**WB1440:** |
**Eng. Optimization: Concept & Applications** |

**ECTS:** |
3 |

**Responsible Instructor:** |
Dr.ir. M. Langelaar |

**Instructor:** |
Prof.dr.ir. A. van Keulen |

**Contact Hours / Week x/x/x/x:** |
0/0/4/0 |

**Education Period:** |
3 |

**Start Education:** |
3 |

**Exam Period:** |
Different, to be announced |

**Course Language:** |
English |

**Required for:** |
wb1441 |

**Expected prior knowledge:** |
Basic knowledge of mechanical engineering and mathematics. Experience with Matlab is helpful. |

**Course Contents:** |
Formulation of optimization problems Typical characteristics of optimization problems Minimization without constraints Constrained minimization Simple optimization algorithms Discrete design variables Approximation concepts Sensitivity analysis |

**Study Goals:** |
The student is able to formulate a proper optimization problem in order to solve a given design problem, and is able to select a suitable approach for solving this problem numerically. Furthermore, he is able to interpret results of completed optimization procedures. More specifically, the student must be able to: 1. formulate an optimization model for various design problems 2. identify optimization model properties such as monotonicity, (non-)convexity and (non-) linearity 3. identify optimization problem properties such as constraint dominance, constraint activity, well boundedness and convexity 4. apply Monotonicity Analysis to optimization problems using the First Monotonicity Principle 5. perform the conversion of constrained problems into unconstrained problems using penalty or barrier methods 6. compute and interpret the Karush-Kuhn-Tucker optimality conditions for constrained optimization problems 7. describe the complications associated with the use of computational models in optimization 8. illustrate the use of compact modeling and response surface techniques for dealing with computationally expensive and noisy optimization models 9. perform design sensitivity analysis using variational, discrete, semi-analytical and finite difference methods 10. identify a suitable optimization algorithm given a certain optimization problem 11. perform design optimization using the optimization routines implemented in the Matlab Optimization Toolbox 12. derive a linearized approximate problem for a given constrained optimization problem, and solve the original problem using a sequence of linear approximations 13. describe the basic concepts used in structural topology optimization |

**Education Method:** |
Lectures (2x2 hours per week), exercises |

**Computer Use:** |
MATLAB is used for exercises and final project. |

**Literature and Study Materials:** |
Course material: P.Y. Papalambros et al. Principles of Optimal Design: Modelling and Computation. References from literature: R.T. Haftka and Z. Gürdal: Elements of Structural Optimization. |

**Assessment:** |
MATLAB exercises, optimization project. |

**Percentage of Design:** |
80% |

**Design Content:** |
The course is focusing on design optimization. |