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Problem Solving Views of Problem solving Well-defined problems Much studied in AI Requires search Domain general heuristics for solving problems What about ill-defined problems? No real mechanisms for dealing with these

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Views of problem solving l.jpg
Views of Problem solving

  • Well-defined problems

    • Much studied in AI

    • Requires search

    • Domain general heuristics for solving problems

  • What about ill-defined problems?

    • No real mechanisms for dealing with these

    • The problem may be solved suddenly by ‘seeing’ the problem differently

    • Often requires developing a suitable representation


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Problem solving as search

INITIAL STATE

GOAL STATE

INITIAL STATE

GOAL STATE

?

Play the game: http://www.mazeworks.com/hanoi/


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Solving most games involves search

  • Examples:

    • Cannibals and missionaries:http://www.learn4good.com/games/puzzle/boat.htm

    • Theseus and the Minotaur:http://www.logicmazes.com/theseus.html

    • More special mazeshttp://www.logicmazes.com/


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Search Space

Problem Solving is a search problem

Initial

state

Solution

Goal

state


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Search spaces can be large

#DISCS #STATES

3 33 = 27

4 34 = 81

5 35 = 243

6 36 = 729


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What if the search space is too large?

  • It is not possible to enumerate the entire search space for many well-defined problems.

  • We must use heuristics

    • Not guaranteed to work but easy to implement

    • Example heuristics

      • Trial and error

      • Hill climbing

      • Means-end analysis


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Edward L. Thorndike (1874-1949) found that many animals search by trial and error

(aka random search)

Found that cats in a “puzzle box” (see left) initially behaved impulsively and apparently random.

After many trials in puzzle box, solution time decreases.

Trial and Error

In order to escape the animal has to perform three different actions: press a pedal, pull on a string, and push a bar up or down


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Hill Climbing search by

  • Find some measure of the distance between your present state and the end state.

    • Take a step in the direction that most reduces that distance


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Getting stuck in a suboptimal solution search by

According to the hill-climbing strategy, at each step, you choose a path that moves you closer to the goal. This strategy can fail when steps are required that initially will move away from the goal


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Means-end analysis search by

  • Try to reduce the largest difference between the initial state and the goal state first.

  • That creates new sub-problems

  • Each of these new sub-problems needs to be solved.


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Setting subgoals in means-end analysis search by

  • Painting your house (GOAL 1)

  • Apply paint (SUBGOAL 2)

  • Need paint and brush (SUBGOAL 3)

  • Go to hardware store (SUBGOAL 4)

  • Went to hardware store (SUBGOAL 4)

  • Got paint and brush (SUBGOAL 3)

  • Apply paint (SUBGOAL 2)

  • Paint the house (GOAL 1)


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What about ill-defined problems? search by

  • No real mechanisms for dealing with these

  • According to Gestalt psychologists, the problem may be solved suddenly by ‘seeing’ the problem differently

  • Often requires developing a suitable representation


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Wrong solution: search by

With these six sticks:

Answer:

Make four of these:

Six stick problem


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Kohler (1945): monkey and banana problem. search by

Kohler observed that chimpanzees appeared to have an insight into the problem before solving it


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Functional Fixedness search by

Maier’s (1931) two-string problem



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Why people get stuck solving problems minutes

  • Functional Fixedness

    • Subjects who utilize an object for a particular function will have more trouble in a problem-solving situation that requires a new and dissimilar function for the object.

    • Young children suffer less from functional fixedness

       Less experience might help...


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Expertise minutes


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Developing Expertise minutes

  • What are differences between novices and experts?

  • How to become an expert?

  • Speed of learning


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See anything unusual? minutes

(collapse of the upper right lobe, upper left in picture)

(normal)

  • Experts need only a few seconds to see what is wrong (or what isn’t)

  • Experts perceive large meaningful patterns in their domain


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Chess Studies minutes

  • De Groot (1965)

  • Instructed 5 chess grandmasters to think out loud

  • Grandmasters only considered about 30 moves and only thought 6 moves ahead.

  • Not that different from novices. However, The 30 moves considered by a grandmaster are really good moves

  • Masters rely on extensive experience: 50,000 patterns



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Number of pieces successfully recalled by chess players after the first study of a chess board.

(Chase & Simon, 1973)


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Conclusion from Chase & Simon (1973) after the first study of a chess board.

  • Chess masters only expert with real chess positions. They do not have better memory in general

  • Expertise allows chunking of salient information to promote memory of good moves

  • Experts organize knowledge differently – reflects a deep understanding.


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Experts see and represent a problem in their own domain at a deeper level than novices…

  • Experts see structural similarities

  • Novices see surface similarity

(Chi, Glaser, and Farr, 1988)


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Novices group these deeper level than novices…

Experts group these

Chi, Feltovich, and Glaser, 1981)


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What makes an expert an expert? deeper level than novices…

  • Talent? IQ? Practice? Genetic factors?

  • Experts are masters mostly in their own domain; the skill does not cross into different domains

  • Study exceptional feats:

    • Memory experts

    • Chess experts

    • Musicians

    • Athletes

(Voss et al., 1983)


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General & Inherited Factors deeper level than novices…

IQ tests*

Short-term memory

Speed of reading

Reasoning ability

Attention

Do not predict

superior performance in a particular domain

Experts are not better problem solvers in general. Expertise is domain specific

* IQ tests might predict some success in high-complexity jobs (e.g. scientist)


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10 year rule deeper level than novices…

  • 10 years of deliberate practice needed to attain an international level

  • Deliberate practice: practice that is highly motivated and involves careful self-monitoring

  • Master chess players spend 10,000 – 20,000 hours playing


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What about talent? deeper level than novices…

  • Maybe exceptional performance in some area can be explained by talent – an innate predisposition that predetermines performance in a domain.

  • Anders Ericsson et al.

     disagree that concept of talent is useful or explains anything (genius is 90% perspiration and 10% inspiration)

     this is controversial!


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What about musical talent? deeper level than novices…

  • Absolute pitch:

    • Most musicians acquired it for their own instruments

    • Can be improved by training


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Difference between good and exceptional musicians is related to the amount of practice

Graph from Ericsson et al. (1996) showing the cumulative amount of practice by two groups of aspiring musical performers (experts and good violinists) and those who planned to teach music


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