In every engineering field, models are used to assess the performance of structures/products/systems. In order to improve the performance of a system, certain parameters of the design can usually be adapted. Computational optimization refers to the use of algorithms to automate the search for an optimal design. The adequate algorithm to be used depends on characteristics of the problem, properties of the model and the number of parameters to be optimized.|
After having completed the course, the student is able to:
- Formulate a design assignment as an optimization problem.
- Classify an optimization problem by its type of parameters, objective function and constraints.
- Choose appropriate mathematical solution algorithms for specific optimization problems.
- Use an optimization software toolbox to solve optimization problems.
In the Computational Optimization course the concepts of unconstrained and constrained optimizations are covered. The most important methods for systematic mathematical optimization are explained, and applied using practical examples. In the first part of the course, local (gradient-based) optimization methods are covered in detail, while global optimization methods are covered in the second part of the course. The course is designed for Mechanical Engineering students, and examples from structural mechanics will be covered in the lectures and assignments.|
The course is a blend of mathematics, programming and engineering, and of interest for Master students from all Mechanical Engineering specializations.
The following topics will be covered in the course:
- Design optimization, design variables, objective function, constraints.
- Unconstrained optimization, line search.
- Constrained optimization, Lagrange multipliers.
- Local optimization methods for linear and non-linear problems.
- Calculation of gradients.
- Global optimization methods.
- Surrogate model based global optimization.
- Topology optimization.
- Practical approaches to optimization in engineering.