THEORY 2 Flashcards

1
Q

Objective functions, design variable and constraint definition. What is the Pareto optimal set?

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2
Q

Number of solutions of an optimization problem

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3
Q

Exhaustive methods

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4
Q

Single objective optimization / scalar optimization: mathematical definition

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5
Q

Definition of global minimum, local minimum, convexity

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6
Q

Graph of the main single optimization methods

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7
Q

Gradient: definition and physical meaning. Taylor’s expansion

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8
Q

Optimality conditions (unconstrained)

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9
Q

Optimality conditions (constrained): KKT conditions

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10
Q

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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11
Q

5 properties of a good algorithm

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12
Q

Grid and random methods, Pattern search and Simplex method

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13
Q

Basic descend methods

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14
Q

Penalty methods

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15
Q

MOP: mathematical definition of the Pareto optimal solution and meaning. Local vs global Pareto optimal solution.

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16
Q

Pareto optimal necessary condition. Ideal vs Nadir solution

17
Q

Low discrepancy sequences. Definition of uniformity and discrepancy

18
Q

Feasibility and boundedness

19
Q

Scalarization techniques

20
Q

Some typical primal algorithms

21
Q

Lagrange multipliers

22
Q

John Fritz optimal condition

23
Q

Discrete programming

24
Q

Genetic algorithms: introduction and explanation. Binary coding representation for discrete, continuous and multi design variables. Description of the process in detail

25
Q

Holland theorem: schema properties and number of elements with a schema at a certain generation

26
Q

Constraints in GAs

27
Q

Termination conditions for GA and no free lunch theorem

28
Q

Multiobjective optimization with GA. Main advantages. How to assign the fitness and how to guarantee even distribution?

29
Q

Global sensitivity analysis

30
Q

Global approximation: least square

31
Q

Machine learning: introduction to neural networks. Structure of the artificial neural network, example of a multi layer feed forward network and activation functions.

32
Q

Learning / training. Back propagation

33
Q

Cross validation and regularization

34
Q

Architecture of the neural network

35
Q

k-optimality: selection of the final design solution

36
Q

Topology optimization