1. ZEIT4700 – S1, 2016 Mathematical Modeling and Optimization
School of Engineering and Information Technology

2. Mathematical Modelling & Optimization - basics
What is Optimization ?
Systematic process of identifying design variables so as to maximimze/minimize “objectives” of a design.
Why/when is it needed?
When best performance resources/time/cost are limited.
When design boundaries need to be pushed.
(So, all the time!)
How to define an optimization problem ?
Objective functions (What is being optimized?)
Variables (What defines/controls a design?)
Constraints (What conditions must be satisfied?)

3. Optimization – types / classification
Single-objective / multi-objective
Unimodal / multi-modal
Single / multi - variable
Discrete / continuous / mixed variables
Constrained / unconstrained
Deterministic / Robust
Single / multi-disciplinary

4. Optimization - methods
Classical
Gradient based
Simplex
Heuristic / metaheuristics
Evolutionary Algorithms
Simulated Annealing
Ant Colony Optimization
Particle Swarm Optimization .

5. Approximations
Design of experiments
Surrogate Models / Meta-models

6. Robust optimization
Optimization under uncertainties, e.g. manufacturing tolerance
Formulation
Uncertainty Quantification
Search algorithms

7. Assessment Project 1 (Individual reports) (~10%)
Identify and analyze an optimized object in nature
Project 2 (Individual) (~25%)
Formulate and solve a design problem of your interest
Viva (~15%)
(Must demonstrate adequate understanding
of content and projects undertaken)

8. Resources
Course material and suggested reading can be accessed at