Problem solving and Creativity

1. Problem solving and Creativity

2. Problem solving • What is problem solving? • Weak and strong methods • Much of our life is spent solving problems? • Homework problems • Managing money • Video games • Ending conflict

3. What makes these problems? • Four aspects to a problem • Goal • What is to be accomplished? • Givens • What is known from the start of the problem? • Means of transformation • How can the initial state be modified? • Obstacles • Something that stands between the initial state and the goal. • What would happen if one of these aspects were missing?

4. Types of problems • Well-defined problems • All four aspects of the problem are specified. • Towers of Hanoi • Mazes • Ill-defined problems • One or more of the aspects of the problem are not well specified. • Stopping a war

5. How do we solve problems? • Sometimes a problem is novel • Then we use general problem solving strategies • “weak” methods • Sometimes a problem is more familiar • Then we can use our background knowledge • “strong methods”

6. Problem solving as search • Consider a well-defined problem • The givens are known • The means of transformation are known • The goal is known • The obstacle is generally that there are so many possible solutions it is hard to find the right one • We must search for the right solution

7. What if the search space is too large? • It is not possible to enumerate the entire search space for all well-defined problems. • Chess: After a few moves, there are too many possible moves and counter moves to consider all of them. • We must use constraints • Heuristics (general guidelines) • It is likely to lead to a good solution, but not guaranteed to work

8. Hill climbing • 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. • A potential local minimum problem.

9. Means-end analysis • Try to reduce the largest difference between the initial state and the goal state first. • How should you get from UNT to the Empire State Building? • Fly from Dallas to New York • That takes care of the biggest difference, but now creates new sub-problems • Getting from UNT to the airport • Getting from a New York airport to the Empire State Building • Each of these new sub-problems needs to be solved

10. Working backward • Sometimes it is hard to solve a problem by starting at the initial state • Many puzzles are intentionally designed to be hard to solve from the givens. • It can be useful to start at the end state and work backward

11. Summary of Weak Methods • Problems involve overcoming obstacles • Weak methods of problem solving • Domain general heuristics for solving problems • Best for well-defined problems • No real mechanisms for dealing with ill-defined problems • Domain knowledge needed for this.

12. Phenomena in Problem Solving • Insight Problems • Functional Fixedness • Using external representations

13. Why study problem solving? • Important questions • How do great problem solvers work? • How do people solve very difficult problems? • Could we get a computer to do this? • What are people’s limitations in solving problems? • Separate fact from fiction in problem solving • There are many stories about the way great problem solvers work that are just not true.

14. Myths of insight • Weisberg has debunked a number of myths • Coleridge and Xanadu • The story is that the poem was written in a single (perhaps drug-induced) session • Kekulé and the benzene ring • Chemists were search for the structure of benzene • Kekulé was said to have visualized a snake eating its tail • These stories are just myths. • There are many surviving drafts of Xanadu • The story of the snake biting its tail was told 35 years after Kekulé discovered the structure of benzene

15. Characteristics of insight problems • People initially have no idea how to solve the problem • There is no linear “feeling of warmth” • There is no sense that one is getting closer to solving the problem. • Often, there is a period of “incubation” • Perhaps you walk away from the problem for a while • The solution comes in a flash • Often, it feels as though the solution is fully formed

16. How to study insight? • Insight problems are hard to study. • Cannot ask people for their intuitions • There is no feeling of warmth • People have an “aha” experience • What we want to know is what causes the “aha” • Insight problems are rare • There are only a few laboratory examples that work • They are are also rare in real life

17. Functional Fixedness • Why does incubation help? • We may get locked into a way of thinking about the objects in a problem • Time away from the problem • We may eventually be able to see objects in a new way

18. Using External Representations • Sometimes organizing information is the problem. • Nurse A can only work after 2pm • Nurse B can only work Monday, Wednesday and Friday • Nurse C can work Tuesday and Thursday before Noon • Nurse D can work any day between 10am and 4pm • How should this schedule be arranged? • An external representation would be useful.

