THEORY 3 Flashcards
Objective functions, design variable and constraint definition. What is the Pareto optimal set?
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Number of solutions of an optimization problem
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Exhaustive methods
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Single objective optimization / scalar optimization: mathematical definition
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Definition of global minimum, local minimum, convexity
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Graph of the main single optimization methods
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Gradient: definition and physical meaning. Taylor’s expansion
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Optimality conditions (unconstrained)
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Optimality conditions (constrained): KKT conditions
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Non linear optimization: is it possible to guarantee a global optimum? Why? List the 2 main heuristic rules on which the algorithms are based. What is the general search procedure for optimization problems?
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5 properties of a good algorithm
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Grid and random methods, Pattern search and Simplex method
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Basic descend methods
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Penalty methods
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MOP: mathematical definition of the Pareto optimal solution and meaning. Local vs global Pareto optimal solution.
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Pareto optimal necessary condition. Ideal vs Nadir solution
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Low discrepancy sequences. Definition of uniformity and discrepancy
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Feasibility and boundedness
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Scalarization techniques
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Lagrange multipliers
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John Fritz optimal condition
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Discrete programming
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Genetic algorithms: introduction and explanation. Binary coding representation for discrete, continuous and multi design variables. Description of the process in detail
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Holland theorem: schema properties and number of elements with a schema at a certain generation
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Constraints in GAs
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Termination conditions for GA and no free lunch theorem
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Multiobjective optimization with GA. Main advantages. How to assign the fitness and how to guarantee even distribution?
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Global sensitivity analysis
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Global approximation: least square
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Machine learning: introduction to neural networks. Structure of the artificial neural network, example of a multi layer feed forward network and activation functions.
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Learning / training. Back propagation
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Cross validation and regularization
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Architecture of the neural network
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k-optimality: selection of the final design solution
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Topology optimization
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Design of experiments: why choosing an OAT approach is not useful? How is it possible to represent in a graphical way a 2 levels 2 DV problem? What is screening? Fractional factorial DOE
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Principles for defining a good fractional factorial DOE
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Increasing the number of levels in a DOE for a non linear model. Difference in the n° of experiments required by a full factorial plan and the actual n° of coefficients of the empirical model. Algorithms and methods for high number of levels.
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Integrated controls
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