Undergraduate Teaching 2017-18

Engineering Tripos Part IIB, 4M17: Practical Optimisation, 2015-16

Engineering Tripos Part IIB, 4M17: Practical Optimisation, 2015-16

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Module Leader

Dr G Csanyi

Lecturers

Dr G Csanyi and Dr G Parks

Timing and Structure

Michaelmas term. 12 lectures + 4 computer lab sessions. Assessment: 100% coursework

Prerequisites

3M1

Aims

The aims of the course are to:

  • Teach some of the basic optimisation methods used to tackle difficult, real-world optimisation problems.
  • Develop an appreciation of practical issues associated with their implementation.
  • Provide experience in applying such methods on challenging problems and in assessing and comparing the performance of different algorithms.

Objectives

As specific objectives, by the end of the course students should be able to:

  • Understand the basic mathematics underlying convex optimisation.
  • Be able to write and benchmark simple algorithms to solve a convex optimisation problem.
  • Understand the technique of Markov-Chain Monte Carlo simulation, and apply it to solve a Travelling Salesman Problem.
  • Understand the ways in which different heuristic and stochastic optimization methods work and the circumstances in which they are likely to perform well or badly.
  • Understand the principles of multiobjective optimization and the benefits of such of approaching real-world optimization problems from a multiobjective perspective.

Content

  • Common Issues: performance measures, convergence criteria
  • Line search and bracketing methods
  • Multidimensional  gradient-based optimisation: conjugate gradients
  • Behaviour of gradient based optimisation methods in high dimensions
  • Constrained optimisation
  • Direct search methods: Nelder-Mead
  • Monte Carlo Sampling: basic concepts, solution representation and generation, sampling biasing
  • Simulated Annealing: basic concepts, solution representation and generation, the annealing schedule, enhancements and modifications
  • Genetic Algorithms: basic concepts, solution representation, selection, crossover, mutation
  • Tabu Search: basic concepts, solution representation, local search, intensification, diversification
  • Multiobjective Optimization: archiving, multiobjective simulated annealing, multiobjective genetic algorithms
  • Case Study: multiobjective optimization of pressurised water reactor reload cores

Coursework

  1. Solution of a moderate size Travelling Salesman Problem (TSP) (50%)
  2. Investigation of the performance of two stochastic optimization methods on a hard problem (50%)

Booklists

Please see the Booklist for Group M Courses for references for this module.

Examination Guidelines

Please refer to Form & conduct of the examinations.

Last modified: 10/07/2015 00:19