THEORY 2

Question 1

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

Answer 1

a

Question 2

Number of solutions of an optimization problem

Answer 2

a

Question 3

Exhaustive methods

Answer 3

a

Question 4

Single objective optimization / scalar optimization: mathematical definition

Answer 4

a

Question 5

Definition of global minimum, local minimum, convexity

Answer 5

aa

Question 6

Graph of the main single optimization methods

Answer 6

a

Question 7

Gradient: definition and physical meaning. Taylor’s expansion

Answer 7

a

Question 8

Optimality conditions (unconstrained)

Answer 8

a

Question 9

Optimality conditions (constrained): KKT conditions

Answer 9

a

Question 10

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?

Answer 10

a

Question 11

5 properties of a good algorithm

Answer 11

a

Question 12

Grid and random methods, Pattern search and Simplex method

Answer 12

a

Question 13

Basic descend methods

Answer 13

a

Question 14

Penalty methods

Answer 14

a

Question 15

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

Answer 15

a

Question 16

Pareto optimal necessary condition. Ideal vs Nadir solution

Answer 16

a

Question 17

Low discrepancy sequences. Definition of uniformity and discrepancy

Answer 17

a

Question 18

Feasibility and boundedness

Answer 18

a

Question 19

Scalarization techniques

Answer 19

a

Question 20

Some typical primal algorithms

Answer 20

a

Question 21

Lagrange multipliers

Answer 21

a

Question 22

John Fritz optimal condition

Answer 22

a

Question 23

Discrete programming

Answer 23

a

Question 24

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

Answer 24

a

Question 25

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

Answer 25

a

Question 26

Constraints in GAs

Answer 26

a

Question 27

Termination conditions for GA and no free lunch theorem

Answer 27

a

Question 28

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

Answer 28

a

Question 29

Global sensitivity analysis

Answer 29

a

Question 30

Global approximation: least square

Answer 30

a

Question 31

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

Answer 31

a

Question 32

Learning / training. Back propagation

Answer 32

a

Question 33

Cross validation and regularization

Answer 33

a

Question 34

Architecture of the neural network

Answer 34

a

Question 35

k-optimality: selection of the final design solution

Answer 35

a

Question 36

Topology optimization

Answer 36

a