Problem Solving ⢠Ways of solving problems ⢠Pitfalls in problem ...
Problem Solving ⢠Ways of solving problems ⢠Pitfalls in problem ...
Problem Solving ⢠Ways of solving problems ⢠Pitfalls in problem ...
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<strong>Problem</strong> <strong>Solv<strong>in</strong>g</strong><br />
• <strong>Ways</strong> <strong>of</strong> <strong>solv<strong>in</strong>g</strong> <strong><strong>problem</strong>s</strong><br />
– Means-end analysis<br />
– Analogy<br />
– Bra<strong>in</strong>storm<strong>in</strong>g<br />
• <strong>Pitfalls</strong> <strong>in</strong> <strong>problem</strong> <strong>solv<strong>in</strong>g</strong><br />
– Functional fixedness<br />
– Mental set<br />
– Wrong representation<br />
– Start<strong>in</strong>g at wrong po<strong>in</strong>t
Means-end Analysis<br />
• <strong>Problem</strong> <strong>solv<strong>in</strong>g</strong> as search<br />
– For <strong>solv<strong>in</strong>g</strong> well-def<strong>in</strong>ed <strong>problem</strong><br />
• Start<br />
• Goals & Subgoals<br />
• Operators - methods for mov<strong>in</strong>g from state to state<br />
• Heuristics<br />
– Strategies for choos<strong>in</strong>g an operator to apply<br />
– Not guaranteed to be correct, but generally helpful<br />
• Hillclimb<strong>in</strong>g<br />
– Choose operator that moves closest to the goal<br />
– Can get stuck <strong>in</strong> local maxima - states that are closer to the goal<br />
than any neighbor<strong>in</strong>g states, but still are not the goal<br />
– Leave local maxima by back-track<strong>in</strong>g or add<strong>in</strong>g randomness
<strong>Problem</strong> <strong>solv<strong>in</strong>g</strong> as search<br />
Start<br />
A<br />
B<br />
C<br />
D<br />
E<br />
F<br />
G<br />
Goal
For w<strong>in</strong>n<strong>in</strong>g tic-tac-toe<br />
Play <strong>in</strong> the middle<br />
Heuristics<br />
For <strong>solv<strong>in</strong>g</strong> anagrams like: GAKBNI<br />
Try plac<strong>in</strong>g letters together that<br />
<strong>of</strong>ten occur together<br />
For dat<strong>in</strong>g a person met at a c<strong>of</strong>fee house<br />
Ask what they are dr<strong>in</strong>k<strong>in</strong>g
The eight-tiles puzzle<br />
1 52 23<br />
1 2<br />
3<br />
4<br />
5<br />
36<br />
4 5 6<br />
7 8<br />
Start<br />
6<br />
7 8<br />
Goal<br />
Operators: Move space up, down, left, or right<br />
Heuristic: Choose operator that makes more<br />
tiles <strong>in</strong> correct space
1 2<br />
4 5 5<br />
Backtrack<strong>in</strong>g<br />
3 Backtrack by tak<strong>in</strong>g back recent<br />
moves and apply<strong>in</strong>g new operators<br />
7 6 8<br />
Goal = global maximum<br />
Stuck at local maximum<br />
by hill climb<strong>in</strong>g
Heuristics
<strong>Problem</strong> <strong>solv<strong>in</strong>g</strong> by analogy<br />
• Use solved <strong>problem</strong> to solve new <strong>problem</strong><br />
• Analogy = Superficial features are different, but<br />
same at a deep level<br />
– Solar system and atom<br />
• Analogies are missed unless people are given h<strong>in</strong>ts<br />
that they are related, or multiple related stories<br />
• People are too <strong>in</strong>fluenced by superficial similarities<br />
– Use word processor commands that were learned with<br />
superficially similar documents (bibliographies, menus)<br />
– Decision mak<strong>in</strong>g is <strong>in</strong>fluenced by superficial features<br />
• Does the scenario rem<strong>in</strong>d people <strong>of</strong> Vietnam or WWII?
<strong>Problem</strong> <strong>Solv<strong>in</strong>g</strong> by Bra<strong>in</strong>storm<strong>in</strong>g<br />
• Generate ideas without critical exam<strong>in</strong>ation<br />
• Useful for ill-def<strong>in</strong>ed <strong><strong>problem</strong>s</strong><br />
• Creativity with SCAMPER<br />
– Substitute, Comb<strong>in</strong>e, Add, Magnify/m<strong>in</strong>ify<br />
– Place, Elim<strong>in</strong>ate, Reverse/Reorder<br />
• Divergent th<strong>in</strong>k<strong>in</strong>g - explore many possibilities<br />
– 100 uses for a brick<br />
– Remote associates test<br />
Type Ghost Story<br />
Food Catcher Hot<br />
Canadian Golf Sandwich<br />
Tug Gravy Show<br />
Writer<br />
Dog<br />
Club<br />
Boat
People are <strong>of</strong>ten too <strong>in</strong>fluenced by exist<strong>in</strong>g solutions
<strong>Pitfalls</strong> <strong>of</strong> <strong>Problem</strong> <strong>Solv<strong>in</strong>g</strong><br />
• Functional fixedness<br />
– Tendency to view th<strong>in</strong>gs <strong>in</strong> terms <strong>of</strong> their familiar uses<br />
– Two-str<strong>in</strong>g <strong>problem</strong>, candle <strong>problem</strong><br />
– Better solutions if objects not “pre-utilized”<br />
– Young children don’t suffer as much fixedness<br />
• Mental set<br />
– Bias to solve <strong><strong>problem</strong>s</strong> <strong>in</strong> a way that has worked <strong>in</strong> the past<br />
– Luch<strong>in</strong>s’ water jugs<br />
– Prim<strong>in</strong>g <strong>of</strong> solutions
Fewer solutions when tools were used (as tools) previously
<strong>Problem</strong>: Attach the candle to the wall somehow<br />
Solution: use tacks’ box as a support<br />
More solutions when tacks are outside <strong>of</strong> box
Avoid functional fixedness by look<strong>in</strong>g at the world with fresh eyes
<strong>Pitfalls</strong> <strong>of</strong> <strong>Problem</strong> <strong>Solv<strong>in</strong>g</strong><br />
• Wrong representation<br />
– Experts spend more time figur<strong>in</strong>g out how to represent a <strong>problem</strong><br />
than novices (40% compared to 7%)<br />
– The monk <strong>problem</strong><br />
– The miss<strong>in</strong>g dom<strong>in</strong>oes <strong>problem</strong><br />
• Start<strong>in</strong>g at the wrong po<strong>in</strong>t<br />
– Often it is useful to go from goal to start<br />
– Choose the start<strong>in</strong>g po<strong>in</strong>t that has fewer choice po<strong>in</strong>ts
Can 31 dom<strong>in</strong>oes cover the checkerboard with two miss<strong>in</strong>g squares?
Reason<strong>in</strong>g backwards is helpful if there are more choice po<strong>in</strong>ts from<br />
start<strong>in</strong>g po<strong>in</strong>t than from goal.
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