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Re: [aima-talk] about A* search

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  • mohammad assarian
    If we are at node n and my goals are in t1,t2,.... tn. The most aware way from n to Ti shows with H* but we have an estimate of future that we shows with H and
    Message 1 of 9 , Sep 26, 2005
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      If we are at node n and my goals are in t1,t2,.... tn. The most aware way from n to Ti shows with H* but we have an estimate of future that we shows with H and the relation between H and H* is H<H* that means our aware to the rest of way is less than the real aware.You can read Artificial Intelligenc book of Nillson .

      M.Assarian
      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
      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 2 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 3 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 4 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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          • 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 5 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 6 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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                >
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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 7 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 8 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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