Week 1 - Problem Solving

• Problem solving


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


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


  An action/ series of actions that transform current state into goal state
• Wessels 4 stages in problem solving

  1. Define the problem

  2. Devise a strategy

  3. Execute the strategy

  4. Evaluate progress towards the goal
• Defining the problem


  • What is the goal state? Current state? And available actions?
• Devising a strategy


  • Select an available action/ series of actions that we think will bring current state closer to goal state
• Executing the strategy


  • Carry out intended action/ series of actions
• Evaluating progress towards the goal

  • Measure our new distance between current state and goal state
• Features of easy problems

  • Current state and goal state are close together
  • Fewer actions to solve
  • Fewer available actions to search through
  • Being an expertise in a domain
• Features of hard problems

  • Current state and goal state are far apart
  • Take more actions to solve
  • More available actions to search through
  • Being a novice in a domain / less expertise
• Some problems are unsolvable because there are no series of actions that can be taken to bring the current state to goal state
• Well-defined problem


  All aspects of the problem are clearly specified (current state, goal state and available actions are all known)
• Example of a well-defined problem


  • Following a recipe to bake a familiar cake
• Example of a hard to solve well-defined problem

  • Chess
• Ill-defined problem


  Some aspects of the problem are not clearly specified (current state, goal state or available actions)
• Example of an ill-defined problem


  • Manage the economy, living a good life
• Insight in problem solving


  Some problems are not solved sequentially through the 4 stages but rather come to us in a flash of insight an AHA! moment
• We still run through the 4 stages of problem solving when we have an insight, but unconsciously, hence the solution coming to us in a FLASH
• Mental representation


  The way our beliefs, knowledge and memories are stored within our minds
• Mental representations are not necessarily accurate, it is only our knowledge of things thus it's not necessarily the truth
• Mental representation of a problem

  Our knowledge about its different components, starting state, goal state and available actions
• Not all intelligent behaviour is considered problem solving, as reflex jerks such as taking hand off hot pan does not involve mental representation of current state, goal state and available actions
• Solving problems well/ accurately

  • Find the appropriate mental representation of the problem and relax our mental representations
• Appropriate mental representation of current state

  • What is the current state of the world?
  • What do I know? What don't I know?
• Appropriate mental representation of goal state

  • What is the goal state?
  • In what ways is this state different to the current state?
• Appropriate mental representation of available actions

  • What are the available actions?
  • What are constraint of my actions?
• Functional fixedness


  A "mental block" against using an object in a new way that is required to solve a problem i.e. not thinking outside the box, narrow representation of possible uses of an object
• Example of functional fixedness


  • Box of tacks and candle problem
• Children and creative thinkers are more commonly found to have functional fixedness
• Reducing functional fixedness


  • Individual trained in using objects in different way, labelling objects in nonsense ways, asking people to come up with alternative uses for objects
• A good representation is not enough to solve a problem, we need to be able to devise and execute appropriate solution that reduces distance between current and goal
• Strategies for devising actions

  • Algorithmic strategies
  • Heuristics strategies
• Algorithmic strategies


  Procedures that takes actions that are guaranteed to find solution for a problem
• Algorithms are not universal and do not work for ill-defined problems
• Heuristic strategies


  A 'rule of thumb' that is easy to use, fast and often helpful but not guaranteed to reach a solution
• Heuristics strategies are developed from experience
• General purpose heuristics


  Heuristics applicable across a broad class of problems
• Example of an algorithm


  • Sorting
• Generate-test heuristic


  Repeatedly generate a possible solution and test to see if its correct
• Example of generate-test heuristic


  • Solving anagram by randomly reordering letters and checking if it makes an English word