Laurent DUMAS

 Archives : course 2009

 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):

Mercredi 17 mars    Cours    14-17h: introduction and examples
Mercredi 24 mars    Cours    14-17h: deterministic methods: descent methods (steepest gradient)+computer session
Vendredi 26 mars    Cours    8h-11h: deterministic methods: descent methods (BFGS) + computer session: BFGS-banana.sci
Mercredi 31 mars    Cours    14-17h: binary genetic algorithm+ computer session GA-binary2010.sci
Mercredi 05 mai     Cours    14-17h: real valued genetic algorithm+ computer session GA-real2010.sci
Mardi 11 mai          Cours    8h-11h: evolution strategies, adaptativity principles + computer session ES-CSA2010.sci
Vendredi 14 mai    Cours    8h-11h: PSO, DE, constraints handling, robust optimization+ computer session ES-CSA2010-can.sci
Mercredi 26 mai     Cours    14-17h: multi-objective optimization NSGA-2010.sci
Vendredi 28 mai     Cours    14-17h: examples in industry and medicine

Exam: 09 juin: énoncé

Rattapage: 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 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