Master of Eng. in Automation & IT
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Automation & IT   Course   Modules   Optimization

Optimization of Technical Systems


Qualification aims

Students will learn, understand and be able to apply to technical processes

  • practical optimization using precise mathematical and stochastic procedures

In particular, they will use "state of the art" optimization software in order to

  • record and analyse new tasks and problems,
  • choose suitable solution methods,
  • ascertain and evaluate correct solutions.


Students can

  • optimize technical systems
  • implement, train and debug neural networks
  • judge the importance of human-centered AI
  • consider fairness, transparency, and ethics in AI

by

  • understanding, applying and evaluating numerical methods and algorithms
  • understanding and applying optimization theory
  • understanding and applying machine learning and artificial intelligence methods and algorithms
  • analyzing new tasks and problems
  • choosing suitable optimization methods
  • using “state of the art” optimization software and optimization algorithms
  • implementing representations, image features
  • applying optimization algorithms (stochastic gradient descent)
  • understanding backpropagation
  • choosing suitable network architectures
  • analyzing generative models
  • ascertaining and evaluation correct solutions
  • understanding bias in data
  • using tools for visualizing model states
  • summarizing results in reports
  • presenting results in oral presentations

to

  • be able to improve the behavior of technical systems
  • solve practical engineering tasks in classification and prediction
  • be qualified for a professional career as automation engineer



Courses

The module consists of three courses:


Numerical Methods

Tutor

Prof. Bartz-Beielstein

Credit points

3 CP

Term

Fall

Contents

  • Matrices
  • Differences, Derivatives, and Boundary Conditions
  • Inverses and Delta Functions
  • Eigenvalues and Eigenvectors
  • Positive Definite Matrices
  • Numerical Linear Algebra: LU, QR, SVD
  • Numerical integration of standard differential equation systems (linear, non-linear, formal procedures (Runge-Kutta etc.)
  • Boundary value problems
  • Differential Equations of Equilibrium
  • Cubic Splines and Fourth Order Equations
  • Gradient and Divergence
  • Laplace's Equation
  • Finite Differences and Fast Poisson Solvers
  • The Finite Element Method
  • Stochastic simulation
  • Design and organisation of a Monte Carlo simulator


Optimization

Tutor

Prof. Bartz-Beielstein

Credit points

4 CP

Term

Fall

Contents

  • Optimization criteria
  • Optimization basics (calculus of variation, Euler formula, Hamilton formula, maximum principle, etc.)
  • Linear Programming (LP)
  • Nonlinear Programming (NLP)
  • Quadratic Programming (QP)
  • Integer Programming (IP)
  • Direct (extrapolation-free) searching procedures (pattern search)
  • Stochastic procedures (simulated annealing, evolutionary algorithms)
  • Application of optimization procedures to practical problems


Machine Learning and AI

Tutor

Prof. Bartz-Beielstein

Credit points

3 CP

Term

Spring

Contents

  • Image Classification: Data-driven Approach, k-Nearest Neighbor, train/val/test splits, L1/L2 distances, cross-validation
  • Linear Regression, Logistic Regression, Softmax Regression
  • Optimization: Stochastic Gradient Descent
  • Neural Networks, Backpropagation
  • Convolutional Neural Networks: Architectures, Convolution / Pooling Layers
  • Understanding and Visualizing Convolutional Neural Networks


Bibliography

  • Stoer, J., et.al.: Introduction to numerical analysis. ISBN 0-387-95452-X
  • Kincaid, D., et.al.: Numerical analysis. ISBN 0-534-38905-8
  • Gill, P.E., Murray, W., Wright, M.: Practical Optimization. Academic Press, London, 1989
  • Edgar, T.F., Himmelblau, D.M.: Optimization of chemical processes. Mc Graw-Hill, 2001
  • Gekeler, E.W.: Mathematical Methods for Mechanics with MATLAB Experiments. Springer, Berlin 2008
  • Neumann, K. und Morlock, M: Operations Research. 2. Aufl. Hanser, München 2002
  • Bartz-Beielstein, T.: Experimental Research in Evolutionary Computation. 1.Aufl., Springer, Berlin 2006
  • Markon, S., Kita, H., Kise, H., Bartz-Beielstein, T.: Modern Supervisory and Optimal Control with Applications in the Control of Passenger Traffic Systems in Buildings. Springer, Berlin, Heidelberg, New York, 2006
  • Nelli, F.: Python Data Analytics, Springer, Berlin 2015
  • Moncecchi, G., Garreta, R.: Learning scikit-learn Machine Learning in Python. 2013
  • Goodfellow, I., Bengio, Y., and Courville, A.: Deep Learning. MIT press, 2016