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État de l'art des méthodes“d'optimisation globale”

Published online by Cambridge University Press:  15 August 2002

Gérard Berthiau  and
Patrick Siarry
Gérard Berthiau
Affiliation:
Université de Nantes, CRTT-GE44, boulevard de l'Université, BP. 406, 44602 Saint-Nazaire, France ; gerard.berthiau@ge44.univ-nantes.fr.
Patrick Siarry
Affiliation:
Université de Paris 12, LERISS, 61 avenue du Général de Gaulle, 94010 Créteil, France ; siarry@univ-paris12.fr.
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Abstract

We present a review of the main “global optimization" methods. The paper comprises one introduction and two parts. In the introduction, we recall some generalities about non linear constraint-less optimization and we list some classifications which have been proposed for the global optimization methods. We then describe, in the first part, various “classical" global optimization methods, most of which available long before the appearance of Simulated Annealing (a key event in this field). There exists plenty of papers and books dealing with these methods, and studying in particular their convergence properties. The second part of the paper is devoted to more recent or atypical methods, mostly issued from combinatorial optimization. The three main methods are “metaheuristics": Simulated Annealing (and derived techniques), Tabu Search and Genetic Algorithms; we also describe three other less known methods. For these methods, theoretical studies of convergence are less abundant in the literature, and the use of convergence results is by far more limited in practice. However, the fitting of some of these techniques to continuous variables problems gave very promising results; that question is not discussed in detail in the paper, but useful references allowing to deepen the subject are given.

Keywords

Global optimizationmetaheuristicsconvergencecontinuous optimization.
Type
Research Article
Information
RAIRO - Operations Research , Volume 35 , Issue 3 , July 2001 , pp. 329 - 365
Copyright
© EDP Sciences, 2001

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