Week 1

• Problem solving


  The process of constructing and applying mental representation of problems of finding solutions to those problems
• Problem


  A situation in which there is a discrepancy between the current state of the world and the goal state
• Solution


  An action that transforms the current state to the goal state
• Well-defined problems


  • All aspects of the problem are clearly specified (not always easy to solve or even solvable)
• Ill-defined problems


  • Some aspects of the problem are not clearly specified
• Do not run the four stages consciously, instead the solution seems to come to use in a flash of insight, also known as the 'aha' moment
• Wessel's stages of problem solving

  1. Define the problem

  2. Devise a strategy

  3. Execute the strategy

  4. Evaluate progress towards the goal
• Factors that affect the difficulty of the problem

  • Greater distance between the goal state and current state leads to greater difficulty of problem solving
  • More difficult problems often also require more actions to be taken
  • It is easier to solve a problem when there are fewer possible actions to search through
  • Expertise in a domain also affects the ease of problem solving
• Mental representation


  The way that our beliefs, knowledge, and memories are stored within our minds
• A mental representation of a problem is our knowledge about its different components
• Mental representations can be wrong, inaccurate, or missing information
• Representation of the available actions does not include all possible actions
• Functional fixedness


  A mental block against an object in a new way that is required to solve a problem
• Functional fixedness is less strong in children compared with adults
• Functional fixedness can be reduced if individuals are trained in using objects in different ways
• Algorithms


  A procedure that is guaranteed to find the solution for a problem
• Algorithms


  • A set of 'steps' and a stopping condition
  • Only exists for some types of problems
  • No algorithms for ill-defined problems
  • Not guaranteed to reach a solution efficiently
• Algorithms


  • Insertion sort algorithm
• Heuristics


  A 'rule of thumb' that is easy, fast to use, and often helpful
• Heuristics are not guaranteed to reach a solution
• Heuristics are often developed from experience
• Generate-test heuristic


  Involves repeatedly generating a possible solution and testing to see whether that solution is correct
• The generate-test heuristic can be helpful if the search space (the set of all possible solutions that the solver is willing to consider) is small
• The usefulness of the generate-test heuristic decreases as the search space grows in size
• The generate-test heuristic is used if there is no way of measuring how close the current state is to the goal state
• The generate-test heuristic is not useful if we cannot test whether a solution is correct
• Difference-reduction heuristic


  To take whatever action that produces the greatest reduction in the difference between the current state of the word and the goal state
• The difference-reduction heuristic can fail when solutions require you to backtrack or move sideways from your goal
• Create subgoals


  An intermediate state between the current state and the goal state
• Subgoals need to be carefully chosen and carried out in the correct order to be effective
• Pursuit of subgoals may stop you from solving the original problem
• Particular care must be taken for non-independent subgoals
• Means-end analysis


  Identifying various ends and considering what means available to achieve each
• Means-end analysis involves breaking down problems into subgoals using difference-reduction heuristic to solve each goal
• Incubation


  Taking time away from solving a problem can help to find the solution
• Incubation helps for insight problems, which depend on a single key insight into the problem
• Incubation helps forget misguided strategies that were considered before interruption, and helps overcome a bias towards repeat state avoidance