Problem Solving

1
Overview

• Introduction
• Crucial Features of Problem Solving
• History of Problem Solving
• Brief History of Cognitive Models
• Problem Space
• Types of Problems
• Representation
• Methods of Problem Solving
• Production Systems
• Issues in Problem Solving
• Decision Making

2
Problem Solving Two Crucial Features

• A problem exists when a goal must be achieved and
  a solution is not immediately obvious.
• Problem solving often involves attempting
  different ways to solve the problem

3
History of Problem Solving

• Early Psychologists _at_ Wurzburg
• Oswald Kulpe, Karl Buhler, Otto Selz
• Looked at mental processes engaged
• 1940s and 50s Gestalt Psychologists
• Investigated how people solve difficult problems
  Insight
• Four Stages of Problem Solving Preparation,
  Incubation, Insight, Verification
• 1958 Sir Fredrick Bartlett Characterized it a
  exploration

4
History of Problem Solving

• 1960s Herbert Simon
• Focused on the processnot merely insight
• Based research on a series of complex problems
• Used concurrent verbalizations Identified mental
  operations, representations and strategies used
  in problem solving
• Developed series of computer programs to simulate
  human problem solving
• 1972 Newell and Simon
• Proposed a comprehensive theory of problem
  solving
• Still at the heart of contemporary thought today
• At the forefront of Cognitive Model Development

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Four Components
Initial State
Goal State
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Cognitive Models Fundamental Motivations

• Embodied Cognition
• Normally modeled as disembodieda purely
  cognitive system
• Misleading but why?
• Example Visual capacity to detect is not uniform
• Primary motivation Model human constraints

• Computational Models of Both Performance and
  Cognition
• Most research in the field of human performance
• Lacks computational modeling
• Qualitative interpretation of empirical results
• Verbally expressed and evaluated theory
• Primary motivation Advance state of
  psychological theory in an underdeveloped area

• The Executive Process and Multiple-Task
  Performance
• Executive process coordination
• Insights provided by multiple task situations
• Limitations on the central capacity for cognitive
  processing
• Primary motivation Further understanding human
  performance in Multi-task situations

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Developmental Background
EPIC Architecture (Executive
Process-Interactive Control) Perceptual
Processors Cognitive Processors Motor
Processors Interaction between a simulated human
and task environment

• GOMS
• (Goals,Operators, Methods, Selection rules)
• Family of UI modeling techniques
• Based on Model Human Processor
• GOMS family
• KLM-GOMS
• CMN-GOMS
• NGOMSL
• CPM-GOMS

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Model Human Processor (MHP) Three Interacting
subsystems

• Perceptual
• Sensory input (audio visual)
• Code info symbolically
• Output into audio visual image storage (WM
  buffers)
• Cognitive
• Input from sensory buffers
• Access LTM to determine response
• previously stored info
• Output response into WM
• Motor
• Input response from WM
• Carry out response
• Each with processor memory
• Described by parameters (e.g., capacity, cycle
  time)
• Serial parallel processing
• Serial Pressing key in response to light
• Parallel Driving, reading signs hearing

Adapted from slide by Melody Y. Ivory
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GOMS

• The analysis of knowledge of how to do a task
  in terms of the components of goals, operators,
  methods, and selection rules.
• John Kieras, 1994

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GOMS Definitions

• GOALS
• Something the user tries to accomplish
• Move text
• Operators
• Actions that the user executes
• Click mouse
• Move pointer

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GOMS Definitions

• Methods
• Sequences of steps that accomplish a goal
• Highlight text
• Cut text
• Move to new location
• Paste text
• Selection Rules
• If there are more than one method to accomplish a
  goal
• Selection rules pick method to use!!!
• Decision criteria for choosing among methods
• IF ltmove-text is fewer then 5 lettersgt THEN
  ltretype textgt

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Selection Rules

• If there is more than one method to accomplish a
  goal
• Selection rules pick method to use!
• Other examples
• IF ltconditiongt THEN accomplish ltGOALgt
• IF ltcar has automatic transmissiongt THEN ltselect
  drivegt
• IF ltcar has manual transmissiongt THEN ltfind car
  with automatic transmissiongt

Adapted from brief by James Landay
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Example

• Goal (the big picture)
• Go from hotel to the airport
• Methods (or sub-goals)?
• Walk, take bus, take taxi, rent car, take train
• Operators (or specific actions)
• Locate bus stop wait for bus get on the bus...
• Selection rules (choosing among methods)?
• Example Walking is cheaper, but tiring and slow
• Example Taking a bus is complicated abroad

Adapted from example by James Landay
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Family of Modeling Techniques

• Original GOMS analyses had limitations
• Designed for expert behavior
• Errors were problematic
• GOMS family
• KLM-GOMS Keystroke Level Model (1983)
• CMN-GOMS Card, Moran Newell (1983)
• NGOMSL Natural GOMS Language (Kieras, 1988)
• CPM-GOMS Cognitive-Perceptual-Motor GOMS (Bonnie
  John, 1990)

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Executive Process-Interactive Control (EPIC)

• Executive Process
• Interactive Control
• Multimodal
• High Performance
• Multiple Tasks

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EPIC Architecture

• Designed to explicitly couple
• Basic information processing and perceptual motor
  mechanisms
• With
• A cognitive analysis of procedure skill
• Therefore, EPIC consists of

Simulated Task Environment
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Multiple Tasks and Executive Processes

• Executive control process is just another set of
  production rules.
• Executive control process can cause a task to
  follow a different strategy by placing in WM an
  item that task rules test for, thus enabling one
  set of rules, and disabling another.
• Executive control process may control sensory
  and motor peripherals directly.

