 7 of 9 , Oct 13, 2005
                • 0 Attachment
                  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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