Course/ Computer
Sessions on
NUMERICAL OPTIMIZATION
Laurent Dumas
Archives: session 2006
DEGREE: Master of Science
in Mathematics, IMAMIS Program
DATES AND LOCATION: from
January, 22th to January 31th, 2007, University of the Philippines-Diliman
OUTLINE OF THE COURSE:
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 an applicative
problem called 'I-Beam optimization'.
DETAILED PROGRAM:
Monday, January 22th:
17h30-19h (course):
Introduction and examples
Tuesday, January 23th:
16h-17h30(course):
Stochastic optimization methods: genetic algorithms
and evolution strategies
17h30-19h (computer session):
Implementation of an ES with Scilab
Validation on classical test functions
Wednesday, January 24th:
17h30-19(course):
Stochastic optimization methods: constraints handling
Thursday, January 25th:
16h-17h30(course):
Stochastic optimization methods: parameter tuning
17h30-19h (computer session):
Implementation of an ES with Scilab: constraints handling
Application to the I-Beam problem
Friday, January 26th:
17h30-19h:
Stochastic optimization methods: multi objective optimization
------------------- Second week --------------------------------------------
Monday, January 29th:
17h30-19h(course):
Deterministic optimization method: basic methods,
line searches, steepest descent
Tuesday, January 30th:
16h-17h30 (course):
Deterministic optimization methods: Newton methods
17h30-19h (computer session)
Implementation of the BFGS method
Validation on classical test functions
Wednesday, January 31th:
16h-17h30(course):
Resolution of 'real world' problems: FBG synthesis,
aerodynamic shape optimization, LJ cluster optimization
17h30-19h (computer session):
Robust optimization.
Application to the I-Beam problem
On February 2nd, I also gave a talk at UP-Baguio: the slides and
the Scilab programs are available at this page
BIBLIOGRAPHY:
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:
A tutorial '
How to build an avolutionary algorithm
' by the EVONET community
An introduction article on '
Evolution strategies
' by HG Beyer and HP Schweifel
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:
Description of the I-Beam problem
Robust optimization of the I-Beam
A short tutorial
'Introduction to Fiber Bragg Gratings
'
A talk 'Optimisation of
optical communication systems by means of genetic algorithms'
by myself
A PhD dissertation “
Synthesis and characterization of fiber Bragg gratings
” by J. Skaar (chapters 2 and 3.1 mainly)
An article
'Real-coded genetic algorithm for Bragg grating parameter synthesis'
by G. Cormier and R. Boudreau
An article '
Multi-objective and constrained design of fibre Bragg gratings using evolutionary
algorithms
' by S. Manos and L. Poladian
An article "Semi
deterministic vs Genetic Algorithms for global optimization of multichannel
optical filters
" by myself, B. Ivorra, B. Mohammadi, P. Redont and O. Durand
Articles on the LJ problem:
article 1
article 2
, article
3
, article 4
thesis
FINAL SCILAB PROGRAMS
An evolution strategy: ES.sci
A BFGS method with backtracking linesearch: BFGS.sci
I Beam optimization with ES and dynamic penalty:
Ibeam-ES.sci
I Beam robust optimization with ES and static penalty:
Ibeam-ES-robust.sci
SOME PHOTOS FROM THE COURSE:
Here are some pictures taken during my stay at UP Diliman and UP Baguio:
UP-photos-2007.zip
(zip file, 30Mo)
FINAL EXAM:
The final exam consist in a project to write in Scilab:
The subject (.doc file) is here
The documents must be sent at dumas@ann.jussieu.fr.
You can also use this email in case of technical problems or misunderstandings
during the project writing.
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