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

Optimization of Technical Systems

Qualification aims

This module equips students with the ability to apply numerical methods, develop mathematical models, and utilize data-driven optimization techniques to solve real-world problems, analyze large datasets, and enhance technical systems' performance through the use of advanced computational tools and optimization software.


Students can

  • apply numerical methods
  • develop mathematical models for technical systems
  • data-driven optimization techniques

by

  • translating real-world problems into computable form
  • analyzing large datasets
  • applying optimization algorithms (stochastic gradient descent)
  • understanding bias in data
  • utilizing programming and computational tools
  • using “state of the art” optimization software and optimization algorithms
  • using tools for visualizing model states

to

  • solve optimization problems in technical systems, improving their efficiency and performance
  • identify optimal solutions using various constraints and parameters
  • predict system behavior and improve decision-making processes


Module Content

Numerical Methods

  • 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

  • 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


Data-driven Optimization

  • Data from real-world problems (industry, economy, science)
  • Data preparation
  • Linear regression, logistic regression
  • Hypothesis testing
  • Classification, Linear discriminant analysis
  • Tree-based methods
  • Sequential parameter optimization (SPO)
  • Model selection
  • Treatment of missing values and huge data sets
  • Data visualization
  • Data mining, CRISP-DM Process
  • Learning, especially advanced modelling techniques: Bootstrap, bagging, meta learner (e.g. random forests), empirical learning problems
  • Evaluation of modelling results (e.g., error measures, overfitting, cross valida-tion, precision and recall)


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
  • Witten, I. H., Frank, E.: Data Mining, Hanser, 2nd ed., 2005
  • Hastie, T., Tibshirani, R., Friedeman, J.: The Elements of Statistical Learning. Springer, 2001
  • James, G., Witten, D., Hastie, T., and Tibshirani, R.: An Introduction to Statistical Learning with Applications in R. Springer, 4th edition, 2014
  • Law, A.M., Kelton, W.D.: Simulation Modeling and Analysis. McGraw-Hill, Boston, 2000
  • Bartz-Beielstein, T. et al.: Experimental Methods for the Analysis of Optimization Algorithms. Springer, 2010
  • Williams, G.: Data Mining with Rattle and R: The Art of Excavating Data for Knowledge Discovery. Springer, New York, 2011


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