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)


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 problemDescription 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