Laurent DUMAS
Course Objectives:
Many problems occuring in industry consist in minimizing (or
maximizing) a certain cost function. This course is aimed to present
various optimization methods in order to solve such problems.
After a general introduction on numerical optimization,
two different families of optimization methods will be presented:
first, the the stochastic methods (genetic algorithms, evolution strategies,
etc...) and then deterministic descent-type methods (gradient, newton,
etc…). A numerical implementation with Scilab of these differents methods
will be done during the computer sessions, before being applied for the
resolution of applicative problems
Course prerequisites:
No specific prerequisites are needed for this course.
It is accessible with basic tools in analysis (functions of
n variables).
Syllabus
(électif 11, S4, see timetable):
Cours 1 (18 Mars, 14h-17h): Introduction et exemples
Cours 2: (25 Mars, 14h-17h): Optimisation sans contraintes (méthodes
générales de descente, recherche linéaire) /
Initiation à Scilab, méthode de descente (steepest.sci)
Cours 3 (1er Avril, 14h-17h): Optimisation sans contrainte (méthode
de Newton et quasi Newton, gradient conjugué) / Initiation à
Scilab, algorithmes génétiques (AG-ECP.sci)
Cours 4: (15 Avril, 14h-17h): Recuit simulé (annealing.sci), Algorithmes Génétiques
(AG-ECPv2.sci, AG-ECPv3.sci)
Cours 5 (17 Avril, 8h-11h) : Algorithmes Génétiques
mutli-objectifs, Stratégies d'évolution (ES.sci).
Cours 6 (13 Mai, 14h-17h) : Traitement des contraintes (ecp-canette-AG.sci)
Cours 7: (15 Mai, 8h-11h): Optimisation robuste (ecp-Ibeam-ES-robust.sci) / Scilab: modèle
RBF (ecp-RBF.sci)
Cours 8: (20 Mai, 14h-17h): Modèles approchés
et optimisation (ECP-surrogate.sci)
Cours 9: (23 Mai, 8h-11h) : Applications médicales
et industrielles de l'optimisation (bragg.sci et
artères.sci)
Examen le 27 Mai (énoncé)
Rattrapage le 31 Aout (énoncé)
References:
Numercial optimization, theoretical and practical aspects: JF
Bonnans, JC Gilbert, C. Lemaréchal, C. Sagastizbal, Springer
Verlag 2003.
Genetic Algorithms on search, optimization and machine learning:
D. Goldberg, 1989
Multi-Objective
Optimization Using Evolutionary Algorithms, K. Deb, 2001
On the web:
Theoretical part:
An online course on 'Numerical Optimization'
at Oxford University
An online course on 'Optimization inengineering
design' at the Georgia Institute of Technology
A book Numerical recipes in C or Fortran
77 (Chapter 10 mainly)
An introduction article on 'Numerical Solution of Optimization
Test-Cases by Genetic Algorithms' by N. Marco and J.A. Desideri
Applicative part:
The I-beam problem: Description
of the I-Beam problem
The FBG problem: a talk 'Optimisation
of optical communication systems by means of genetic algorithms'
by myself
The FBG problem: a PhD dissertation
“Synthesis and characterization
of fiber Bragg gratings” by J. Skaar (chapters 2 and 3.1
mainly)
The FBG problem: an article 'Real-coded genetic
algorithm for Bragg grating parameter synthesis' by G. Cormier
and R. Boudreau
The FBG problem: an article 'Multi-objective
and constrained design of fibre Bragg gratings using evolutionary
algorithms' by S. Manos and L. Poladian
The LJ problem: article 1 article 2, article
3, article
4 thesis