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Lecturer(s)
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Course content
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Lectures A) Classification of optimization problems 1. according to the existence of external constraints - examples 2. according to the type of optimized variables - examples 3. according to the physical (economic, ecological, political, military, ...) nature of the problem - examples 4. according to the types of equations that describe the problem - examples 5. according to the degree of determinism of the result (influence of noise) - examples 6. According to the robustness of the result - examples 7. According to the types of criterion functions and their number - examples B) Classification of optimization methods 1. Local vs. Global methods 2. Local: Simplexes - examples 3. Local: Hill-climbing - examples 4. Global: Direct minimum search (derivative) - examples 5. Global: Stochastic methods - examples 6. Deterministic vs. Stochastic methods - examples 7. Static vs. Dynamic Methods - examples C) Simplex Method - principle, examples and applications D) Hill-climbing Method - principle, examples and applications E) Genetic Algorithms - principle, examples and applications F) Other optimization methods Exercises A) Topological optimization of a variable beam section B) Criterion function formulation and optimization problems C) Criterion function implementation using FEM D) Simplex method implementation E) Genetic algorithm optimization F) Fitting experimental data on a simple material model
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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The course will introduce the main optimization methods and their practical application in mechanical engineering. Students will learn to classify optimization problems, understand the principles of key algorithms and gain practical experience with their implementation on real engineering problems. Problems will be solved using both analytical and numerical procedures.
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Prerequisites
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unspecified
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Assessment methods and criteria
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unspecified
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Recommended literature
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Randy L. Haupt, Sue Ellen Haupt. Practical Genetic Algorithms, John Wiley & Sons, 2004.
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Singireu S. Rao. Engineering Optimization, Theory and Practise. John Wiley & Sons, 1996.
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Thomas Weise. Global Optimization Algorithms ? Theory and Application, free e-book, 2009.
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