Dr Nan Li
+44 (0)20 7594 8853
The Optimisation course is designed to provide students with exposure to a rational integration of design methodologies with the concepts and techniques of modern optimisation theory and practice. Through the course, the students will learn to rationalise and quantify an engineering system or product design problem, develop proper mathematical models to formulate a design optimisation problem, and apply appropriate optimisation algorithms to solve it.
Learning OutcomesOn completion of this module, students will be better able to:
- Define, rationalise, and quantify engineering system and product design problems by formulating appropriate objective functions, and selecting design variables, parameters and constraints.
- Develop mathematical models to formulate design optimisation problems.
- Explain the basic concepts and theory of mathematical optimisation.
- Implement optimisation techniques in engineering design, by effectively selecting the most suitable optimisation strategy (from a range of linear programming, gradient based and non-gradient based optimisation algorithms) for a particular problem.
- Implement optimisation algorithms using software solvers (e.g. in MATLAB, python, etc.)
- Perform a critical evaluation and interpretation of analysis and optimisation results.
- Appraise the advantages and challenges of teamwork in system design and optimisation, appreciating the challenges of applying multidisciplinary design optimisation in the real world.
Description of ContentOptimisation basics:
Basic concepts and formulations
Design space and boundedness
Design of experiments
Model construction workflow
Linear Programming problems, algorithms and implementation;
Gradient-based Unconstrained optimisation:
Gradient descent method
Gradient-based Constrained Optimisation:
Reduced gradient method
Karush-Kuhn-Tucker (KKT) conditions
Generalised reduced gradient method
Sequential quadratic programming (SQP)
Active set strategies
Derivative free optimisation:
Pattern search methods