neuro 240 lecture 19 - problem solving

problem

consists of some initial state in which a person begins and a goal state that is to be obtained, PLUS a non-obviosu way of getting from the initial to goal state

name the 2 types of problems

1. well-structured/defined — specified starting conditions, goal, and methods to achieve the goal

2. ill-structured/defined — some aspects are not completely specified

which example matches what problem: geometry proofs, choosing a career

well-structured = geometry proofs

ill-structured = choosing a career

the stages of problem solving defined by polya (6)

1. form a representation

2. construct a plan

3. execute said plan

4. check/evaluate

5. reformulate

6. repeat

name the 5 problem solving concepts

1. initial/goal states

2. intermediate states

3. representation of the problem

4. operators (actions that move between states)

5. problem space (range of possible states and operators) — only some get you to the goal state

isomorphs

equivalent problems, different representations

• analogy — retrieving a representation of a problem from memory that is similar to the problem you’re currently facing

what did the candle problem show us?

we have a fixed idea for a certain items usage in our heads that can hinder our ability to solve a problem — thinking out of the box is harder to do

top-down perceptions

when we look at a new problem, we tend to encode it in a way consistent with long-term memory

functional fixedness

see an object as having only a fixed, familiar function

• seen in the mayer’s rope problem

algorithms

completely specified sequence of steps that is guaranteed to produce an answer — slow and laborious but provides the right answer

heuristics

short cut/rule of thumb — quick and easy but doesnt guarantee the right answer

means end analysis

identifying the largest difference between current state and goal state and reducing it

subgoal in terms of means end analysis

a step created to reduce a major difference

operator in terms of means end analysis

a action used to reduce a difference

what if an operator cannot be used

create a subgoal to remove the obstacle

working backward is useful for what

well-defined problems (maze, geometry)

hill climbing

at any point, select the operator that moves you closest to the goal state

• the new state should be more similar to the goal, you cna never choose an opeator that moves you away

true or false: hill climbing works for ALL problems

false! not all problems can be solved by moving closer to the goals (linearly)