The objective is to provide students with knowledge and analytical tools to understand and study optimization problems.
- Knowledge and understanding skills: At the end of the course, the student must know the main numerical methods of optimization
- Ability to apply knowledge and understanding: The student should be able to solve a engineering problem with otimization algorithms.
- Autonomy of judgment: The student should be able to identify the type of algorithm to apply.
- Communicative skills: Students should be able to describe what they learned with correct use of language.
- Learning ability: Students should be able to interpret and use manuals useful for optimization analysis.

Mathematical Analysis

The course will offer numerical and methodological basis of design practice. Starting from the concept of parametric modelling the most recent optimization techniques are examined related to both sigle and multi objective design optimization algorithms.
The course is divided in four thematic areas: Design of Experiments, Optimization Algorithms, Response Surfaces Methods.
Exercises are finalized to the development of a design project agreed with small group of students (2 or 3 maximum)

Geometrical parametrization
Bezier Curve
B-spline
Nurbs

DOE (Design of experiment)
Random, Sobol
Factorial
Box-Benken, Latin Square
Taguchi

Statistical analysis of data (t-Student, χ2)

Optimization Algorithms:
Single objective (Cauchy, Conjugate Gradient, Newton, Quasi Newton, BFGS, SQP)
Simplex
Simulated Annealing

Multi-objective (Evolutinary Algorithms)
Game theory (Nash, Stackelberg, Pareto)
MCDM (Multi Criteria Decision Making)

Response Surfaces
Linear, quadratic,
Taylor expansion, Kriging, Neural Networks, Gaussian processes

ROBUST DESIGN

Data Visualization, Self organising maps, clustering

Curves and surfaces for CAGD, Gerald Farin, Rheinbolt, Academic Press, 1997
Design of Experiments, R. J. Del Vecchio, Hanser Publishers, 1997
Engineering Optimization, Singiresu Rao, Wiley 1996
Neural Networks, R. Rojas, Springer, 1996

The course will offer numerical and methodological basis of design practice. Starting from the concept of parametric modelling the most recent optimization techniques are examined related to both sigle and multi objective design optimization algorithms.
The course is divided in four thematic areas: Design of Experiments, Optimization Algorithms, Response Surfaces Methods.
Exercises are finalized to the development of a design project agreed with small group of students (2 or 3 maximum)
Geometrical parametrization
Bezier Curve
B-spline
Nurbs

DOE (Design of experiment)
Random, Sobol
Factorial
Box-Benken, Latin Square
Taguchi

Statistical analysis of data (t-Student, χ2)

Optimization Algorithms:
Single objective (Cauchy, Conjugate Gradient, Newton, Quasi Newton, BFGS, SQP)
Simplex
Simulated Annealing

Multi-objective (Evolutinary Algorithms)
Game theory (Nash, Stackelberg, Pareto)
MCDM (Multi Criteria Decision Making)

Response Surfaces
Linear, quadratic,
Taylor expansion, Kriging, Neural Networks, Gaussian processes

ROBUST DESIGN

Data Visualization, Self organising maps, clustering

Classical lectures plus team work for the design project.

Any changes to the methods described here, which may be necessary to ensure the application of the security protocols related to the COVID19 emergency, will be communicated on the website of the Department, the Degree Program and teaching.

oral examination and discussion of the team work project

This course explores topics closely related to one or more goals of the United Nations 2030 Agenda for Sustainable Development (SDGs)