19. Times can be organized into a matrix • An external representation of the problem. Monday Tuesday Wednesday Thursday Friday 9-10am 10-11am 11am-Noon Noon-1pm 1pm-2pm 2pm-3pm Nurse A 3pm-4pm 4pm-5pm • Minimizes the information that must be kept in the head.

20. Structure of problem • Type of representation used must match structure of problem. • Matrix • Good for scheduling • Days of the week along the columns • Times along the rows • Entries are events. • Network • Good for relationships

21. Problem solving • Using background knowledge • Analogical problem solving and access • Case-based reasoning

22. Weak and strong methods • Just looked at “weak” methods • Domain-general ways of solving problems • Useful when a problem is unfamiliar • Now we look at “strong” methods • Domain-specific solutions • Often derived from past experience • Why are these strong? • It is always easier to solve a problem you have solved before

23. Using background knowledge • Gick & Holyoak (1980) • Had people read a story about a general attacking a fortress. • The roads around the fortress were mined • General split up his forces and had them converge on the fortress from many directions. • Later in the study, they were given Duncker’s radiation problem • Doctor with patient who has an inoperable tumor • Rays strong enough to kill the tumor would damage the healthy tissue • What should the doctor do?

24. Access failure • About 10% of people solve the radiation problem spontaneously • About 30% of people solve it if they first read the story about the general • Not much of a gain • Is this an access problem or a use problem? • If given a hint to use the earlier stories, about 80% of people solve the problem • Suggests that it was an access problem

25. Analogical access • Finding relevant background knowledge is hard • There are many possible experiences that might be relevant • Which ones are most likely to be relevant? • Situations that are similar to ones you have seen before. • In many cases, using highly similar background knowledge is good • Purchase decisions • Knowing what brand of pickles you buy will not help you decide what ketchup to buy • Science (Dunbar) • Microbiologists use results from one bacterium to decide what studies to do on another bacterium • It is rare that distant similarities are useful

26. Retrieving analogs • Gentner, Rattermann, & Forbus • People read a story • Hawk gives feathers to hunter for arrows in exchange for hunter not shooting hawk. • Later, people read another story: • Similar (S): Eagle gives feathers to archer… • Mere Appearance (MA): Eagle flies near archery tournament • Analogy (AN): One country gives missile guidance systems to another in exchange for not attacking it. • No Match (NM): One country has rivers, another does not. • People given S and MA retrieve story • People rate S and AN as similar

27. Models of access • How do we access analogies? • Many models have been developed • Most of them are two-stage models. • Stage 1: Search through memory to find things that are generally similar • Things from the same domain are often retrieved • Only a small number of items pass this filter • Stage 2: Find things that are analogous • Determining analogies is effortful • Do this task only on items that pass stage 1

28. Access and use • Similarities may also affect use of knowledge • Word problems (Ross) • Retrieval affected by domain similarity • Both similar and cross-mapped examples retrieved • People found it hard to apply cross-mapped examples

29. Overcoming access problems • Experts are better at analogical retrieval • They are better at finding good analogies • They are less influenced by cross-mappings • Forming a schema may help access • Comparing a few analogs during learning helps retrieval • Learning about subgoals may help access • An example may be indexed by the sub-problems that it helps to solve

30. Case-based reasoning • An Artificial Intelligence technique • Solves problems based on known episodes • Stages of Case-based reasoning • Access • Adaptation • Evaluation • Updating of memory

31. CHEF: An example • Szechuan cooking (Hammond) • Had a failure cooking beef and broccoli • Broccoli came out soggy • Retrieve past knowledge about similar failures • Other cases of soggy vegetables • Find a case of beef and snow peas • When cooking beef, notice that meat sweats • Solution in that case: Cook vegetables first, put them aside, then cook beef. • Adapt case to current situation

32. Summary • Background knowledge is important for solving problems (Strong methods) • Accessing background knowledge is hard • Analogical access • Driven by surface similarities • Case-based reasoning