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Home > Global Optimization Methods - Theory, Techniques, and Advanced Engineering Applications

Global Optimization Methods - Theory, Techniques, and Advanced Engineering Applications

Lecturers: Andrea Massa (UNITN/DICAM); Paolo Rocca (UNITN/DICAM)

Timetable: June 2023 (to be confirmed)

Course Description:
Optimization techniques are generally classified into deterministic/local and stochastic/global
methods. Although effective in terms of convergence speed, the former methods generally require
a ‘domain knowledge’ since in the case of non-linear and multi-mimina functionals the initial
trial solution must lie in the so-called ‘attraction basin’ of the global solution to avoid the
convergence solution being trapped into local minima of the functional (i.e., wrong solutions
of the problem at hand). In contrast, global optimization methods are potentially able to find
the global optimum of the functional whatever the initial point/s of the search.
The course will review fundamentals and main issues of optimization problems then focusing
on classical/state-of-the-art and recently introduced global optimization approaches. Applicative
examples including exercises covering advanced engineering applications will corroborate the
theoretical concepts.

Course Topics:
- Fundamentals of global optimization,  "no-free-lunch" theorem for optimization;
- Deterministic optimization: Steepest Descent (SD) and Conjugate-Gradient (CG) Methods;
- Stochastic ‘nature-inspired’ optimization algorithms;
   - "Competitive" methods: Genetic Algorithm (GA), Differential Evolution (DE);
   - "Cooperative" methods: Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO).
- Application of global optimization methods to advanced engineering synthesis and design problems;
- Recent advances within the System-by-Design (SbD) framework for the computationally-efficient
  solution of complex engineering problems;
- Applicative examples including exercises regarding specific engineering applications of
  global optimization methodologies.

References:
[1] D. H. Wolpert and W. G. Macready, "No free lunch theorems for optimization," IEEE Trans. Evol.
    Comput., vol. 1, no. 1, pp. 67-82, Apr. 1997.
[2] P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, "Evolutionary optimization
    as applied to inverse problems," Inverse Problems, vol. 25, pp. 1-41, Dec. 2009.
[3] P. Rocca, G. Oliveri, and A. Massa, "Differential evolution as applied to electromagnetics,"
    IEEE Antennas Propag. Mag., vol. 53, no. 1,  pp. 38-49, Feb. 2011.
[4] A. Massa and M. Salucci, “On the design of complex EM devices and systems through the
    system-by-design paradigm - A framework for dealing with the computational complexity,” IEEE
    Trans. Antennas Propag., in press.

Duration: 32 hours ( 4 credits)

Registration: in order to access the course please send an email to dicamphd [at] unitn.it