Contents

• Foreword
  • What the Course Tries to Do
    • Aims
    • Learning Outcomes
    • The Course
    • Syllabus
    • These Notes
    • The Web Version
    • The MX3503 Mailing List
    • Computer Algebra Systems
    • Books
    • Tutorials
    • Acknowledgements
  
  
• Introducing the Simplex Algorithm
  • Constrained Optimisation
  • Some Sample Problems
    • Maximising a Function of Two Variables with Constraints
    • Machine Shop Scheduling
    • A Transport Problem
    • A Blending Problem
  • A More Elaborate Example
  • Linear Programming Problems
  • Standard form
  • A Preview
    • An Example
    • Improving the Solution
  • Questions 1 (Hints and solutions start here.)
  
  
• The One-phase Simplex Algorithm
  • Solutions of Systems of Linear Equations
  • Basic Solutions
  • Row-equivalent matrices
  • Computation of basic solutions
  • Change of basis
  • Return to the Linear Programming Problem
  • The One-phase Simplex Algorithm
  • A partial proof
  • Questions 2 (Hints and solutions start here.)
  
  
• Using Maple
  • Getting Access to Maple
    • Using Maple in a PC Classroom
    • Running MAPLE on sysa
    • Saving your work
    • Printing From Maple
  • Using Maple to Check Results
  • Pivoting Using Maple
  • Cycling in Example 2.26
  • An Extended Exercise
  
  
• The Two-Phase Simplex Algorithm
  • Introduction
  • The Second Phase Described
  • Artificial Variables
    • The M method
    • Another Example
    • Minimising with the Big M Method
  • A Partial Proof
  • Avoiding Non-Negativity
  • An Alternative View
  • Questions 3 (Hints and solutions start here.)
  
  
• Duality
  • Formulation of the Dual
  • The Fundamental Theorem
  • Shadow Prices
  • The Dual Simplex Method
  • Questions 4 (Hints and solutions start here.)
  
  
• The Theory of Games
  • Matrix Games
  • Pure strategies
  • Mixed Strategies
  • The Fundamental Theorem
  • Questions 5 (Hints and solutions start here.)
  
  
• Non-linear Optimisation Problems
  • Relaxing linearity conditions
  • Maxima and Minima
  • Lagrange's Principle
  • Inequality Constraints
  • Convexity
  • Questions 6 (Hints and solutions start here.)
  
  
• Genetic Optimisation
  • A Simple Algorithm
    • Coding the Domain
    • Genetic algorithms: process model
  • Variations
  • Further Discussion
  • The Travelling Salesman Problem
    • Linear Programming Formulation
    • Genetic Algorithm Formulation
  • Example Problems
    • Numerical Optimisation
    • Credit Card Scoring
    • Designing FGGA's
    • The Cocktail Party Effect
    • Mondrians
    • Prisoners Dilemma
  • Multiple Objective Functions
  
  
• Simulated Annealing
  • Introduction
    • Overview
  • An Example - the Travelling Salesman Problem
  • Minimising a Function
  • Comparison
  • Questions 7 (Hints and solutions start here.)
  
  
• Solutions to Exercises
  • Solutions for Questions 1
  • Solutions for Questions 2
  • Solutions for Questions 3
  • Solutions for Questions 4
  • Solutions for Questions 5
  • Solutions for Questions 6
  • Solutions for Questions 7
  
  
• Bibliography
• Index
• About this document ...