Undergraduate Teaching 2023-24

Engineering Tripos Part IIB, 4M17: Practical Optimisation, 2023-24

Engineering Tripos Part IIB, 4M17: Practical Optimisation, 2023-24

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Module Leader

Prof. Geoff Parks


Prof. Garth Wells and Prof. Geoff Parks

Timing and Structure

Michaelmas Term. 13 lectures + 3 coursework sessions. Assessment: 100% coursework. Lectures will be recorded.




The aims of the course are to:

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


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

  • Understand the basic mathematics underlying linear and 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 optimisation 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 approaching real-world optimisation problems from a multiobjective perspective.


  • Introduction (what is Practical Optimisation?)
  • Approximately solving Ax=b (various methods of norm minimization of residuals that lead to LP or convex problems)
  • Geometry of polyhedral and convex sets (review of the simplex method; introduction to algorithmic complexity)
  • Duality theory and its applications
  • Unconstrained optimisation
  • Important convex relaxations in cardinality problems 
  • Circumstances in which 'methods of last resort' are needed
  • 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




Due date

& marks

Coursework activity #1: Investigation of a moderate size Linear Regression problem with various norm and regularization approximations

Learning objective:

  • convert a regression problem into a linear program and solve it with linprog
  • program a simple line search algorithm and experiment the impact of smoothness on convergence rate.
  • understand how different norms affect the solution of an approximation problem.

Individual report

anonymously marked

Deadline: 8th December 2023


Coursework activity #2: Investigation of the performance of two stochastic optimization methods on a hard problem

Learning objective:

  • gain experience in applying stochastic optimisation methods to challenging problems
  • explore and analyse the variation in optimiser performance as algorithm control parameters are modified
  • compare and analyse the performance of different optimisation methods on challenging problems

Individual report

anonymously marked

Deadline: 16th January 2024




Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.


This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

Intellectual Abilities

Knowledge and Understanding

Practical skills

Engineering Analysis (E)

Underpinning Science and Mathematics and associated engineering disciplines

Last modified: 30/05/2023 15:35