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Problem Solving Two Crucial Features (Revisited)

• A problem exists when a goal must be achieved and
  a solution is not immediately obvious.
• Problem solving often involves attempting
  different ways to solve the problem

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http//www.mazeworks.com/hanoi/
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Tower of Hanoi Problem Space
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Discrete Event Systems Representation
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Complete System Behavior
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Problem Solving
Tiger Woods is tied for the lead going into the
last hole of the U.S. Open. His first shot is on
to the green, in good position for a birdie, and
a win. Upon reaching the green, however, he
discovers that his ball has rolled into a small
paper bag that someone left lying on the green.
If he takes the ball from the bag, it will cost
him a penalty shot if he hits the ball in the
bag, it may go wild. What should he do?
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Types of Problems

• Well-defined
• Definite initial state
• Goals and operators known
• Ill-defined
• Solver does not know goals or operators, or even
  current state
• Examples?

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Types of Problems
IX
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Types of Problems
SIX
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Types of Problems

• Are problem strategies unique to domain?
• Some domain-general strategies are components of
  domain-specific ones
• Science as problem-solving

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Types of Problems
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Types of Problems
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Representation

• The beginning representing the problem
• Method of solution often depends on method of
  representation
• Determine relevant features of problem
• Construct a representation using those features
• The cover story can bias the representation

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Representation
What is the maximum number of pieces into which a
cake may be cut using four straight cuts with a
sharp knife?
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Representation
11 pieces
14 pieces
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Methods of Problem Solving

• Algorithms vs. Heuristics
• Algorithm a set of rules that always lead to the
  correct solution
• Heuristics a set of rules of thumb that
  generally lead to a correct solution but do not
  guarantee success.

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Heuristic Search Methods

• Random Search
• Hill climbing technique
• Means-ends analysis

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Heuristic Search Methods
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Heuristic Search Methods
8
4
3
5
9
1
6
7
2
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Heuristic Search Methods

• May not have access to the entire problem space
• Satisficing selecting an option which meets
  minimum success criterion
• Essentially, a stopping rule for problem space
  search
• Sacrifices optimum for satisfactory

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Other Methods

• Analogy
• Case-based reasoning
• Delphi techniques
• Probabilistic Determination
• Production Systems

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Production System

• Few general models but many models related to
  particular problems
• General models
• Problem space hypothesis
• Instantiated in Production Rules
• Production System
• Knowledge as symbols
• Production rules act on symbols
• Problem-solving occurs in working memory

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Approaches to Problem Solving

• Connectionist
• Few models because hard to model temporary
  representations that are needed in
  problem-solving
• Hybrid (Symbolic and Connectionist combined)

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Challenges in Problem Solving

• Past research focused independently on problem
  solving
• Recent research incorporates problem solving with
  other cognitive activities
• Integrate problem solving with cognitive
  activities
• Remembering, Reasoning, and Decision Making

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Which Came First

• Which do YOU think came first problem-solving or
  decision making

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Example

• 2 2 4

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Decision Making
Problem
Objectives
Alternatives
Risk Tolerances
Uncertainty
Consequences
Tradeoffs
Decision
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Elements of Decision Making and Problem Solving

• Finding ways to represent decisions
• Some representations more beneficial than others
• Cognitive illusions
• Heuristics
• Well-defined and ill-defined decisions

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Issues in Decision Making

• Task environment ? Problem-solving
• Psychological traps ? Decision making
• Both relate to how the surroundings effect the
  outcome

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Psychological Traps

• Anchoring trap
• Are there more than 20,000 students at Georgia
  Tech?
• What is your best guess for the number of
  students at Georgia Tech?
• Sunk-cost trap
• Car example

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Psychological Traps

• Framing trap
• Would you accept a 50-50 chance that offered the
  possibility of either losing 300 or gaining
  500?
• Would your prefer to keep a 2,000 balance in the
  bank, to accepting a 50-50 chance of having
  either 1,700 or 2,500 in your account?
• Outguessing Randomness trap
• Coin example

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Issues in Problem Solving

• Task Environment debate
• Greeno and Suchman believe the task environment
  is a major determinant of how a person solves a
  problem
• Previous Experience
• Ways humans perform problem solving
• Group dynamic
• Real world problems solved in groups
• Encourage alternatives
• Problem solving steps spread throughout group
• Same background vs Different background

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Issues in Problem Solving Research

• Ways someone solves a problem
• Traditionally Problem Solving considered solving
  puzzles
• Recently, real-world problems
• How previous experience influences performance on
  a problem
• Use current state of problem and history of
  similar problem-solving experience (ex Chess)
• Unaware that experience has an effect

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Where Problem Solving is Going

• Goal Going beyond solving puzzles
• Goal Integrate with cognitive actives
  (remembering, reasoning, decision making)
• Goal Figure out how people generate
  representations and problem spaces.
• Goal Role of brain and what parts help in PS.

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Questions